Task-oriented handovers (TOH) are fundamental to effective human-robot collaboration, requiring robots to present objects in a way that supports the human’s intended post-handover use. Existing approaches are typically based on object- or task-specific affordances, but their ability to generalize to novel scenarios is limited. To address this gap, we present AFT-Handover, a framework that integrates large language model (LLM)-driven affordance reasoning with efficient texture-based affordance transfer to achieve zero-shot, generalizable TOH. Given a novel object-task pair, the method retrieves a proxy exemplar from a database, establishes part-level correspondences via LLM reasoning, and texturizes affordances for feature-based point cloud transfer. We evaluate AFT-Handover across diverse task-object pairs, showing improved handover success rates and stronger generalization compared to baselines. In a comparative user study, our framework is significantly preferred over the current state-of-the-art, effectively reducing human regrasping before tool use. Finally, we demonstrate TOH on legged manipulators, highlighting the potential of our framework for real-world robot-human handovers.

Place recognition is essential to maintain global consistency in large-scale localization systems. While research in urban environments has progressed significantly using LiDARs or cameras, applications in natural forest-like environments remain largely under-explored. Furthermore, forests present particular challenges due to high self-similarity and substantial variations in vegetation growth over time. In this work, we propose a robust LiDAR-based place recognition method for natural forests, ForestLPR. We hypothesize that a set of cross-sectional images of the forest’s geometry at different heights contains the information needed to recognize revisiting a place. The cross-sectional images are represented by bird’s-eye view (BEV) density images of horizontal slices of the point cloud at different heights. Our approach utilizes a visual transformer as the shared backbone to produce sets of local descriptors and introduces a multi-BEV interaction module to attend to information at different heights adaptively. It is followed by an aggregation layer that produces a rotation-invariant place descriptor. We evaluated the efficacy of our method extensively on real-world data from public benchmarks as well as robotic datasets and compared it against the state-of-the-art (SOTA) methods. The results indicate that ForestLPR has consistently good performance on all evaluations and achieves an average increase of 7.38% and 9.11% on Recall@1 over the closest competitor on intra-sequence loop closure detection and inter-sequence re-localization, respectively, validating our hypothesis1.

Model-free reinforcement learning algorithms have seen remarkable progress, but key challenges remain. Trust Region Policy Optimization (TRPO) is known for ensuring monotonic policy improvement through conservative updates within a trust region, backed by strong theoretical guarantees. However, its reliance on complex second-order optimization limits its practical efficiency. Proximal Policy Optimization (PPO) addresses this by simplifying TRPO’s approach using ratio clipping, improving efficiency but sacrificing some theoretical robustness. This raises a natural question: Can we combine the strengths of both methods? In this paper, we introduce Simple Policy Optimization (SPO), a novel unconstrained first-order algorithm. By slightly modifying the policy loss used in PPO, SPO can achieve the best of both worlds. Our new objective improves upon ratio clipping, offering stronger theoretical properties and better constraining the probability ratio within the trust region. Empirical results demonstrate that SPO outperforms PPO with a simple implementation, particularly for training large, complex network architectures end-to-end.

The autonomous transportation of materials over challenging terrain is a challenge with major economic implications and remains unsolved. This paper introduces LEVA, a high-payload, high-mobility robot designed for autonomous logistics across varied terrains, including those typical in agriculture, construction, and search and rescue operations. LEVA uniquely integrates an advanced legged suspension system using parallel kinematics. It is capable of traversing stairs using a reinforcement learning (RL) controller, has steerable wheels, and includes a specialized box pickup mechanism that enables autonomous payload loading as well as precise and reliable cargo transportation of up to 85 kg across uneven surfaces, steps and inclines while maintaining a Cost of Transportation (CoT) of as low as 0.15. Through extensive experimental validation, LEVA demonstrates its off-road capabilities and reliability regarding payload loading and transport.

Non-prehensile pushing to move and reorient objects to a goal is a versatile loco-manipulation skill. In the real world, the object's physical properties and friction with the floor contain significant uncertainties, which makes the task challenging for a mobile manipulator. In this paper, we develop a learning-based controller for a mobile manipulator to move an unknown object to a desired position and yaw orientation through a sequence of pushing actions. The proposed controller for the robotic arm and the mobile base motion is trained using a constrained Reinforcement Learning (RL) formulation. We demonstrate its capability in experiments with a quadrupedal robot equipped with an arm. The learned policy achieves a success rate of 91.35% in simulation and at least 80% on hardware in challenging scenarios. Through our extensive hardware experiments, we show that the approach demonstrates high robustness against unknown objects of different masses, materials, sizes, and shapes. It reactively discovers the pushing location and direction, thus achieving contact-rich behavior while observing only the pose of the object. Additionally, we demonstrate the adaptive behavior of the learned policy towards preventing the object from toppling.

Mobile robots on construction sites require accurate pose estimation to perform autonomous surveying and inspection missions. Localization in construction sites is a particularly challenging problem due to the presence of repetitive features such as flat plastered walls and perceptual aliasing due to apartments with similar layouts inter and intra floors. In this paper, we focus on the global re-positioning of a robot with respect to an accurate scanned mesh of the building solely using LiDAR data. In our approach, a neural network is trained on synthetic LiDAR point clouds generated by simulating a LiDAR in an accurate real-life large-scale mesh. We train a diffusion model with a PointNet++ backbone, which allows us to model multiple position candidates from a single LiDAR point cloud. The resulting model can successfully predict the global position of LiDAR in confined and complex sites despite the adverse effects of perceptual aliasing. The learned distribution of potential global positions can provide multi-modal position distribution. We evaluate our approach across five real-world datasets and show the place recognition accuracy of$77 \% (\pm 2 ~\mathrm{m})$on average while outperforming baselines at a factor of 2 in mean error.

Robot soccer, in its full complexity, poses an unsolved research challenge. Current solutions heavily rely on engineered heuristic strategies, which lack robustness and adaptability. Deep reinforcement learning has gained significant traction in various complex robotics tasks such as locomotion, manipulation, and competitive games (e.g., AlphaZero, OpenAI Five), making it a promising solution to the robot soccer problem. This paper introduces MARLadona. A decentralized multi-agent reinforcement learning (MARL) training pipeline capable of producing agents with sophisticated team play behavior, bridging the shortcomings of heuristic methods. Furthermore, we created an open-source multi-agent soccer environment. Utilizing our MARL framework and a modified global entity encoder (GEE) as our core architecture, our approach achieves a 66.8 % win rate against HELIOS agent, which employs a state-of-the-art heuristic strategy. In addition, we provided an in-depth analysis of the policy behavior and interpreted the agent's intention using the critic network.

First-order Policy Gradient (FoPG) algorithms such as Backpropagation through Time and Analytical Policy Gradients leverage local simulation physics to accelerate policy search, significantly improving sample efficiency in robot control compared to standard model-free reinforcement learning. However, FoPG algorithms can exhibit poor learning dynamics in contact-rich tasks like locomotion. Previous approaches address this issue by alleviating contact dynamics via algorithmic or simulation innovations. In contrast, we propose guiding the policy search by learning a residual over a simple baseline policy. For quadruped locomotion, we find that the role of residual policy learning in FoPG-based training (FoPG RPL) is primarily to improve asymptotic rewards, compared to improving sample efficiency for model-free RL. Additionally, we provide insights on applying FoPG's to pixel-based local navigation, training a point-mass robot to convergence within seconds. Finally, we showcase the versatility of FoPG RPL by using it to train locomotion and perceptive navigation end-toend on a quadruped in minutes.

Combining manipulation with the mobility of legged robots is essential for a wide range of robotic applications. However, integrating an arm with a mobile base significantly increases the system's complexity, making precise end-effector control challenging. Existing model-based approaches are often constrained by their modeling assumptions, leading to limited robustness. Meanwhile, recent Reinforcement Learning (RL) implementations restrict the arm's workspace to be in front of the robot or track only the position to obtain decent tracking accuracy. In this work, we address these limitations by introducing a whole-body RL formulation for end-effector pose tracking in a large workspace on rough, unstructured terrains. Our proposed method involves a terrain-aware sampling strategy for the robot's initial configuration and end-effector pose commands, as well as a game-based curriculum to extend the robot's operating range. We validate our approach on the ANYmal quadrupedal robot with a six DoF robotic arm. Through our experiments, we show that the learned controller achieves precise command tracking over a large workspace and adapts across varying terrains such as stairs and slopes. On deployment, it achieves a pose-tracking error of 2.64 cm and 3.64°, outperforming existing competitive baselines. The video of our work is available at: wholebody-pose-tracking.

Personal mobile robotic assistants are expected to find wide applications in industry and healthcare. For example, people with limited mobility can benefit from robots helping with daily tasks, or construction workers can have robots perform precision monitoring tasks on-site. However, manually steering a robot while in motion requires significant concentration from the operator, especially in tight or crowded spaces. This reduces walking speed, and the constant need for vigilance increases fatigue and, thus, the risk of accidents. This work presents a virtual leash with which a robot can naturally follow an operator. We use a sensor fusion based on a custom-built RF transponder, RGB cameras, and a LiDAR. In addition, we customize a local avoidance planner for legged platforms, which enables us to navigate dynamic and narrow environments. We successfully validate on the ANYmal platform [1] the robustness and performance of our entire pipeline in real-world experiments. The video is available at: obstacle-avoidant-leader-following.

Robots need to know where they are in the world to operate effectively without human support. One common first step for precise robot localization is visual place recognition. It is a challenging problem, especially when the output is required in an online fashion, and the current state-of-the-art approaches that tackle it usually require either large amounts of labeled training data or rely on parameters that need to be tuned manually, often per dataset. One such parameter often used for sequence-based place recognition is the image similarity threshold that allows to differentiate between pairs of images that represent the same place even in the presence of severe environmental and structural changes, and those that represent different places even if they share a similar appearance. Currently, selecting this threshold is a manual procedure and requires human expertise. We propose an automatic similarity threshold selection technique and integrate it into a complete sequence-based place recognition system. The experiments on a broad range of real-world and simulated data show that our approach is capable of matching image sequences under various illumination, viewpoint and underlying structural changes, runs online, and requires no manual parameter tuning while yielding performance comparable to a manual, dataset-specific parameter tuning. Thus, this paper substantially increases the ease of use of visual place recognition in real-world settings.

As entertainment robots gain popularity, the demand for natural and expressive motion, particularly in dancing, continues to rise. Traditionally, dancing motions have been manually designed by artists, a process that is both labor-intensive and restricted to simple motion playback, lacking the flexibility to incorporate additional tasks such as locomotion or gaze control during dancing. To overcome these challenges, we introduce Deep Fourier Mimic (DFM), a novel method that combines advanced motion representation with Reinforcement Learning (RL) to enable smooth transitions between motions while concurrently managing auxiliary tasks during dance sequences. While previous frequency domain based motion representations have successfully encoded dance motions into latent parameters, they often impose overly rigid periodic assumptions at the local level, resulting in reduced tracking accuracy and motion expressiveness, which is a critical aspect for entertainment robots. By relaxing these locally periodic constraints, our approach not only enhances tracking precision but also facilitates smooth transitions between different motions. Furthermore, the learned RL policy that supports simultaneous base activities, such as locomotion and gaze control, allows entertainment robots to engage more dynamically and interactively with users rather than merely replaying static, predesigned dance routines.

As home robotics gains traction, robots are increasingly integrated into households, offering companionship and assistance. Quadruped robots, particularly those resembling dogs, have emerged as popular alternatives for traditional pets. However, user feedback highlights concerns about the noise these robots generate during walking at home, particularly the loud footstep sound. To address this issue, we propose a sim-to-real based reinforcement learning (RL) approach to minimize the foot contact velocity highly related to the footstep sound. Our framework incorporates three key elements: learning varying PD gains to actively dampen and stiffen each joint, utilizing foot contact sensors, and employing curriculum learning to gradually enforce penalties on foot contact velocity. Experiments demonstrate that our learned policy achieves superior quietness compared to a RL baseline and the carefully handcrafted Sony commercial controllers. Furthermore, the trade-off between robustness and quietness is shown. This research contributes to developing quieter and more user-friendly robotic companions in home environments.

3D Gaussian Splatting (3DGS) has recently gained popularity as a faster alternative to Neural Radiance Fields (NeRFs) in 3D reconstruction and view synthesis methods. Leveraging the spatial information encoded in 3DGS, this work proposes FOCI (Field Overlap Collision Integral), an algorithm that is able to optimize trajectories directly on the Gaussians themselves. FOCI leverages a novel and interpretable collision formulation for 3DGS using the notion of the overlap integral between Gaussians. Contrary to other approaches, which represent the robot with conservative bounding boxes that underestimate the traversability of the environment, we propose to represent the environment and the robot as Gaussian Splats. This not only has desirable computational properties, but also allows for orientation-aware planning, allowing the robot to pass through very tight and narrow spaces. We extensively test our algorithm in both synthetic and real Gaussian Splats, showcasing that collision-free trajectories for the ANYmal legged robot that can be computed in a few seconds, even with hundreds of thousands of Gaussians making up the environment. The project page and code are available at https://rffr.leggedrobotics.com/works/foci/

Throwing is a fundamental skill that enables robots to manipulate objects in ways that extend beyond the reach of their arms. We present a control framework that combines learning and model-based control for prehensile whole-body throwing with legged mobile manipulators. Our framework consists of three components: a nominal tracking policy for the end-effector, a high-frequency residual policy to enhance tracking accuracy, and an optimization-based module to improve end-effector acceleration control. The proposed controller achieved the average of 0.28m landing error when throwing at targets located 6m away. Furthermore, in a comparative study with university students, the system achieved a velocity tracking error of 0.398m/s and a success rate of 56.8%, hitting small targets randomly placed at distances of 3-5m while throwing at a specified speed of 6m/s. In contrast, humans have a success rate of only 15.2%. This work provides an early demonstration of prehensile throwing with quantified accuracy on hardware, contributing to progress in dynamic whole-body manipulation. A video summarizing the proposed method and the hardware tests is available at https://youtu.be/8ItiQrgN_fw.

We present TartanGround, a large-scale, multi-modal dataset to advance the perception and autonomy of ground robots operating in diverse environments. This dataset, collected in various photorealistic simulation environments includes multiple RGB stereo cameras for 360-degree coverage, along with depth, optical flow, stereo disparity, LiDAR point clouds, ground truth poses, semantic segmented images, and occupancy maps with semantic labels. Data is collected using an integrated automatic pipeline, which generates trajectories mimicking the motion patterns of various ground robot platforms, including wheeled and legged robots. We collect 878 trajectories across 63 environments, resulting in 1.44 million samples. Evaluations on occupancy prediction and SLAM tasks reveal that state-of-the-art methods trained on existing datasets struggle to generalize across diverse scenes. TartanGround can serve as a testbed for training and evaluation of a broad range of learning-based tasks, including occupancy prediction, SLAM, neural scene representation, perception-based navigation, and more, enabling advancements in robotic perception and autonomy towards achieving robust models generalizable to more diverse scenarios. The dataset and codebase are available on the webpage: https://tartanair.org/tartanground

Quadruped robots are proliferating in industrial environments where they carry sensor payloads and serve as autonomous inspection platforms. Despite the advantages of legged robots over their wheeled counterparts on rough and uneven terrain, they are still unable to reliably negotiate a ubiquitous feature of industrial infrastructure: ladders. Inability to traverse ladders prevents quadrupeds from inspecting dangerous locations, puts humans in harm’s way, and reduces industrial site productivity. In this paper, we learn quadrupedal ladder climbing via a reinforcement learning-based control policy and a complementary hooked end effector. We evaluate the robustness in simulation across different ladder inclinations, rung geometries, and inter-rung spacings. On hardware, we demonstrate zero-shot transfer with an overall 90% success rate at ladder angles ranging from 70° to 90°, consistent climbing performance during unmodeled perturbations, and climbing speeds 232 × faster than the state of the art. This work expands the scope of industrial quadruped robot applications beyond inspection on nominal terrains to challenging infrastructural features in the environment, highlighting synergies between robot morphology and control policy when performing complex skills. More information can be found at the project website: https://sites.google.com/leggedrobotics.com/climbingladders.

Accurate, efficient, and robust state estimation is more important than ever in robotics as the variety of platforms and complexity of tasks continue to grow. Historically, discrete-time filters and smoothers have been the dominant approach, in which the estimated variables are states at discrete sample times. The paradigm of continuous-time state estimation proposes an alternative strategy by estimating variables that express the state as a continuous function of time, which can be evaluated at any query time. Not only can this benefit downstream tasks such as planning and control, but it also significantly increases estimator performance and flexibility, as well as reduces sensor preprocessing and interfacing complexity. Despite this, continuous-time methods remain underutilized, potentially because they are less well-known within robotics. To remedy this, this work presents a unifying formulation of these methods and the most exhaustive literature review to date, systematically categorizing prior work by methodology, application, state variables, historical context, and theoretical contribution to the field. By surveying splines and Gaussian process together and contextualizing works from other research domains, this work identifies and analyzes open problems in continuous-time state estimation and suggests new research directions.

LiDAR Upsampling is a challenging task for the perception systems of robots and autonomous vehicles, due to the sparse and irregular structure of large-scale scene contexts. Recent works propose to solve this problem by converting LiDAR data from 3D Euclidean space into an image super-resolution problem in 2D image space. Although their methods can generate high-resolution range images with fine-grained details, the resulting 3D point clouds often blur out details and predict invalid points. In this paper, we propose TULIP, a new method to reconstruct high-resolution LiDAR point clouds from low-resolution LiDAR input. We also follow a range image-based approach but specifically modify the patch and window geometries of a Swin- Transformer-based network to better fit the characteristics of range images. We conducted several experiments on three public real-world and simulated datasets. TULIP outperforms state-of-the-art methods in all relevant metrics and generates robust and more realistic point clouds than prior works. The code is available at https://github.com/ethz-asl/TULIP.git.

Deploying perception modules for human-robot handovers is challenging because they require a high degree of reactivity, generalizability, and robustness to work reliably for a diversity of cases. Further complications arise as each object can be handed over in a variety of ways, causing occlusions and viewpoint changes. On legged robots, deployment is particularly challenging because of the limited computational resources and the image-space noise resulting from locomotion. In this paper, we introduce an efficient and object-agnostic real-time tracking framework, specifically designed for human-to-robot handover tasks with a legged manipulator. The proposed method combines optical flow with Siamese-network-based tracking and depth segmentation in an adaptive Kalman Filter framework. We show that we outperform the state-of-the-art for tracking during human-to-robot handovers with our legged manipulator. We demonstrate the generalizability, reactivity, and robustness of our system through experiments in different scenarios and by carrying out a user study. Additionally, as timing is proven to be more important than spatial accuracy for human-robot handovers, we show that we reach close to human timing performance during the approaching phase, both in terms of objective metrics and subjective feedback from the participants of our user study.

Legged robots have the potential to become vital in maintenance, home support, and exploration scenarios. In order to interact with and manipulate their environments, most legged robots are equipped with a dedicated robot arm, which means additional mass and mechanical complexity compared to standard legged robots. In this work, we explore pedipulation - using the legs of a legged robot for manipulation. By training a reinforcement learning policy that tracks position targets for one foot, we enable a dedicated pedipulation controller that is robust to disturbances, has a large workspace through whole-body behaviors, and can reach far-away targets with gait emergence, enabling loco-pedipulation. By deploying our controller on a quadrupedal robot using teleoperation, we demonstrate various real-world tasks such as door opening, sample collection, and pushing obstacles. We demonstrate load carrying of more than 2.0 kg at the foot. Additionally, the controller is robust to interaction forces at the foot, disturbances at the base, and slippery contact surfaces. Videos of the experiments are available at https://sites.google.com/leggedrobotics.com/pedipulate.

Legged robots have the potential to traverse complex terrain and access confined spaces beyond the reach of traditional platforms thanks to their ability to carefully select footholds and flexibly adapt their body posture while walking. However, robust deployment in real-world applications is still an open challenge. In this paper, we present a method for legged locomotion control using reinforcement learning and 3D volumetric representations to enable robust and versatile locomotion in confined and unstructured environments. By employing a two-layer hierarchical policy structure, we exploit the capabilities of a highly robust low-level policy to follow 6D commands and a high-level policy to enable three-dimensional spatial awareness for navigating under overhanging obstacles. Our study includes the development of a procedural terrain generator to create diverse training environments. We present a series of experimental evaluations in both simulation and real-world settings, demonstrating the effectiveness of our approach in controlling a quadruped robot in confined, rough terrain. By achieving this, our work extends the applicability of legged robots to a broader range of scenarios.

Symmetry is a fundamental aspect of many real-world robotic tasks. However, current deep reinforcement learning (DRL) approaches can seldom harness and exploit symmetry effectively. Often, the learned behaviors fail to achieve the desired transformation invariances and suffer from motion artifacts. For instance, a quadruped may exhibit different gaits when commanded to move forward or backward, even though it is symmetrical about its torso. This issue becomes further pronounced in high-dimensional or complex environments, where DRL methods are prone to local optima and fail to explore regions of the state space equally. Past methods on encouraging symmetry for robotic tasks have studied this topic mainly in a single-task setting, where symmetry usually refers to symmetry in the motion, such as the gait patterns. In this paper, we revisit this topic for goal-conditioned tasks in robotics, where symmetry lies mainly in task execution and not necessarily in the learned motions themselves. In particular, we investigate two approaches to incorporate symmetry invariance into DRL -– data augmentation and mirror loss function. We provide a theoretical foundation for using augmented samples in an on-policy setting. Based on this, we show that the corresponding approach achieves faster convergence and improves the learned behaviors in various challenging robotic tasks, from climbing boxes with a quadruped to dexterous manipulation.

Real-time path planning in outdoor environments still challenges modern robotic systems due to differences in terrain traversability, diverse obstacles, and the necessity for fast decision-making. Established approaches have primarily focused on geometric navigation solutions, which work well for structured geometric obstacles but have limitations regarding the semantic interpretation of different terrain types and their affordances. Moreover, these methods fail to identify traversable geometric occurrences, such as stairs. To overcome these issues, we introduce ViPlanner, a learned local path planning approach that generates local plans based on geometric and semantic information. The system is trained using the Imperative Learning paradigm, for which the network weights are optimized end-to-end based on the planning task objective. This optimization uses a differentiable formulation of a semantic costmap, which enables the planner to distinguish between the traversability of different terrains and accurately identify obstacles. The semantic information is represented in 30 classes using an RGB colorspace that can effectively encode the multiple levels of traversability. We show that the planner can adapt to diverse real-world environments without requiring any real-world training. In fact, the planner is trained purely in simulation, enabling a highly scalable training data generation. Experimental results demonstrate resistance to noise, zero-shot sim-to-real transfer, and a decrease of 38.02% in terms of traversability cost compared to purely geometric-based approaches. Code and models are made publicly available: https://github.com/leggedrobotics/viplanner.

Deployment in hazardous environments requires robots to understand the risks associated with their actions and movements to prevent accidents. Despite its importance, these risks are not explicitly modeled by currently deployed locomotion controllers for legged robots. In this work, we propose a risk sensitive locomotion training method employing distributional reinforcement learning to consider safety explicitly. Instead of relying on a value expectation, we estimate the complete value distribution to account for uncertainty in the robot’s interaction with the environment. The value distribution is consumed by a risk metric to extract risk sensitive value estimates. These are integrated into Proximal Policy Optimization (PPO) to derive our method, Distributional Proximal Policy Optimization (DPPO). The risk preference, ranging from risk-averse to risk-seeking, can be controlled by a single parameter, which enables to adjust the robot’s behavior dynamically. Importantly, our approach removes the need for additional reward function tuning to achieve risk sensitivity. We show emergent risk sensitive locomotion behavior in simulation and on the quadrupedal robot ANYmal. Videos of the experiments and code are available at https://sites.google.com/leggedrobotics.com/risk-aware-locomotion.

We present SpaceHopper, a three-legged, small-scale robot designed for future mobile exploration of asteroids and moons. The robot weighs 5.2 kg and has a body size of 245 mm while using space-qualifiable components. Furthermore, SpaceHopper’s design and controls make it well-adapted for investigating dynamic locomotion modes with extended flight-phases. Instead of gyroscopes or fly-wheels, the system uses its three legs to reorient the body during flight in preparation for landing. We control the leg motion for reorientation using Deep Reinforcement Learning policies. In a simulation of Ceres’ gravity (0.029 g), the robot can reliably jump to commanded positions up to 6 m away. Our real-world experiments show that SpaceHopper can successfully reorient to a safe landing orientation within 9.7 deg inside a rotational gimbal and jump in a counterweight setup in Earth’s gravity. Overall, we consider SpaceHopper an important step towards controlled jumping locomotion in low-gravity environments.

Autonomous robots must navigate reliably in unknown environments even under compromised exteroceptive perception, or perception failures. Such failures often occur when harsh environments lead to degraded sensing, or when the perception algorithm misinterprets the scene due to limited generalization. In this paper, we model perception failures as invisible obstacles and pits, and train a reinforcement learning (RL) based local navigation policy to guide our legged robot. Unlike previous works relying on heuristics and anomaly detection to update navigational information, we train our navigation policy to reconstruct the environment information in the latent space from corrupted perception and react to perception failures end-to-end. To this end, we incorporate both proprioception and exteroception into our policy inputs, thereby enabling the policy to sense collisions on different body parts and pits, prompting corresponding reactions. We validate our approach in simulation and on the real quadruped robot ANYmal running in real-time (<10ms CPU inference). In a quantitative comparison with existing heuristic-based locally reactive planners, our policy increases the success rate over 30% when facing perception failures. Project Page: https://bit.ly/45NBTuh.

Accurate grasping is the key to several robotic tasks including assembly and household robotics. Executing a successful grasp in a cluttered environment requires multiple levels of scene understanding: First, the robot needs to analyze the geometric properties of individual objects to find feasible grasps. These grasps need to be compliant with the local object geometry. Second, for each proposed grasp, the robot needs to reason about the interactions with other objects in the scene. Finally, the robot must compute a collision-free grasp trajectory while taking into account the geometry of the target object. Most grasp detection algorithms directly predict grasp poses in a monolithic fashion, which does not capture the composability of the environment. In this paper, we introduce an end-to-end architecture for object-centric grasping. The method uses pointcloud data from a single arbitrary viewing direction as an input and generates an instance-centric representation for each partially observed object in the scene. This representation is further used for object reconstruction and grasp detection in cluttered table-top scenes. We show the effectiveness of the proposed method by extensively evaluating it against state-of-the-art methods on synthetic datasets, indicating superior performance for grasping and reconstruction. Additionally, we demonstrate real-world applicability by decluttering scenes with varying numbers of objects. Videos and Code icgraspnet.github.io.

Autonomous navigation across unstructured terrains, including forests and construction areas, faces unique challenges due to intricate obstacles and the element of the unknown. Lacking pre-existing maps, these scenarios necessitate a motion planning approach that combines agility with efficiency. Critically, it must also incorporate the robot’s kinematic constraints to navigate more effectively through complex environments. This work introduces a novel planning method for center-articulated vehicles (CAV), leveraging motion primitives within a receding horizon planning framework using onboard sensing. The approach commences with the offline creation of motion primitives, generated through forward simulations that reflect the distinct kinematic model of center-articulated vehicles. These primitives undergo evaluation through a heuristic-based scoring function, facilitating the selection of the most suitable path for real-time navigation. To account for disturbances, we develop a pose-stabilizing controller, tailored to the kinematic specifications of center-articulated vehicles. During experiments, our method demonstrates a 67% improvement in SPL (Success Rate weighted by Path Length) performance over existing strategies. Furthermore, its efficacy was validated through real-world experiments conducted with a tree harvester vehicle - SAHA.

Shifting from traditional control strategies to Deep Reinforcement Learning (RL) for legged robots poses inherent challenges, especially when addressing real-world physical constraints during training. While high-fidelity simulations provide significant benefits, they often bypass these essential physical limitations. In this paper, we experiment with the Constrained Markov Decision Process (CMDP) framework instead of the conventional unconstrained RL for robotic applications. We evaluated five constrained policy optimization algorithms for quadrupedal locomotion using three different robot models. Our aim is to evaluate their applicability in real-world scenarios. Our robot experiments demonstrate the critical role of incorporating physical constraints, yielding successful sim-to-real transfers, and reducing operational errors on physical systems. The CMDP formulation streamlines the training process by separately handling constraints from rewards. Our findings underscore the potential of constrained RL for the effective development and deployment of learned controllers in robotics.

Current visual navigation systems often treat the environment as static, lacking the ability to adaptively interact with obstacles. This limitation leads to navigation failure when encountering unavoidable obstructions. In response, we introduce IN-Sight, a novel approach to self-supervised path planning, enabling more effective navigation strategies through interaction with obstacles. Utilizing RGB-D observations, IN-Sight calculates traversability scores and incorporates them into a semantic map, facilitating long-range path planning in complex, maze-like environments. To precisely navigate around obstacles, IN-Sight employs a local planner, trained imperatively on a differentiable costmap using representation learning techniques. The entire framework undergoes end-to-end training within the state-of-the-art photorealistic Intel SPEAR Simulator. We validate the effectiveness of IN-Sight through extensive benchmarking in a variety of simulated scenarios and ablation studies. Moreover, we demonstrate the system’s real-world applicability with zero-shot sim-to-real transfer, deploying our planner on the legged robot platform ANYmal, showcasing its practical potential for interactive navigation in real environments.

The precise and safe control of heavy material handling machines presents numerous challenges due to the hard-to-model hydraulically actuated joints and the need for collision-free trajectory planning with a free-swinging end-effector tool. In this work, we propose an RL-based controller that commands the cabin joint and the arm simultaneously. It is trained in a simulation combining data-driven modeling techniques with first-principles modeling. On the one hand, we employ a neural network model to capture the highly nonlinear dynamics of the upper carriage turn hydraulic motor, incorporating explicit pressure prediction to handle delays better. On the other hand, we model the arm as velocity-controllable and the free-swinging end-effector tool as a damped pendulum using first principles. This combined model enhances our simulation environment, enabling the training of RL controllers that can be directly transferred to the real machine. Designed to reach steady-state Cartesian targets, the RL controller learns to leverage the hydraulic dynamics to improve accuracy, maintain high speeds, and minimize end-effector tool oscillations. Our controller, tested on a mid-size prototype material handler, is more accurate than an inexperienced operator and causes fewer tool oscillations. It demonstrates competitive performance even compared to an experienced professional driver.

Power consumption is a frequently over-looked aspect in robotics, especially in the context of legged robots. Nevertheless, improving the efficiency of walking robots is crucial to overcome the current limitations in runtime. This work proposes a novel method for precisely estimating actuator power consumption based on LSTM neural networks. The performance of this approach is benchmarked against currently employed models and validated on real hardware using certified instruments. The proposed method is integrated into the Isaac Gym framework and utilized to train a power-efficient policy. Instead of optimizing for handcrafted cost functions, such as the often used torque-square minimization, our approach for the first time trains RL policies that minimize the effective energy consumption. Hardware results demonstrate a reduction of approximately 25% in the robot’s total power consumption, with a notable 50% decrease observed for the knee actuator. Additionally, the newly developed policy generates significantly smoother and quieter motions.

Automation of hydraulic material handling machinery is currently limited to semi-static pick-and-place cycles. Dynamic throwing motions which utilize the passive joints, can greatly improve time efficiency as well as increase the dumping workspace. In this work, we use Reinforcement Learning (RL) to design dynamic controllers for material handlers with under-actuated arms as commonly used in logistics. The controllers are tested both in simulation and in real-world experiments on a 12-ton test platform. The method is able to exploit the passive joints of the gripper to perform dynamic throwing motions. With the proposed controllers, the machine is able to throw individual objects to targets outside the static reachability zone with good accuracy for its practical applications. The work demonstrates the possibility of using RL to perform highly dynamic tasks with heavy machinery, suggesting a potential for improving the efficiency and precision of autonomous material handling tasks.

Radiance field methods such as Neural Radiance Fields (NeRFs) or 3D Gaussian Splatting (3DGS), have revo-lutionized graphics and novel view synthesis. Their ability to synthesize new viewpoints with photo-realistic quality, as well as capture complex volumetric and specular scenes, makes them an ideal visualization for robotic teleoperation setups. Direct camera teleoperation provides high-fidelity operation at the cost of maneuverability, while reconstruction-based approaches offer controllable scenes with lower fidelity. With this in mind, we propose replacing the traditional reconstruction-visualization components of the robotic teleoperation pipeline with online Radiance Fields, offering highly maneuverable scenes with photorealistic quality. As such, there are three main contributions to state of the art: (1) online training of Radiance Fields using live data from multiple cameras, (2) support for a variety of radiance methods including NeRF and 3DGS, (3) visualization suite for these methods including a virtual reality scene. To enable seamless integration with existing setups, these components were tested with multiple robots in multiple configurations and were displayed using traditional tools as well as the VR headset. The results across methods and robots were compared quantitatively to a baseline of mesh reconstruction, and a user study was conducted to compare the different visualization methods. The code and additional samples are available at https://leggedrobotics.github.io/rffr.github.io/.

Quadruped robots have shown remarkable mobility on various terrains through reinforcement learning. Yet, in the presence of sparse footholds and risky terrains such as stepping stones and balance beams, which require precise foot placement to avoid falls, model-based approaches are often used. In this paper, we show that end-to-end reinforcement learning can also enable the robot to traverse risky terrains with dynamic motions. To this end, our approach involves training a generalist policy for agile locomotion on disorderly and sparse stepping stones before transferring its reusable knowledge to various more challenging terrains by finetuning specialist policies from it. Given that the robot needs to rapidly adapt its velocity on these terrains, we formulate the task as a navigation task instead of the commonly used velocity tracking which constrains the robot’s behavior and propose an exploration strategy to overcome sparse rewards and achieve high robustness. We validate our proposed method through simulation and real-world experiments on an ANYmal-D robot achieving peak forward velocity of ≥2.5 m/s on sparse stepping stones and narrow balance beams. Video: youtu.be/Z5X0J8OH6z4

This article surveys recent progress and discusses future opportunities for simultaneous localization and mapping (SLAM) in extreme underground environments. SLAM in subterranean environments, from tunnels, caves, and man-made underground structures on Earth, to lava tubes on Mars, is a key enabler for a range of applications, such as planetary exploration, search and rescue, disaster response, and automated mining, among others. SLAM in underground environments has recently received substantial attention, thanks to theDARPA Subterranean (SubT) Challenge, a global robotics competition aimed at assessing and pushing the state of the art in autonomous robotic exploration and mapping in complex underground environments. This article reports on the state of the art in underground SLAM by discussing different SLAM strategies and results across six teams that participated in the three-year-long SubT competition. In particular, the article has four main goals. First, we review the algorithms, architectures, and systems adopted by the teams; particular emphasis is put on light detection and ranging (LIDAR)-centric SLAM solutions (the go-to approach for virtually all teams in the competition), heterogeneous multirobot operation (including both aerial and ground robots), and real-world underground operation (from the presence of obscurants to the need to handle tight computational constraints). We do not shy away from discussing the “dirty details” behind the different SubT SLAM systems, which are often omitted from technical papers. Second, we discuss the maturity of the field by highlighting what is possible with the current SLAM systems and what we believe is within reach with some good systems engineering. Third, we outline what we believe are fundamental open problems, which are likely to require further research to break through. Finally, we provide a list of open-source SLAM implementations and datasets that have been produced during the SubT challenge and related efforts and constitute a useful resource for researchers and practitioners.

Modern robotic systems are required to operate in challenging environments, which demand reliable localization under challenging conditions. LiDAR-based localization methods, such as the iterative closest point (ICP) algorithm, can suffer in geometrically uninformative environments that are known to deteriorate point cloud registration performance and push optimization toward divergence along weakly constrained directions. To overcome this issue, this work proposes: 1) a robust fine-grained localizability detection module and 2) a localizability-aware constrained ICP optimization module, which couples with the localizability detection module in a unified manner. The proposed localizability detection is achieved by utilizing the correspondences between the scan and the map to analyze the alignment strength against the principal directions of the optimization as part of its fine-grained LiDAR localizability analysis. In the second part, this localizability analysis is then integrated into the scan-to-map point cloud registration to generate drift-free pose updates by enforcing controlled updates or leaving the degenerate directions of the optimization unchanged. The proposed method is thoroughly evaluated and compared to state-of-the-art methods in simulated and real-world experiments, demonstrating the performance and reliability improvement in LiDAR-challenging environments. In all the experiments, the proposed framework demonstrates accurate and generalizable localizability detection and robust pose estimation without environment-specific parameter tuning.

Deep learning has had remarkable success in robotic perception, but its data-centric nature suffers when it comes to generalizing to ever-changing environments. By contrast, physics-based optimization generalizes better, but it does not perform as well in complicated tasks due to the lack of high-level semantic information and reliance on manual parametric tuning. To take advantage of these two complementary worlds, we present PyPose: a robotics-oriented, PyTorch-based library that combines deep perceptual models with physics-based optimization. PyPose's architecture is tidy and well-organized, it has an imperative style interface and is efficient and user-friendly, making it easy to integrate into real-world robotic applications. Besides, it supports parallel computing of any order gradients of Lie groups and Lie algebras and 2nd-order optimizers, such as trust region methods. Experiments show that PyPose achieves more than 10× speedup in computation compared to the state-of-the-art libraries. To boost future research, we provide concrete examples for several fields of robot learning, including SLAM, planning, control, and inertial navigation.

Quadrupedal robots are conquering various applications in indoor and outdoor environments due to their capability to navigate challenging uneven terrains. Exteroceptive information greatly enhances this capability since perceiving their surroundings allows them to adapt their controller and thus achieve higher levels of robustness. However, sensors such as LiDARs and RGB cameras do not provide sufficient information to quickly and precisely react in a highly dynamic environment since they suffer from a bandwidth-latency trade-off. They require significant bandwidth at high frame rates while featuring significant perceptual latency at lower frame rates, thereby limiting their versatility on resource constrained platforms. In this work, we tackle this problem by equipping our quadruped with an event camera, which does not suffer from this tradeoff due to its asynchronous and sparse operation. In leveraging the low latency of the events, we push the limits of quadruped agility and demonstrate high-speed ball catching for the first time. We show that our quadruped equipped with an event-camera can catch objects with speeds up to 15 m/s from 4 meters, with a success rate of 83%. Using a VGA event camera, our method runs at 100 Hz on an NVIDIA Jetson Orin.

Adaptive falling and recovery skills greatly extend the applicability of robot deployments. In the case of legged mobile manipulators, the robot arm could adaptively stop the fall and assist the recovery. Prior works on falling and recovery strategies for legged mobile manipulators usually rely on assumptions such as inelastic collisions and falling in defined directions to enable real-time computation. This paper presents a learning-based approach to reducing fall damage and recovery. An asymmetric actor-critic training structure is used to train a time-invariant policy with time-varying reward functions. In simulated experiments, the policy recovers from 98.9% of initial falling configurations. It reduces base contact impulse, peak joint internal forces, and base acceleration during the fall compared to the baseline methods. The trained control policy is deployed and extensively tested on the ALMA robot hardware. A video summarizing the proposed method and the hardware tests is available at https://youtu.be/avwg2HqGi8s

Reinforcement learning (RL) has emerged as a powerful approach for locomotion control of highly articulated robotic systems. However, one major challenge is the tedious process of tuning the reward function to achieve the desired motion style. To address this issue, imitation learning approaches such as adversarial motion priors have been proposed, which encourage a pre-defined motion style. In this work, we present an approach to enhance the concept of adversarial motion prior-based RL, allowing for multiple, discretely switchable motion styles. Our approach demonstrates that multiple styles and skills can be learned simultaneously without significant performance differences, even in combination with motion data-free skills. We conducted several real-world experiments using a wheeled-legged robot to validate our approach. The experiments involved learning skills from existing RL controllers and trajectory optimization, such as ducking and walking, as well as novel skills, such as switching between a quadrupedal and humanoid configuration. For the latter skill, the robot was required to stand up, navigate on two wheels, and sit down. Instead of manually tuning the sit-down motion, we found that a reverse playback of the stand-up movement helped the robot discover feasible sit-down behaviors and avoided the need for tedious reward function tuning.

Elevation maps are commonly used to represent the environment of mobile robots and are instrumental for locomotion and navigation tasks. However, pure geometric information is insufficient for many field applications that require appearance or semantic information, which limits their applicability to other platforms or domains. In this work, we extend a 2.5D robot-centric elevation mapping framework by fusing multi-modal information from multiple sources into a popular map representation. The framework allows inputting data contained in point clouds or images in a unified manner. To manage the different nature of the data, we also present a set of fusion algorithms that can be selected based on the information type and user requirements. Our system is designed to run on the GPU, making it real-time capable for various robotic and learning tasks. We demonstrate the capabilities of our framework by deploying it on multiple robots with varying sensor configurations and showcasing a range of applications that utilize multi-modal layers, including line detection, human detection, and colorization.

Robotic object manipulation requires knowledge of the environment's state. In particular, the object poses of fixed elements in the environment relative to the robot and the in-hand poses of grasped objects are of interest. For insertion tasks with tight tolerances, the accuracy of vision systems to estimate the object and in-hand pose is not high enough. This work proposes a state estimation system that delivers precise estimates for both estimation problems. It uses contact detections and the precise forward kinematics that robot arms provide thanks to their high-resolution joint encoders. We propose a reinforcement-learning-based exploration strategy that decides how the robot should engage with the environment to reduce state uncertainty. The system is evaluated in several simulation and hardware experiments. We show that the learned policy can propose meaningful actions for object localization. In hardware experiments with precision-milled objects, sub-millimeter accuracy is achieved for the in-hand pose estimation task. With objects relevant to industrial tasks, i.e., a melting fuse and a fuse box, millimeter-level accuracy can be reached for both in-hand pose estimation and fixed object localization. In an integrated experiment, we show how a robot grasps a fuse, estimates the in-hand pose, and inserts it into a fuse box.

Scientific exploration of planetary bodies is an activity well-suited for robots. Unfortunately, the regions that are richer in potential discoveries, such as impact craters, caves, and volcanic terraces, are hard to access with wheeled robots. Recent advances in legged-based approaches have shown the potential of the technology to overcome difficult terrains such as slopes and slippery surfaces. In this work, we focus on locomotion for sandy slopes, comparing standard walking policies with a novel crawling-based gait for quadrupedal robots. We fine-tuned a state-of-the-art locomotion framework and introduced hardware modifications to the robot ANYmal, which enables walking on its knees. Moreover, we integrated a novel metric for stability, the stability margin, in the training process to increase robustness in such conditions. We benchmarked the locomotion policies in simulation and in real-world experiments on a martian soil simulant. Our results show a significant improvement in terms of robustness and stability, especially at higher slope angles beyond 15 degrees.

Legged robots are designed to perform highly dynamic motions. However, it remains challenging for users to retarget expressive motions onto these complex systems. In this paper, we present a Differentiable Optimal Control (DOC) framework that facilitates the transfer of rich motions from either animals or animations onto these robots. Interfacing with either motion capture or animation data, we formulate retargeting objectives whose parameters make them agnostic to differences in proportions and numbers of degrees of freedom between input and robot. Optimizing these parameters over the manifold spanned by optimal state and control trajectories, we minimize the retargeting error. We demonstrate the utility and efficacy of our modeling by applying DOC to a Model-Predictive Control (MPC) formulation, showing retargeting results for a family of robots of varying proportions and mass distribution. With a hardware deployment, we further show that the retargeted motions are physically feasible, while MPC ensures that the robots retain their capability to react to unexpected disturbances.

Dynamic locomotion in rough terrain requires accurate foot placement, collision avoidance, and planning of the underactuated dynamics of the system. Reliably optimizing for such motions and interactions in the presence of imperfect and often incomplete perceptive information is challenging. We present a complete perception, planning, and control pipeline, which can optimize motions for all degrees of freedom of the robot in real time. To mitigate the numerical challenges posed by the terrain, a sequence of convex inequality constraints is extracted as local approximations of foothold feasibility and embedded into an online model-predictive controller. Steppability classification, plane segmentation, and a signed distance field are precomputed per elevation map to minimize the computational effort during the optimization. A combination of multiple-shooting, real-time iteration, and a filter-based line search is used to solve the formulated problem reliably and at high rate. We validate the proposed method in scenarios with gaps, slopes, and stepping stones in simulation and experimentally on the ANYmal quadruped platform, resulting in state-of-the-art dynamic climbing.

This article presents a hybrid motion planning and control approach applicable to various ground robot types and morphologies. Our two-step approach uses a sampling-based planner to compute an approximate motion, which is then fed to numerical optimization for refinement. The sampling-based stage finds a long-term global plan consisting of a contact schedule and sequence of keyframes, i.e., stable whole-body configurations. Subsequently, the optimization refines the solution with a short-term planning horizon to satisfy all nonlinear dynamics constraints. The proposed hybrid planner can compute plans for scenarios that would be difficult for trajectory optimization or sampling planner alone. We present tasks of traversing challenging terrain that requires discovering a contact schedule, navigating nonconvex obstacles, and coordinating many degrees of freedom. Our hybrid planner has been applied to three different robots: a quadruped, a wheeled quadruped, and a legged excavator. We validate our hybrid locomotion planner in the real world and simulation, generating behaviors we could not achieve with previous methods. The results show that computing and executing hybrid locomotion plans is possible on hardware in real time.

Exoskeleton robots found application in neurorehabilitation, telemanipulation, and power augmentation. The human–robot attachment system of an exoskeleton should transmit all the interaction forces while keeping the anatomical and robotic joint axes aligned. Existing attachment concepts were bounding the performance of modern exoskeletons due to insufficient stiffness for high-performance force control, time-consuming adaption processes, and/or bulkiness. Therefore, we developed an augmented attachment system for a recent fully actuated nine-degree-of-freedom upper limb exoskeleton. The proposed system was compared to a conventional solution in a case study with four participants. The proposed attachment system lowered the relative motion between the human and the robot under static loads for all defined landmarks by 45% on average. The occurrence of undesired contacts in the trials was mitigated by 74%, thus improving conditions for closed-loop force control. Furthermore, the proposed system adapted better to the user's anatomy facilitating more accurate alignment and less obstruction. On average, self-attachment took$\mathbf {43(8.3)}$$\mathrm{s}$to don(doff). Thereby, the alignment of anatomic landmarks had typically less than 15 mm offset to a thorough expert alignment, making self-attachment eligible. The augmented attachment system and the insights gained by the case study are expected to enable improvement of the physical human–robot interaction of exoskeletons.

We developed an exoskeleton for neurorehabilitation that covered all relevant degrees of freedom of the human arm while providing enough range of motion, speed, strength, and haptic-rendering function for therapy of severely affected (e.g., mobilization) and mildly affected patients (e.g., strength and speed). The ANYexo 2.0, uniting these capabilities, could be the vanguard for highly versatile therapeutic robotics applicable to a broad target group and an extensive range of exercises. Thereby, the practical adoption of these devices in clinics will be fostered. The unique kinematic structure of the robot and the bio-inspired controlled shoulder coupling allowed training for most activities of daily living. We demonstrated this capability with 15 sample activities, including interaction with real objects and the own body with the robot in transparent mode. The robot's joints can reach$200 \%$,$398 \%$, and$354 \%$of the speed required during activities of daily living at the shoulder, elbow, and wrist, respectively. Further, the robot can provide isometric strength training. We present a detailed analysis of the kinematic properties and propose algorithms for intuitive control implementation.

In this paper, we deal with the problem of creating globally consistent pose graphs in a centralized multi-robot SLAM framework. For each robot to act autonomously, individual onboard pose estimates and maps are maintained, which are then communicated to a central server to build an optimized global map. However, inconsistencies between onboard and server estimates can occur due to onboard odometry drift or failure. Furthermore, robots do not benefit from the collaborative map if the server provides no feedback in a computationally tractable and bandwidth-efficient manner. Motivated by this challenge, this paper proposes a novel collaborative mapping framework to enable accurate global mapping among robots and server. In particular, structural differences between robot and server graphs are exploited at different spatial scales using graph spectral analysis to generate necessary constraints for the individual robot pose graphs. The proposed approach is thoroughly analyzed and validated using several real-world multi-robot field deployments where we show improvements of the onboard system up to 90%.

In this paper, we present a real-time whole-body planner for collision-free legged mobile manipulation. We enforce both self-collision and environment-collision avoidance as soft constraints within a Model Predictive Control (MPC) scheme that solves a multi-contact optimal control problem. By penalizing the signed distances among a set of representative primitive collision bodies, the robot is able to safely execute a variety of dynamic maneuvers while preventing any self-collisions. Moreover, collision-free navigation and manipulation in both static and dynamic environments are made viable through efficient queries of distances and their gradients via a euclidean signed distance field. We demonstrate through a comparative study that our approach only slightly increases the computational complexity of the MPC planning. Finally, we validate the effectiveness of our framework through a set of hardware experiments involving dynamic mobile manipulation tasks with potential collisions, such as locomotion balancing with the swinging arm, weight throwing, and autonomous door opening.

This paper introduces a novel approach for whole-body motion planning and dynamic occlusion avoidance. The proposed approach reformulates the visibility constraint as a likelihood maximization of visibility probability. In this formulation, we augment the primary cost function of a whole-body model predictive control scheme through a relaxed log barrier function yielding a relaxed log-likelihood maximization formulation of visibility probability. The visibility probability is computed through a probabilistic shadow field that quantifies point light source occlusions. We provide the necessary algorithms to obtain such a field for both 2D and 3D cases. We demonstrate 2D implementations of this field in simulation and 3D implementations through real-time hardware experiments. We show that due to the linear complexity of our shadow field algorithm to the map size, we can achieve high update rates, which facilitates onboard execution on mobile platforms with limited computational power. Lastly, we evaluate the performance of the proposed MPC reformulation in simulation for a quadrupedal mobile manipulator.

This paper presents a novel strategy for autonomous teamed exploration of subterranean environments using legged and aerial robots. Tailored to the fact that subterranean settings, such as cave networks and underground mines, often involve complex, large-scale and multi-branched topologies, while wireless communication within them can be particularly challenging, this work is structured around the synergy of an onboard exploration path planner that allows for resilient long-term autonomy, and a multi-robot coordination framework. The onboard path planner is unified across legged and flying robots and enables navigation in environments with steep slopes, and diverse geometries. When a communication link is available, each robot of the team shares submaps to a centralized location where a multi-robot coordination framework identifies global frontiers of the exploration space to inform each system about where it should re-position to best continue its mission. The strategy is verified through a field deployment inside an underground mine in Switzerland using a legged and a flying robot collectively exploring for 45 min, as well as a longer simulation study with three systems.

Enabling autonomous operation of large-scale construction machines, such as excavators, can bring key benefits for human safety and operational opportunities for applications in dangerous and hazardous environments. To facilitate robot autonomy, robust and accurate state-estimation remains a core component to enable these machines for operation in a diverse set of complex environments. In this work, a method for multi-modal sensor fusion for robot state-estimation and localization is presented, enabling operation of construction robots in real-world scenarios. The proposed approach presents a graph-based prediction-update loop that combines the benefits of filtering and smoothing in order to provide consistent state estimates at high update rate, while maintaining accurate global localization for large-scale earth-moving excavators. Furthermore, the proposed approach enables a flexible integration of asynchronous sensor measurements and provides consistent pose estimates even during phases of sensor dropout. For this purpose, a dual-graph design for switching between two distinct optimization problems is proposed, directly addressing temporary failure and the subsequent return of global position estimates. The proposed approach is implemented on-board two Menzi Muck walking excavators and validated during real-world tests conducted in representative operational environments.

Model Predictive Control (MPC) schemes have proven their efficiency in controlling high degree-of-freedom (DoF) complex robotic systems. However, they come at a high computational cost and an update rate of about tens of hertz. This relatively slow update rate hinders the possibility of stable haptic teleoperation of such systems since the slow feedback loops can cause instabilities and loss of transparency to the operator. This work presents a novel framework for transparent teleoperation of MPC-controlled complex robotic systems. In particular, we employ a feedback MPC approach [1] and exploit its structure to account for the operator input at a fast rate which is independent of the update rate of the MPC loop itself. We demonstrate our framework on a mobile manipulator platform and show that it significantly improves haptic teleoperation's transparency and stability. We also highlight that the proposed feedback structure is constraint satisfactory and does not violate any constraints defined in the optimal control problem. To the best of our knowledge, this work is the first realization of the bilateral teleoperation of a legged manipulator using a whole-body MPC framework.

To safely deploy legged robots in the real world it is necessary to provide them with the ability to reliably detect unexpected contacts and accurately estimate the corresponding contact force. In this paper, we propose a collision detection and identification pipeline for a quadrupedal manipulator. We first introduce an approach to estimate the collision time span based on band-pass filtering and show that this information is key for obtaining accurate collision force estimates. We then improve the accuracy of the identified force magnitude by compensating for model inaccuracies, unmodeled loads, and any other potential source of quasi-static disturbances acting on the robot. We validate our framework with extensive hardware experiments in various scenarios, including trotting and additional unmodeled load on the robot.

Despite the progress in legged robotic locomotion, autonomous navigation in unknown environments remains an open problem. Ideally, the navigation system utilizes the full potential of the robots' locomotion capabilities while operating within safety limits under uncertainty. The robot must sense and analyze the travers ability of the surrounding terrain, which depends on the hardware, locomotion control, and terrain properties. It may contain information about the risk, energy, or time consumption needed to traverse the terrain. To avoid hand-crafted traversability cost functions we propose to collect traversability information about the robot and locomotion policy by simulating the traversal over randomly generated terrains using a physics simulator. Thousand of robots are simulated in parallel controlled by the same locomotion policy used in reality to acquire 57 years of real-world locomotion experience equivalent. For deployment on the real robot, a sparse convolutional network is trained to predict the simulated traversability cost, which is tailored to the deployed locomotion policy, from an entirely geometric representation of the envi-ronment in the form of a 3D voxel-occupancy map. This rep-resentation avoids the need for commonly used elevation maps, which are error-prone in the presence of overhanging obstacles and multi-floor or low-ceiling scenarios. The effectiveness of the proposed travers ability prediction network is demonstrated for path planning for the legged robot ANY mal in various indoor and natural environments.

Perceiving the surrounding environment is crucial for autonomous mobile robots. An elevation map provides a memory-efficient and simple yet powerful geometric represen-tation of the terrain for ground robots. The robots can use this information for navigation in an unknown environment or perceptive locomotion control over rough terrain. Depending on the application, various post processing steps may be incorpo-rated, such as smoothing, inpainting or plane segmentation. In this work, we present an elevation mapping pipeline leveraging GPU for fast and efficient processing with additional features both for navigation and locomotion. We demonstrated our map-ping framework through extensive hardware experiments. Our mapping software was successfully deployed for underground exploration during DARPA Subterranean Challenge and for various experiments of quadrupedal locomotion.

A kitchen assistant needs to operate human-scale objects, such as cabinets and ovens, in unmapped environments with dynamic obstacles. Autonomous interactions in such environments require integrating dexterous manipulation and fluid mobility. While mobile manipulators in different form factors provide an extended workspace, their real-world adoption has been limited. Executing a high-level task for general objects requires a perceptual understanding of the object as well as adaptive whole-body control among dynamic obstacles. In this paper, we propose a two-stage architecture for autonomous interaction with large articulated objects in unknown environments. The first stage, object-centric planner, only focuses on the object to provide an action-conditional sequence of states for manipulation using RGB-D data. The second stage, agent-centric planner, formulates the whole-body motion control as an optimal control problem that ensures safe tracking of the generated plan, even in scenes with moving obstacles. We show that the proposed pipeline can handle complex static and dynamic kitchen settings for both wheel-based and legged mobile manipulators. Compared to other agent-centric planners, our proposed planner achieves a higher success rate and a lower execution time. We also perform hardware tests on a legged mobile manipulator to interact with various articulated objects in a kitchen. For additional material, please check: www.pair.toronto.edularticulated-mm/.

LiDAR-based localization and mapping is one of the core components in many modern robotic systems due to the direct integration of range and geometry, allowing for precise motion estimation and generation of high quality maps in real-time. Yet, as a consequence of insufficient environmental constraints present in the scene, this dependence on geometry can result in localization failure, happening in self-symmetric surroundings such as tunnels. This work addresses precisely this issue by proposing a neural network-based estimation approach for detecting (non-)localizability during robot operation. Special attention is given to the localizability of scan-to-scan registration, as it is a crucial component in many LiDAR odometry estimation pipelines. In contrast to previous, mostly traditional detection approaches, the proposed method enables early detection of failure by estimating the localizability on raw sensor measurements without evaluating the underlying registration optimization. Moreover, previous approaches remain limited in their ability to generalize across environments and sensor types, as heuristic-tuning of degeneracy detection thresholds is required. The proposed approach avoids this problem by learning from a collection of different environments, allowing the network to function over various scenarios. Furthermore, the network is trained exclusively on simulated data, avoiding arduous data collection in challenging and degenerate, often hard-to-access, environments. The presented method is tested during field experiments conducted across challenging environments and on two different sensor types without any modifications. The observed detection performance is on par with state-of-the-art methods after environment-specific threshold tuning11Supplementary Video: https://youtu.be/fm08PFwMO0c.

The common approach for local navigation on challenging environments with legged robots requires path planning, path following and locomotion, which usually requires a locomotion control policy that accurately tracks a commanded velocity. However, by breaking down the navigation problem into these sub-tasks, we limit the robot's capabilities since the individual tasks do not consider the full solution space. In this work, we propose to solve the complete problem by training an end-to-end policy with deep reinforcement learning. Instead of continuously tracking a precomputed path, the robot needs to reach a target position within a provided time. The task's success is only evaluated at the end of an episode, meaning that the policy does not need to reach the target as fast as possible. It is free to select its path and the locomotion gait. Training a policy in this way opens up a larger set of possible solutions, which allows the robot to learn more complex behaviors. We compare our approach to velocity tracking and additionally show that the time dependence of the task reward is critical to successfully learn these new behaviors. Finally, we demonstrate the successful deployment of policies on a real quadrupedal robot. The robot is able to cross challenging terrains, which were not possible previously, while using a more energy-efficient gait and achieving a higher success rate. Supplementary videos can be found on the project website: https://sites.google.com/leggedrobotics.com/end-to-end-loco-navigation

Navigating off-road with a fast autonomous vehicle depends on a robust perception system that differentiates traversable from non-traversable terrain. Typically, this depends on a semantic understanding which is based on supervised learning from images annotated by a human expert. This requires a significant investment in human time, assumes correct expert classification, and small details can lead to misclassification. To address these challenges, we propose a method for predicting high- and low-risk terrains from only past vehicle experience in a self-supervised fashion. First, we develop a tool that projects the vehicle trajectory into the front camera image. Second, occlusions in the 3D representation of the terrain are filtered out. Third, an autoencoder trained on masked vehicle trajectory regions identifies low- and high-risk terrains based on the reconstruction error. We evaluated our approach with two models and different bottleneck sizes with two different training and testing sites with a four-wheeled off-road vehicle. Comparison with two independent test sets of semantic labels from similar terrain as training sites demonstrates the ability to separate the ground as low-risk and the vegetation as high-risk with 81.1% and 85.1% accuracy.

The vast majority of state-of-the-art walking robots employ flat or ball feet for locomotion, presenting limitations while stepping on obstacles, slopes, or unstructured terrain. Moreover, traditional feet for quadrupeds lack sensing systems that are able to provide information about the environment and about the foot interaction with the surroundings. This further diminishes their value. Inspired by our previous work on soft feet for bipedal robots, we present the SoftFoot-Q, an articulated adaptive foot for quadrupeds. This device is conceived to be robust and able to overcome the limitations of currently employed feet. The core idea behind our adaptive foot design is first introduced and validated through a simplified mathematical formulation of the problem. Subsequently, we present the chosen mechanical implementation to attempt overcoming current limitations. The realized prototype of adaptive foot is integrated and tested on the compliantly actuated quadrupedal robot ANYmal together with an ROS-based real-time foot pose reconstruction software. Both extensive field tests and indoor experiments show noticeable performance improvements, in terms of reduced slippage of the robot, with respect to both flat and ball feet.

Terrain geometry is, in general, nonsmooth, nonlinear, nonconvex, and, if perceived through a robot-centric visual unit, appears partially occluded and noisy. This article presents the complete control pipeline capable of handling the aforementioned problems in real-time. We formulate a trajectory optimization problem that jointly optimizes over the base pose and footholds, subject to a height map. To avoid converging into undesirable local optima, we deploy a graduated optimization technique. We embed a compact, contact-force free stability criterion that is compatible with the nonflat ground formulation. Direct collocation is used as transcription method, resulting in a nonlinear optimization problem that can be solved online in less than ten milliseconds. To increase robustness in the presence of external disturbances, we close the tracking loop with a momentum observer. Our experiments demonstrate stair climbing, walking on stepping stones, and over gaps, utilizing various dynamic gaits.

In this article, we show that learned policies can be applied to solve legged locomotion control tasks with extensive flight phases, such as those encountered in space exploration. Using an off-the-shelf deep reinforcement learning algorithm, we train a neural network to control a jumping quadruped robot while solely using its limbs for attitude control. We present tasks of increasing complexity leading to a combination of 3-D (re)orientation and landing locomotion behaviors of a quadruped robot traversing simulated low-gravity celestial bodies. We show that our approach easily generalizes across these tasks and successfully trains policies for each case. Using sim-to-real transfer, we deploy trained policies in the real world on the SpaceBok robot placed on an experimental testbed designed for 2-D microgravity experiments. The experimental results demonstrate that repetitive controlled jumping and landing with natural agility is possible.

Manipulators can be added to legged robots, allowing them to interact with and change their environment. Legged mobile manipulation planners must consider how contact forces generated by these manipulators affect the system. Current planning strategies either treat these forces as immutable during planning or are unable to optimize over these contact forces while operating in real-time. This paper presents the Stability and Task Oriented Receding-Horizon Motion and Manipulation Autonomous Planner (STORMMAP) that is able to generate continuous plans for the robot’s motion and manipulation force trajectories that ensure dynamic feasibility and stability of the platform, and incentivizes accomplishing manipulation and motion tasks specified by a user. A variety of simulated experiments on a quadruped with a manipulator mounted to its torso demonstrate the versatility of STOR-MMAP. In contrast to existing state of the art methods, the approach described in this paper generates continuous plans in under ten milliseconds, an order of magnitude faster than previous strategies.

We present a model predictive controller (MPC) that automatically discovers collision-free locomotion while simultaneously taking into account the system dynamics, friction constraints, and kinematic limitations. A relaxed barrier function is added to the optimization’s cost function, leading to collision avoidance behavior without increasing the problem’s computational complexity. Our holistic approach does not require any heuristics and enables legged robots to find whole-body motions in the presence of static and dynamic obstacles. We use a dynamically generated euclidean signed distance field for static collision checking. Collision checking for dynamic obstacles is modeled with moving cylinders, increasing the responsiveness to fast-moving agents. Furthermore, we include a Kalman filter motion prediction for moving obstacles into our receding horizon planning, enabling the robot to anticipate possible future collisions. Our experiments1demonstrate collision-free motions on a quadrupedal robot in challenging indoor environments. The robot handles complex scenes like overhanging obstacles and dynamic agents by exploring motions at the robot’s dynamic and kinematic limits.

The problem of dynamic locomotion over rough terrain requires both accurate foot placement together with an emphasis on dynamic stability. Existing approaches to this problem prioritize immediate safe foot placement over longer term dynamic stability considerations, or relegate the coordination of foot placement and dynamic stability to heuristic methods. We propose a multi-layered locomotion framework that unifies Control Barrier Functions (CBFs) with Model Predictive Control (MPC) to simultaneously achieve safe foot placement and dynamic stability. Our approach incorporates CBF based safety constraints both in a low frequency kinodynamic MPC formulation and a high frequency inverse dynamics tracking controller. This ensures that safety-critical execution is considered when optimizing locomotion over a longer horizon. We validate the proposed method in a 3D stepping-stone scenario in simulation and experimentally on the ANYmal quadruped platform.

Planning for legged-wheeled machines is typically done using trajectory optimization because of many degrees of freedom, thus rendering legged-wheeled planners prone to falling prey to bad local minima. We present a combined sampling and optimization-based planning approach that can cope with challenging terrain. The sampling-based stage computes whole-body configurations and contact schedule, which speeds up the optimization convergence. The optimization-based stage ensures that all the system constraints, such as non-holonomic rolling constraints, are satisfied. The evaluations show the importance of good initial guesses for optimization. Furthermore, they suggest that terrain/collision (avoidance) constraints are more challenging than the robot model’s constraints. Lastly, we extend the optimization to handle general terrain representations in the form of elevation maps.

Modern, torque-controlled service robots can regulate contact forces when interacting with their environment. Model Predictive Control (MPC) is a powerful method to solve the underlying control problem, allowing to plan for whole-body motions while including different constraints imposed by the robot dynamics or its environment. However, an accurate model of the robot-environment is needed to achieve a satisfying closed-loop performance. Currently, this necessity undermines the performance and generality of MPC in manipulation tasks. In this work, we combine an MPC-based whole-body controller with two adaptive schemes, derived from online system identification and adaptive control. As a result, we enable a general mobile manipulator to interact with unknown environments, without any need for re-tuning parameters or pre-modeling the interacting objects. In combination with the MPC controller, the two adaptive approaches are validated and benchmarked with a ball-balancing manipulator in door opening and object lifting tasks.

Reliable robot pose estimation is a key building block of many robot autonomy pipelines, with LiDAR localization being an active research domain. In this work, a versatile self-supervised LiDAR odometry estimation method is presented, in order to enable the efficient utilization of all available LiDAR data while maintaining real-time performance. The proposed approach selectively applies geometric losses during training, being cognizant of the amount of information that can be extracted from scan points. In addition, no labeled or ground-truth data is required, hence making the presented approach suitable for pose estimation in applications where accurate ground-truth is difficult to obtain. Furthermore, the presented network architecture is applicable to a wide range of environments and sensor modalities without requiring any network or loss function adjustments. The proposed approach is thoroughly tested for both indoor and outdoor real-world applications through a variety of experiments using legged, tracked and wheeled robots, demonstrating the suitability of learning-based LiDAR odometry for complex robotic applications.

We present a learning algorithm for training a single policy that imitates multiple gaits of a walking robot. To achieve this, we use and extend MPC-Net, which is an Imitation Learning approach guided by Model Predictive Control (MPC). The strategy of MPC-Net differs from many other approaches since its objective is to minimize the control Hamiltonian, which derives from the principle of optimality. To represent the policies, we employ a mixture-of-experts network (MEN) and observe that the performance of a policy improves if each expert of a MEN specializes in controlling exactly one mode of a hybrid system, such as a walking robot. We introduce new loss functions for single- and multi-gait policies to achieve this kind of expert selection behavior. Moreover, we benchmark our algorithm against Behavioral Cloning and the original MPC implementation on various rough terrain scenarios. We validate our approach on hardware and show that a single learned policy can replace its teacher to control multiple gaits.

Quadrupedal robots are skillful at locomotion tasks while lacking manipulation skills, not to mention dexterous manipulation abilities. Inspired by the animal behavior and the duality between multi-legged locomotion and multi-fingered manipulation, we showcase a circus ball challenge on a quadrupedal robot, ANYmal. We employ a model-free reinforcement learning approach to train a deep policy that enables the robot to balance and manipulate a light-weight ball robustly using its limbs without any contact measurement sensor. The policy is trained in the simulation, in which we randomize many physical properties with additive noise and inject random disturbance force during manipulation, and achieves zero-shot deployment on the real robot without any adjustment. In the hardware experiments, dynamic performance is achieved with a maximum rotation speed of 15 °/s, and robust recovery is showcased under external poking. To our best knowledge, it is the first work that demonstrates the dexterous dynamic manipulation on a real quadrupedal robot.

The Sequential Linear Quadratic (SLQ) algorithm is a continuous-time version of the well-known Differential Dynamic Programming (DDP) technique with a Gauss-Newton Hessian approximation. This family of methods has gained popularity in the robotics community due to its efficiency in solving complex trajectory optimization problems. However, one major drawback of DDP-based formulations is their inability to properly incorporate path constraints. In this paper, we address this issue by devising a constrained SLQ algorithm that handles a mixture of constraints with a previously implemented projection technique and a new augmented-Lagrangian approach. By providing an appropriate multiplier update law, and by solving a single inner and outer loop iteration, we are able to retrieve suboptimal solutions at rates suitable for real-time model-predictive control applications. We particularly focus on the inequality-constrained case, where three augmented-Lagrangian penalty functions are introduced, along with their corresponding multiplier update rules. These are then benchmarked against a relaxed log-barrier formulation in a cart-pole swing up example, an obstacle-avoidance task, and an object-pushing task with a quadrupedal mobile manipulator.

Navigation on challenging terrain topographies requires the understanding of robots’ locomotion capabilities to produce optimal solutions. We present an integrated framework for real-time autonomous navigation of mobile robots based on elevation maps. The framework performs rapid global path planning and optimization that is aware of the locomotion capabilities of the robot. A GPU-aided, sampling-based path planner combined with a gradient-based path optimizer provides optimal paths by using a neural network-based locomotion cost predictor which is trained in simulation. We show that our approach is capable of planning and optimizing paths three orders of magnitude faster than RRT* on GPU-enabled hardware, enabling real-time deployment on mobile platforms. We successfully evaluate the framework on the ANYmal C quadrupedal robot in both simulations and real-world environments for path planning tasks on multiple complex terrains.

In this paper, we introduce a method for visual relocalization using the geometric information from a 3D surfel map. A visual database is first built by global indices from the 3D surfel map rendering, which provides associations between image points and 3D surfels. Surfel reprojection constraints are utilized to optimize the keyframe poses and map points in the visual database. A hierarchical camera relocalization algorithm then utilizes the visual database to estimate 6-DoF camera poses. Learned descriptors are further used to improve the performance in challenging cases. We present evaluation under real-world conditions and simulation to show the effectiveness and efficiency of our method, and make the final camera poses consistently well aligned with the 3D environment.

Our paper proposes a model predictive controller as a single-task formulation that simultaneously optimizes wheel and torso motions. This online joint velocity and ground reaction force optimization integrates a kinodynamic model of a wheeled quadrupedal robot. It defines the single rigid body dynamics along with the robot’s kinematics while treating the wheels as moving ground contacts. With this approach, we can accurately capture the robot’s rolling constraint and dynamics, enabling automatic discovery of hybrid maneuvers without needless motion heuristics. The formulation’s generality through the simultaneous optimization over the robot’s whole-body variables allows for a single set of parameters and makes online gait sequence adaptation possible. Aperiodic gait sequences are automatically found through kinematic leg utilities without the need for predefined contact and lift-off timings, reducing the cost of transport by up to 85 %. Our experiments demonstrate dynamic motions on a quadrupedal robot with non-steerable wheels in challenging indoor and outdoor environments. The paper’s findings contribute to evaluating a decomposed, i.e., sequential optimization of wheel and torso motion, and single-task motion planner with a novel quantity, the prediction error, which describes how well a receding horizon planner can predict the robot’s future state. To this end, we report an improvement of up to 71 % using our proposed single-task approach, making fast locomotion feasible and revealing wheeled-legged robots’ full potential.

When dealing with the haptic teleoperation of multi-limbed mobile manipulators, the problem of mitigating the destabilizing effects arising from the communication link between the haptic device and the remote robot has not been properly addressed. In this work, we propose a passive control architecture to haptically teleoperate a legged mobile manipulator, while remaining stable in the presence of time delays and frequency mismatches in the master and slave controllers. At the master side, a discrete-time energy modulation of the control input is proposed. At the slave side, passivity constraints are included in an optimization-based whole-body controller to satisfy the energy limitations. A hybrid teleoperation scheme allows the human operator to remotely operate the robot’s end- effector while in stance mode, and its base velocity in locomotion mode. The resulting control architecture is demonstrated on a quadrupedal robot with an artificial delay added to the network.

Navigation planning for legged robots has distinct challenges compared to wheeled and tracked systems due to the ability to lift legs off the ground and step over obstacles. While most navigation planners assume a fixed traversability value for a single terrain patch, we overcome this limitation by proposing a reachability-based navigation planner for legged robots. We approximate the robot morphology by a set of reachability and body volumes, assuming that the reachability volumes need to always be in contact with the environment, while the body should be contact-free. We train a convolutional neural network to predict foothold scores which are used to restrict geometries which are considered suitable to step on. Using this representation, we propose a navigation planner based on probabilistic roadmaps. Through validation of only low-cost graph edges during graph expansion and an adaptive sampling scheme based on roadmap node density, we achieve real-time performance with fast update rates even in cluttered and narrow environments. We thoroughly validate the proposed navigation planner in simulation and demonstrate its performance in real-world experiments on the quadruped ANYmal.

This work presents a novel design concept that achieves multi-legged locomotion using a three-dimensional cam system. A computational framework has been developed to analyze and dimension this cam apparatus, that can perform arbitrary end effector motions within its design constraints. The mechanism enables continuous gait transition and inherent force compliance. With only two motors, any trajectory of a continuous set of gaits can be followed. One motor is used to actuate the system and a second one to morph its movement. To illustrate a possible application of this system, a working prototype of a bipedal robot is developed and validated in hardware. It showcases a smooth velocity change by transitioning through different gaits from standing still to walking fast at 124mm/s within 2.0s, while following the given end effector trajectory with an error of only 2.47mm.

In this article we present a data-driven approach for automated arm control of a hydraulic excavator. Except for the link lengths of the excavator, our method does not require machine-specific knowledge nor gain tuning. Using data collected during operation of the excavator, we train a general purpose model to effectively represent the highly non-linear dynamics of the hydraulic actuation and joint linkage. Together with the link lengths a simulation is set up to train a neural network control policy for end-effector position tracking using reinforcement learning (RL). The control policy directly outputs the actuator commands that can be applied to the machine without unfounded filtering or modification. The proposed method is implemented and tested on a 12t hydraulic excavator, controlling its 4 main arm joints to track desired positions of the shovel in free-space. The results demonstrate the feasibility of directly applying control policies trained in simulation to the physical excavator for accurate and stable position tracking.

This article presents a planning and control pipeline for legged-wheeled (hybrid) machines. It consists of a Trajectory Optimization based planner that computes references for end-effectors and joints. The references are tracked using a whole-body controller based on a hierarchical optimization approach. Our controller is capable of performing terrain adaptive whole-body control. Furthermore, it computes both torque and position/velocity references, depending on the actuator capabilities. We perform experiments on a Menzi Muck M545, a full size 31 Degrees of Freedom (DoF) walking excavator with five limbs: four wheeled legs and an arm. We show motions that require full-body coordination executed in realistic conditions. To the best of our knowledge, this is the first work that shows the execution of whole-body motions on a full size walking excavator, using all DoFs for locomotion.

During robot-assisted therapy of hemiplegic patients, interaction with the patient must be intrinsically safe. Straight-forward collision avoidance solutions can provide this safety requirement with conservative margins. These margins heavily reduce the robot's workspace and make interaction with the patient's unguided body parts impossible. However, interaction with the own body is highly beneficial from a therapeutic point of view. We tackle this problem by combining haptic rendering techniques with classical computer vision methods. Our proposed solution consists of a pipeline that builds collision objects from point clouds in real-time and a controller that renders haptic interaction. The raw sensor data is processed to overcome noise and occlusion problems. Our proposed approach is validated on the 6 DoF exoskeleton ANYexo for direct impacts, sliding scenarios, and dynamic collision surfaces. The results show that this method has the potential to successfully prevent collisions and allow haptic interaction for highly dynamic environments. We believe that this work significantly adds to the usability of current exoskeletons by enabling virtual haptic interaction with the patient's body parts in human-robot therapy.

A high-quality free-motion rendering is one of the most vital traits to achieve an immersive human-robot interaction. Rendering free-motion is notably challenging for rehabilitation exoskeletons due to their relatively high weight and powerful actuators required for strength training and support. In the presence of dynamic human movements, accurate feedback linearization of the robot's dynamics is necessary to allow for a linear synthesis of interaction wrench controllers. Hence, we introduce a virtual model controller that uses two 6-DoF force sensors to control the interaction wrenches of a multi-DoF torque-controlled exoskeleton over the joint accelerations and inverse dynamics. Furthermore, we propose a disturbance observer for controlling the joint acceleration to diminish the influence of modeling errors on the inverse dynamics. To provide a high-bandwidth, low-bias estimation of the system's acceleration, we introduce a bias-observer which fuses the information from joint encoders and seven low priced IMUs. We have validated the performance of our proposed control structure on the shoulder and arm exoskeleton ANYexo. The experimental comparison of the controllers shows a reduction of the felt inertia and maximum reflected joint torque by a factor of more than three compared to state of the art. The controllers' robustness w.r.t. a model mismatch is validated. The experiments show that the closed-loop acceleration control improves the tracking, particularly at joints with low inertia. The proposed controllers' performance sets a new benchmark in haptic transparency for comparable devices and should be transferable to other applications.

This paper introduces SpaceBok, a quadrupedal robot created to investigate dynamic legged locomotion for the exploration of low-gravity celestial bodies. With a hip height of 500 mm and a mass of 20 kg, its dimensions are comparable to a medium-sized dog. The robot's leg configuration is based on an optimized parallel motion mechanism that allows the integration of parallel elastic elements to store and release energy for powerful jumping maneuvers. High-torque brushless motors in combination with customized single-stage planetary gear transmissions enable force control at the foot contact points based on motor currents. We present successful walking, trotting, and pronking experiments. Thereby, Spacebok achieved maximal jump heights in single jump experiments of up to 1.05 m (more than twice the hip height) and a walking velocity of 1m/s. Moreover, simulation results for low gravity on the moon suggest that our robot can move with up to 1.1m/s at an approximate cost of transport of 1 in moon gravity when using the pronking gait.

Mobile robots are becoming very popular in real-world outdoors applications, where there are many challenges in robot control and perception. One of the most critical problems is to characterise the terrain traversed by the robot. This knowledge is indispensable for optimal terrain negotiation. Currently, most approaches are performing terrain classification from vision, but there is not enough research on terrain identification from a direct interaction of the robot with the environment. In our work, we proposed new methods for classification of force/torque data from an interaction of the legged robot foot with the ground, gathered during the walking process. We provided machine learning methods for terrain classification from raw force/torque signals for which we achieved 93% accuracy on a challenging dataset with 160 minutes of recorded fixed-length steps. We also worked on a dataset where the assumption of a fixed-length step is not valid. In this case, the final result is around 80% of accuracy. The most important fact is that the data in both cases was recorded while the robot was walking, no particular movements or controlled environment were needed. Additionally, we also proposed a clustering method which allows us to learn about the class membership based on the recorded data only, without any human supervision.

The task of robotic mobile manipulation poses several scientific challenges that need to be addressed to execute complex manipulation tasks in unstructured environments, in which collaboration with humans might be required. Therefore, we present ALMA, a motion planning and control framework for a torque-controlled quadrupedal robot equipped with a six degrees of freedom robotic arm capable of performing dynamic locomotion while executing manipulation tasks. The online motion planning framework, together with a whole-body controller based on a hierarchical optimization algorithm, enables the system to walk, trot and pace while executing operational space end-effector control, reactive human-robot collaboration and torso posture optimization to increase the arm's workspace. The torque control of the whole system enables the implementation of compliant behavior, allowing a user to safely interact with the robot. We verify our framework on the real robot by performing tasks such as opening a door and carrying a payload together with a human.

The high agility of legged systems allows them to operate in rugged outdoor environments. In these situations, knowledge about the terrain geometry is key for foothold planning to enable safe locomotion. However, on penetrable or highly compliant terrain (e.g. grass) the visibility of the supporting ground surface is obstructed, i.e. it cannot directly be perceived by depth sensors. We present a method to estimate the underlying terrain topography by fusing haptic information about foot contact closure locations with exteroceptive sensing. To obtain a dense support surface estimate from sparsely sampled footholds we apply Gaussian process regression. Exteroceptive information is integrated into the support surface estimation procedure by estimating the height of the penetrable surface layer from discrete penetration depth measurements at the footholds. The method is designed such that it provides a continuous support surface estimate even if there is only partial exteroceptive information available due to shadowing effects. Field experiments with the quadrupedal robot ANYmal show how the robot can smoothly and safely navigate in dense vegetation.

Locomotion planning for legged systems requires reasoning about suitable contact schedules. The contact sequence and timings constitute a hybrid dynamical system and prescribe a subset of achievable motions. State-of-the-art approaches cast motion planning as an optimal control problem. In order to decrease computational complexity, one common strategy separates footstep planning from motion optimization and plans contacts using heuristics. In this paper, we propose to learn contact schedule selection from high-level task descriptors using Bayesian Optimization. A bi-level optimization is defined in which a Gaussian Process model predicts the performance of trajectories generated by a motion planning nonlinear program. The agent, therefore, retains the ability to reason about suitable contact schedules, while explicit computation of the corresponding gradients is avoided. We delineate the algorithm in its general form and provide results for planning single-legged hopping. Our method is capable of learning contact schedule transitions that align with human intuition. It performs competitively against a heuristic baseline in predicting task appropriate contact schedules.

We present a fully-integrated sensing and control system which enables mobile manipulator robots to execute building tasks with millimeter-scale accuracy on building construction sites. The approach leverages multi-modal sensing capabilities for state estimation, tight integration with digital building models, and integrated trajectory planning and whole-body motion control. A novel method for high-accuracy localization updates relative to the known building structure is proposed. The approach is implemented on a real platform and tested under realistic construction conditions. We show that the system can achieve sub-cm end-effector positioning accuracy during fully autonomous operation using solely onboard sensing.

The computational power of mobile robots is currently insufficient to achieve torque level whole-body Model Predictive Control (MPC) at the update rates required for complex dynamic systems such as legged robots. This problem is commonly circumvented by using a fast tracking controller to compensate for model errors between updates. In this work, we show that the feedback policy from a Differential Dynamic Programming (DDP) based MPC algorithm is a viable alternative to bridge the gap between the low MPC update rate and the actuation command rate. We propose to augment the DDP approach with a relaxed barrier function to address inequality constraints arising from the friction cone. A frequency-dependent cost function is used to reduce the sensitivity to high-frequency model errors and actuator bandwidth limits. We demonstrate that our approach can find stable locomotion policies for the torque-controlled quadruped, ANYmal, both in simulation and on hardware.

This article presents a trajectory planning framework for all-terrain vehicles with legs and wheels such as walking excavators. Our formulation takes into account the whole body of the robot while computing the plans for locomotion. Hence, we can produce motion plans over the rough terrain that would be hard to plan without considering all Degrees of Freedom (DoF) simultaneously. Our planner can also optimize over the contact schedule for all limbs, thereby finding the feasible motions even for the infeasible initial contact schedule. Furthermore, we introduce a novel formulation of the support area constraint. We generate plans for a Menzi Muck M545, a 31 DoF walking excavator with five limbs: four wheeled legs and an arm. We show motion plans for traversing a variety of terrains that require whole-body planning. To the best of our knowledge, this is the first work that addresses motion planning in rough terrain for vehicles with legs and wheels.

Jumping locomotion has the potential to enable legged robots to overcome obstacles and travel efficiently on low-gravity celestial bodies. We present how the 22 kg quadruped robot SpaceBok exploits lunar gravity conditions to perform energy-efficient jumps. The robot achieves repetitive, vertical jumps of more than 0.9m meter and powerful single leaps of up to 1.3m. We present the implementation of a reaction wheel, which allows for control of the robots pitch orientation during the flight phase. We also demonstrate the implementation of a parallel elasticity in the legs providing the capability of temporarily storing and reusing energy during jumping. The jumping and attitude controller are subsequently presented. Finally, we analyze the energetics of the system and show that jumping with the integrated elasticity significantly reduces energy consumption compared to non-elastic jumps.

We present a reformulation of a contact-implicit optimization (CIO) approach that computes optimal trajectories for rigid-body systems in contact-rich settings. A hard-contact model is assumed, and the unilateral constraints are imposed in the form of complementarity conditions. Newton's impact law is adopted for enhanced physical correctness. The optimal control problem is formulated as a multi-staged program through a multiple-shooting scheme. This problem structure is exploited within the FORCES Pro framework to retrieve optimal motion plans, contact sequences and control inputs with increased computational efficiency. We investigate our method on a variety of dynamic object manipulation tasks, performed by a six degrees of freedom robot. The dynamic feasibility of the optimal trajectories, as well as the repeatability and accuracy of the task-satisfaction are verified through simulations and real hardware experiments on one of the manipulation problems.

Robots working in natural, urban, and industrial settings need to be able to navigate challenging environments. In this paper, we present a motion planner for the perceptive rough-terrain locomotion with quadrupedal robots. The planner finds safe footholds along with collision-free swing-leg motions by leveraging an acquired terrain map. To this end, we present a novel pose optimization approach that enables the robot to climb over significant obstacles. We experimentally validate our approach with the quadrupedal robot ANYmal by autonomously traversing obstacles such steps, inclines, and stairs. The locomotion planner re-plans the motion at every step to cope with disturbances and dynamic environments. The robot has no prior knowledge of the scene, and all mapping, state estimation, control, and planning is performed in real-time onboard the robot.

Predominately, robotic construction is applied as prefabrication in structured indoor environments with standard building materials. Our work, on the other hand, focuses on utilizing irregular materials found on-site, such as rubble and rocks, for autonomous construction. We present a pipeline to detect arbitrarily placed objects in a scene and form a structure out of the detected objects. The next best stacking pose is selected using a searching method employing gradient descent with random initial orientations, exploiting a physics engine. This approach is validated in an experimental setup using a robotic manipulator by constructing balancing vertical stacks without mortars and adhesives. We show the results of eleven consecutive trials to form such towers autonomously using four arbitrarily in front of the robot placed rocks.

The development of robots that can dance has received considerable attention. However, they are often either limited to a pre-defined set of movements and music or demonstrate little variance when reacting to external stimuli, such as microphone or camera input. In this paper, we contribute with a novel approach allowing a legged robot to listen to live music while dancing in synchronization with the music in a diverse fashion. This is achieved by extracting the beat from an onboard microphone in real-time, and subsequently creating a dance choreography by picking from a user-generated dance motion library at every new beat. Dance motions include various stepping and base motions. The process of picking from the library is defined by a probabilistic model, namely a Markov chain, that depends on the previously picked dance motion and the current music tempo. Finally, delays are determined online by time-shifting a measured signal and a reference signal, and minimizing the least squares error with the time-shift as parameter. Delays are then compensated for by using a combined feedforward and feedback delay controller which shifts the robot whole-body controller reference input in time. Results from experiments on a quadrupedal robot demonstrate the fast convergence and synchrony to the perceived music.

Traditional legged robots are capable of traversing challenging terrain, but lack of energy efficiency when compared to wheeled systems operating on flat environments. The combination of both locomotion domains overcomes the trade-off between mobility and efficiency. Therefore, this paper presents a novel motion planner and controller which together enable a legged robot equipped with skates to perform skating maneuvers. These are achieved by an appropriate combination of planned reaction forces and gliding motions. Our novel motion controller formulates a Virtual Model Controller and an optimal contact force distribution which takes into account the nonholonomic constraints introduced by the skates. This approach has been tested on the torque-controllable robot ANY mal equipped with passive wheels and ice skates as end-effectors. We conducted experiments on flat and inclined terrain, whereby we show that skating motions reduces the cost of transport by up to 80 % with respect to traditional walking gaits.

This paper presents the design and experimental evaluations of an articulated robotic limb called Capler-Leg. The key element of Capler-Leg is its single-stage cable-pulley transmission combined with a high-gap radius motor. Our cable-pulley system is designed to be as light-weight as possible and to additionally serve as the primary cooling element, thus significantly increasing the power density and efficiency of the overall system. The total weight of active elements on the leg, i.e. the stators and the rotors, contribute more than 60 % of the total leg weight, which is an order of magnitude higher than most existing robots. The resulting robotic leg has low inertia, high torque transparency, low manufacturing cost, no backlash, and a low number of parts. The Capler-Leg system itself, serves as an experimental setup for evaluating the proposed cable-pulley design in terms of robustness and efficiency. A continuous jump experiment shows a remarkable 96.5 % recuperation rate, measured at the battery output. This means that almost all the mechanical energy output during push-off is returned back to the battery during touch-down.

Adapting to the ground enables stable footholds in legged locomotion by exploiting the structure of the terrain. On that account, we present a passive adaptive planar foot with three rotational degrees of freedom that is lightweight and thus suited for highly dynamic legged robots. Its low laying pivot joint provides high stability towards kinking. Information about the relative foot sole pose, and accordingly, the ground orientation is gathered by inertial measurement units (IMUs) placed on the foot sole and the shank. A complementary filter is presented that fuses these orientation estimates with an angular encoder to obtain a drift-free relative foot sole pose. The passive adaptive planar foot has been tested and compared to the classical point foot design on a variety of terrains and shows superior traction performance, especially on compressible soils. Being mounted on the quadrupedal robot ANYmal, the foot provides a reliable contact detection based on the fusion of the built-in 6-axis force/torque transducer and the IMUs. This allows to walk and trot on uneven terrain, loose soils, as well as climbing up a ramp and stairs while keeping the entire foot sole in ground contact all the time.

Conventional skid or wheel based helicopter landing gears severely limit off-field landing possibilities, which are crucial when operating in scenarios such as mountain rescue. In this context, slopes beyond 8° and small obstacles can already pose a substantial hazard. An adaptive landing gear is proposed to overcome these limitations. It consists of four legs with one degree of freedom each. The total weight was minimized to demonstrate economic practicability. This was achieved by an innovative actuation, composed of a parallel arrangement of motor and brake, which relieves the motor from large impact loads during hard landings. The loads are alleviated by a spring-damper system acting in series to the actuation. Each leg is individually force controlled for optimal load distribution on compliant ground and to avoid tipping. The operation of the legs is fully autonomous during the landing phase. A prototype was designed and successfully tested on an unmanned helicopter with a maximum take-off weight of 78 kg. Finally, the implementation of the landing gear concept on aircraft of various scales was discussed.

Predominately, robotic construction is applied as prefabrication in structured indoor environments with standard building materials. Our work, on the other hand, focuses on utilizing irregular materials found on-site, such as rubble and rocks, for autonomous construction. We present a pipeline that detects randomly placed objects in a scene that are used by our next best stacking pose searching method employing gradient descent with a random initial orientation, exploiting a physics engine. This approach is validated in an experimental setup using a robotic manipulator by constructing balancing vertical stacks without mortars and adhesives. We show the results of eleven consecutive trials to form such towers autonomously using four arbitrarily in front of the robot placed rocks.

Quadrupedal locomotion can be described as a constrained optimization problem that is very hard to solve due to the high dimensional, nonlinear and non-smooth system dynamics. In this paper, we propose a formulation that can be solved within few seconds using sequential quadratic programming. This method considers only a simplified model that just sufficiently represents the system dynamics. The output is a very coarse plan, which can be accurately and robustly followed on a real system using hierarchical whole-body control combined with inverted pendulum-based reactive stepping. Using the fully torque controllable quadrupedal robot ANYmal, we present successful experiments for walking, trotting, and gait transitions even under substantial external disturbances.

This paper presents a framework which allows a quadrupedal robot to execute dynamic gaits including trot, pace and dynamic lateral walk, as well as a smooth transition between them. Our method relies on an online ZMP based motion planner which continuously updates the reference motion trajectory as a function of the contact schedule and the state of the robot. The planner is coupled with a hierarchical whole-body controller which optimizes the whole-body motion and contact forces by solving a cascade of prioritized tasks. We tested our framework on ANYmal, a fully torque controllable quadrupedal robot which is actuated by series-elastic actuators.

Ropeways must be stopped when there is strong cross-wind because the ensuing oscillations are a safety risk. In this paper, we developed a controller for an actuated mass onboard the gondola aiming to increase the gondola's damping, thus reducing the oscillations and permitting operation to continue. We modeled the gondola as a pendulum, acknowledged the limitation on the actuated mass' displacement, and included input and parametric uncertainty. We synthesized the controller through a two-step process. First, we used numerical optimization to compute a static full state feedback controller specifically designed to reduce the effects that cross-wind gusts and random disturbances have on the gondola. For this purpose, we included a wind model in the cost function. Then, we used this controller in a model to synthesize an H∞controller with reduced actuator requirements. Analysis of the linearized system showed that the proposed H∞controller robustly stabilized the system despite the modeled uncertainty. Furthermore, it made the peak magnitude of the gondola's oscillations in the median of 1005 simulations 51.4 percent less than that of the uncontrolled system, and 19.3 percent less than that of the system using a passive dynamic vibration absorber.

A novel method for visual place recognition is introduced and evaluated, demonstrating robustness to perceptual aliasing and observation noise. This is achieved by increasing discrimination through a more structured representation of visual observations. Estimation of observation likelihoods are based on graph kernel formulations, utilizing both the structural and visual information encoded in covisibility graphs. The proposed probabilistic model is able to circumvent the typically difficult and expensive posterior normalization procedure by exploiting the information available in visual observations. Furthermore, the place recognition complexity is independent of the size of the map. Results show improvements over the state-of-theart on a diverse set of both public datasets and novel experiments, highlighting the benefit of the approach.

The present paper introduces a manipulator that is developed to combine safe and dynamic interaction tasks. The system is built from lightweight carbon fiber links and novel high-performance series elastic actuator units that provide dynamic movement capability, low-impedance joint torque control, and inherent interaction safety. This enabled the implementation of a model-based direct force control method purely based on joint torque regulation. Using unified force and motion control, the end-effector position can be accurately and dynamically tracked in task space while acting safely upon (unexpected) contacts with the environment. The force control component is implemented in a novel way that shows reduced forces in comparison to existing methods when navigating across a surface of unpredictable orientation and friction. ANYpulator is tested using a haptic feedback method that renders the system dynamics and contact forces back to the user.

Flying and walking robots can use their complementary features in terms of viewpoint and payload capability to the best in a heterogeneous team. To this end, we present our online collaborative navigation framework for unknown and challenging terrain. The method leverages the flying robot's onboard monocular camera to create both a map of visual features for simultaneous localization and mapping and a dense representation of the environment as an elevation map. This shared knowledge from the flying platform enables the walking robot to localize itself against the global map, and plan a global path to the goal by interpreting the elevation map in terms of traversability. While following the planned path, the absolute pose corrections are fused with the legged state estimation and the elevation map is continuously updated with distance measurements from an onboard laser range sensor. This allows the legged robot to safely navigate towards the goal while taking into account any changes in the environment. In this setup, our approach is independent of external localization, relative observations between the robots, and does not require an initial guess about the pose of the robots. The presented methods are fully integrated and we demonstrate their capabilities in an experiment with a hexacopter and a quadrupedal robot.

This paper introduces ANYmal, a quadrupedal robot that features outstanding mobility and dynamic motion capability. Thanks to novel, compliant joint modules with integrated electronics, the 30 kg, 0.5 m tall robotic dog is torque controllable and very robust against impulsive loads during running or jumping. The presented machine was designed with a focus on outdoor suitability, simple maintenance, and user-friendly handling to enable future operation in real world scenarios. Performance tests with the joint actuators indicated a torque control bandwidth of more than 70 Hz, high disturbance rejection capability, as well as impact robustness when moving with maximal velocity. It is demonstrated in a series of experiments that ANYmal can execute walking gaits, dynamically trot at moderate speed, and is able to perform special maneuvers to stand up or crawl very steep stairs. Detailed measurements unveil that even full-speed running requires less than 280 W, resulting in an autonomy of more than 2 h.

Legged robots require a robust and fast responding feet contact detection strategy. Common force sensors are often too heavy and can be easily damaged during impacts with the terrain. Therefore, it is desirable to detect a contact without a force sensor. This paper introduces a probabilistic contact detection strategy which considers full dynamics and differential/forward kinematics to maximize the use of available information for contact estimation. This papers shows that such strategy is much more accurate than the state-of-the-art strategy that only take one measure into account, with a quadrupedal robot.

This paper presents a framework for planning safe and efficient paths for a legged robot in rough and unstructured terrain. The proposed approach allows to exploit the distinctive obstacle negotiation capabilities of legged robots, while keeping the complexity low enough to enable planning over considerable distances in short time. We compute typical terrain characteristics such as slope, roughness, and steps to build a traversability map. This map is used to assess the costs of individual robot footprints as a function of the robot-specific obstacle negotiating capabilities for steps, gaps and stairs. Our sampling-based planner employs the RRT* algorithm to optimize path length and safety. The planning framework has a hierarchical architecture to frequently replan the path during execution as new terrain is perceived with onboard sensors. Furthermore, a cascaded planning structure makes use of different levels of simplification to allow for fast search in simple environments, while retaining the ability to find complex solutions, such as paths through narrow passages. The proposed navigation planning framework is integrated on the quadrupedal robot StarlETH and extensively tested in simulation as well as on the real platform.

In this paper, we present a monocular visual-inertial odometry algorithm which, by directly using pixel intensity errors of image patches, achieves accurate tracking performance while exhibiting a very high level of robustness. After detection, the tracking of the multilevel patch features is closely coupled to the underlying extended Kalman filter (EKF) by directly using the intensity errors as innovation term during the update step. We follow a purely robocentric approach where the location of 3D landmarks are always estimated with respect to the current camera pose. Furthermore, we decompose landmark positions into a bearing vector and a distance parametrization whereby we employ a minimal representation of differences on a corresponding σ-Algebra in order to achieve better consistency and to improve the computational performance. Due to the robocentric, inverse-distance landmark parametrization, the framework does not require any initialization procedure, leading to a truly power-up-and-go state estimation system. The presented approach is successfully evaluated in a set of highly dynamic hand-held experiments as well as directly employed in the control loop of a multirotor unmanned aerial vehicle (UAV).

Quadrupedal locomotion on sloped terrains poses different challenges than walking in a mostly flat environment. The robot's configuration needs to be explicitly controlled in order to avoid slipping and kinematic limits. To this end, information about the terrain's inclination is required for carefully planning footholds, the pose of the main body, and modulation of the ground reaction forces. This is even more important for dynamic trotting, as only two support legs are available to compensate for gravity and drive a desired motion. We propose a reliable method for estimating the parameters of the terrain quadrupedal robots move on, in the face of limited perception capabilities and drifting robot pose estimates. By fusing inertial measurements, kinematic data from joint encoders and contact information from force sensors, the local inclination can be robustly estimated and used to optimize the contact forces to reduce slippage. The estimated terrain information, namely the pitch and roll angles of the ground plane, is exploited in an extended version of our previous model-based control approach. Our improved control framework enabled StarlETH, a medium-sized, fully autonomous, torque-controllable quadrupedal robot, to trot on slopes of up to 21°.

Methods of optimizing a single trajectory are mature enough for planning in many applications. Yet such optimization methods applied to high Degree-Of-Freedom robots either consume too much time to be real-time or approximate the dynamics such that they lack physical consistency. In this paper, we present a method of precomputing optimized trajectories and compressing the information to get a compact representation of the optimal policy function. By varying the initial configuration of a robot and optimizing multiple trajectories, the controller gains knowledge about the optimal policy function. Such computation can be performed on a powerful workstation or even supercomputers instead of an onboard computer of the robot. The precomputed optimal trajectories are stored in a Single-hidden Layer Feedforward neural Network (SLFN) using Optimally Pruned Extreme Learning Machine (OP-ELM). This ensures minimal representation of the model and fast evaluation of the SLFN. We first explain our method using a simple time-optimal control problem with an analytical solution. We then demonstrate how this method can work even for high dimensional state by optimizing a foothold strategy of a full quadruped robot in simulation.

Developing control methods that allow legged robots to move with skill and agility remains one of the grand challenges in robotics. In order to achieve this ambitious goal, legged robots must possess a wide repertoire of motor skills. A scalable control architecture that can represent a variety of gaits in a unified manner is therefore desirable. Inspired by the motor learning principles observed in nature, we use an optimization approach to automatically discover and fine-tune parameters for agile gaits. The success of our approach is due to the controller parameterization we employ, which is compact yet flexible, therefore lending itself well to learning through repetition. We use our method to implement a flying trot, a bound and a pronking gait for StarlETH, a fully autonomous quadrupedal robot.

This paper describes a hierarchical operational space control (OSC) method based on least square optimization and outlines different ways to reduce the dimensionality of the optimization vector. The framework allows to emulate various behaviors by prioritized task-space motion, joint torque, and contact force optimization. Moreover, a methodology is introduced to partially excite the natural dynamics of the robot by open-loop motor regulation while the entire behavior is stabilized by hierarchical OSC. As a major contribution, the presented control strategies are tested and validated in real hardware walking, trotting, and pronking experiments using a fully torque controllable quadrupedal robot.

In this paper we present a method for fusing optical flow and inertial measurements. To this end, we derive a novel visual error term which is better suited than the standard continuous epipolar constraint for extracting the information contained in the optical flow measurements. By means of an unscented Kalman filter (UKF), this information is then tightly coupled with inertial measurements in order to estimate the egomotion of the sensor setup. The individual visual landmark positions are not part of the filter state anymore. Thus, the dimensionality of the state space is significantly reduced, allowing for a fast online implementation. A nonlinear observability analysis is provided and supports the proposed method from a theoretical side. The filter is evaluated on real data together with ground truth from a motion capture system.

This paper provides an overview about StarlETH: a compliant quadrupedal robot that is designed to study fast, efficient, versatile, and robust locomotion. The platform is driven by highly compliant series elastic actuation, which makes the system fully torque controllable, energetically efficient, and well suited for dynamic maneuvers. Using model-based control strategies, this medium dog-sized machine is capable of various gaits ranging from static walking to dynamic running over challenging terrain. StarlETH is equipped with an onboard PC, batteries, and various sensor equipment that enables enduring autonomous operation. In this paper, we provide an overview about the underlying locomotion control algorithms, outline a real-time control and simulation environment, and conclude the work with a number of experiments to demonstrate the performance of the presented hardware and controllers.

This paper introduces a novel batch optimization based calibration framework for legged robots. Given a non-degenerate calibration dataset and considering the stochastic models of the sensors, the task is formulated as a maximum likelihood problem. In order to facilitate the derivation of consistent measurement equations, the trajectory of the robot and other auxiliary variables are included into the optimization problem. This formulation can be transformed into a nonlinear least squares problem which can be readily solved. Applied to our legged robot StarIETH, the framework estimates kinematic parameters (segment lengths, body dimensions, angular offsets), accelerometer and gyroscope biases, as well as full inter-sensor calibrations. The generic structure easily allows the inclusion of additional sensor modalities. Based on datasets obtained on the real robot the consistency and performance of the presented approach are successfully evaluated.

Quadrupedal animals move through their environments with unmatched agility and grace. An important part of this is the ability to choose between different gaits in order to travel optimally at a certain speed or to robustly deal with unanticipated perturbations. In this paper, we present a control framework for a quadrupedal robot that is capable of locomoting using several gaits. We demonstrate the flexibility of the algorithm by performing experiments on StarlETH, a recently-developed quadrupedal robot. We implement controllers for a static walk, a walking trot, and a running trot, and show that smooth transitions between them can be performed. Using this control strategy, StarlETH is able to trot unassisted in 3D space with speeds of up to 0.7m/s, it can dynamically navigate over unperceived 5-cm high obstacles and it can recover from significant external pushes.

This paper addresses the problem of evaluating and estimating the mechanical robustness of footholds for legged robots in unstructured terrain. In contrast to approaches that rely on human expert knowledge or human defined criteria to identify appropriate footholds, our method uses the robot itself to assess whether a certain foothold is adequate or not. To this end, one of the robot's legs is employed to haptically explore an unknown foothold. The robustness of the foothold is defined by a simple metric as a function of the achievable ground reaction forces. This haptic feedback is associated with the foothold shape to estimate the robustness of untouched footholds. The underlying shape clustering principles are tested on synthetic data and in hardware experiments using a single-leg testbed.

This paper presents a state estimation approach for legged robots based on stochastic filtering. The key idea is to extract information from the kinematic constraints given through the intermittent contacts with the ground and to fuse this information with inertial measurements. To this end, we design an unscented Kalman filter based on a consistent formulation of the underlying stochastic model. To increase the robustness of the filter, an outliers rejection methodology is included into the update step. Furthermore, we present the nonlinear observability analysis of the system, where, by considering the special nature of 3D rotations, we obtain a relatively simple form of the corresponding observability matrix. This yields, that, except for the global position and the yaw angle, all states are in general observable. This also holds if only one foot is in contact with the ground. The presented filter is evaluated on a real quadruped robot trotting over an uneven and slippery terrain.

This paper presents the application of reinforcement learning to improve the performance of highly dynamic single legged locomotion with compliant series elastic actuators. The goal is to optimally exploit the capabilities of the hardware in terms of maximum jump height, jump distance, and energy efficiency of periodic hopping. These challenges are tackled with the reinforcement learning method Policy Improvement with Path Integrals (PI2) in a model-free approach to learn parameterized motor velocity trajectories as well as highlevel control parameters. The combination of simulation and hardware-based optimization allows to efficiently obtain optimal control policies in an up to 10-dimensional parameter space. The robotic leg learns to temporarily store energy in the elastic elements of the joints in order to improve the jump height and distance. In addition, we present a method to learn time-independent control policies and apply it to improve the energetic efficiency of periodic hopping.

This paper introduces the mechanical design and the control concept of the Series Compliant Articulated Robotic Leg ScarlETH which was developed at ETH Zurich for fast, efficient, and versatile locomotion. Inspired by biological systems, we seek to achieve this through large compliances in the joints which enable natural dynamics, allow temporary energy storage, and improve the passive adaptability. A sophisticated chain and cable pulley design minimizes the segment masses, places the overall CoG close to the hip joint, and maximizes the range of motion. Nonlinearities in the damping and an appropriate low-level controller allow for precise torque control during stance and for fast task space position control during swing. This paved the road for the combined application of a virtual model controller for ground contact and a modified Raibert style controller for flight phase which was successfully tested in planar running.

In this paper, we are presenting a method to estimate terrain properties (such as small-scale geometry or surface friction) to improve the assessment of stability and the guiding of foot placement of legged robots in rough terrain. Haptic feedback, expressed through joint motor currents and ground contact force measurements that arises when prescribing a predefined motion was collected for a variety of ground samples (four different shapes and four different surface properties). Features were extracted from this data and used for training and classification by a multiclass AdaBoost machine learning algorithm. In a single leg testbed, the algorithm could correctly classify about 94% of the terrain shapes, and about 73% of the surface samples.

In the present study, we applied the principles of passive dynamic walking onto the three dimensional motion of a simplified quadrupedal model. We extended the simulation framework of a planar system to include a rolling degree of freedom and searched for limit cycles that represent periodic gaits. Among the eight different gaits that we identified, were three kinds of trots and paces, as well as a lateral and diagonal single foot sequence. We could show that a distinct relation exists between the lateral spacing of the legs and the relative phase of the front and the back legs, and a certain trade-off between efficiency and dynamic stability. In agreement with established bipedal models, our results showed that the lateral rolling motion is invariably unstable.

SLIP models are generally known as one of the best and simplest abstractions describing the spring-like leg behavior found in human and animal running, and have thus been subject to exhaustive investigation. To exploit these findings in real robots, we utilize an operational space controller that projects the behavior of the SLIP model onto the dynamics of an actual segmented robotic leg. Additionally, we introduce a method to compensate for the energetic losses at the impact collisions, which are not accounted for in the simplified SLIP assumptions. This allows the direct application of existing dead-beat control strategies to arbitrary robotic legs, for which we can show that the collision and compensation effects in the actual leg enlarge the regions of stable running and reduce the minimally required locomotion speed. The necessary joint torque profiles can be generated in large part passively, for example by using high compliance series elastic actuators.

In the present study, we investigate a control strategy for hopping motions of an articulated leg that is driven by series elastic actuation. A highly compliant spring in the knee joint allows the exploitation of periodic energy storage but creates a major control challenge by severely limiting the bandwidth of closed-loop position or force control. This handicap is intensified by slow actuators, substantial delays, and the kinematic coupling of the articulated design. With classic closed-loop control strategies failing, an adaptive open-loop control algorithm is presented, that, over a series of jumps, estimates the compression of the actuator springs, and gradually modifies the motor inputs in order to minimize slipping and create a purely vertical motion.

Capitalizing on advances in CMOS and MEMS technologies, microrobots have the potential to dramatically change many aspects of medicine by navigating bodily fluids to perform targeted diagnosis and therapy. Onboard energy storage and actuation is very difficult at the microscale, but externally applied magnetic fields provide an unparalleled means of wireless power and control. Recent results have provided a model for accurate real-time control of soft-magnetic bodies with axially symmetric geometries. In this paper, we extend the model to consider the real-time control of assembled-MEMS devices that may have significantly more complex geometries. We validate the model through FEM and experiments. The model captures the characteristics of complex 3-D structures and allows us, for the first time, to consider full 6-DOF control of untethered devices, which can act asinvivomicrorobots or as end-effectors of micromanipulation systems.