Existing preference optimization methods often assume scenarios where paired preference feedback (preferred/positive vs. dis-preferred/negative examples) is available. This requirement limits their applicability in scenarios where only unpaired feedback—for example, either positive or negative— is available. To address this, we introduce a novel approach that decouples learning from positive and negative feedback. This decoupling enables control over the influence of each feedback type and, importantly, allows learning even when only one feedback type is present. A key contribution is demonstrating stable learning from negative feedback alone, a capability not well-addressed by current methods. Our approach builds upon the probabilistic framework introduced in (Dayan and Hinton, 1997), which uses expectation-maximization (EM) to directly optimize the probability of positive outcomes (as opposed to classic expected reward maximization). We address a key limitation in current EM-based methods: they solely maximize the likelihood of positive examples, while neglecting negative ones. We show how to extend EM algorithms to explicitly incorporate negative examples, leading to a theoretically grounded algorithm that offers an intuitive and versatile way to learn from both positive and negative feedback. We evaluate our approach for training language models based on human feedback as well as training policies for sequential decision-making problems, where learned value functions are available.

We show that offline actor-critic reinforcement learning can scale to large models - such as transformers - and follows similar scaling laws as supervised learning. We find that offline actor-critic algorithms can outperform strong, supervised, behavioral cloning baselines for multi-task training on a large dataset; containing both sub-optimal and expert behavior on 132 continuous control tasks. We introduce a Perceiver-based actor-critic model and elucidate the key features needed to make offline RL work with self- and cross-attention modules. Overall, we find that: i) simple offline actor critic algorithms are a natural choice for gradually moving away from the currently predominant paradigm of behavioral cloning, and ii) via offline RL it is possible to learn multi-task policies that master many domains simultaneously, including real robotics tasks, from sub-optimal demonstrations or self-generated data.

Reinforcement learning solely from an agent’s self-generated data is often believed to be infeasible for learning on real robots, due to the amount of data needed. However, if done right, agents learning from real data can be surprisingly efficient through re-using previously collected sub-optimal data. In this paper we demonstrate how the increased understanding of off-policy learning methods and their embedding in an iterative online/offline scheme ("collect and infer") can drastically improve data-efficiency by using all the collected experience, which empowers learning from real robot experience only. Moreover, the resulting policy improves significantly over the state of the art on a recently proposed real robot manipulation benchmark. Our approach learns end-to-end, directly from pixels, and does not rely on additional human domain knowledge such as a simulator or demonstrations.

The majority of language model training builds on imitation learning. It covers pretraining, supervised fine-tuning, and affects the starting conditions for reinforcement learning from human feedback (RLHF). The simplicity and scalability of maximum likelihood estimation (MLE) for next token prediction led to its role as predominant paradigm. However, the broader field of imitation learning can more effectively utilize the sequential structure underlying autoregressive generation. We focus on investigating the inverse reinforcement learning (IRL) perspective to imitation, extracting rewards and directly optimizing sequences instead of individual token likelihoods and evaluate its benefits for fine-tuning large language models. We provide a new angle, reformulating inverse soft-Q-learning as a temporal difference regularized extension of MLE. This creates a principled connection between MLE and IRL and allows trading off added complexity with increased performance and diversity of generations in the supervised fine-tuning (SFT) setting. We find clear advantages for IRL-based imitation, in particular for retaining diversity while maximizing task performance, rendering IRL a strong alternative on fixed SFT datasets even without online data generation. Our analysis of IRL-extracted reward functions further indicates benefits for more robust reward functions via tighter integration of supervised and preference-based LLM post-training.

Systems which incrementally create 3D semantic maps from image sequences must store and update representations of both geometry and semantic entities. However, while there has been much work on the correct formulation for geometrical estimation, state-of-the-art systems usually rely on simple semantic representations which store and update independent label estimates for each surface element (depth pixels, surfels, or voxels). Spatial correlation is discarded, and fused label maps are incoherent and noisy. We introduce a new compact and optimisable semantic representation by training a variational auto-encoder that is conditioned on a colour image. Using this learned latent space, we can tackle semantic label fusion by jointly optimising the low-dimenional codes associated with each of a set of overlapping images, producing consistent fused label maps which preserve spatial correlation. We also show how this approach can be used within a monocular keyframe based semantic mapping system where a similar code approach is used for geometry. The probabilistic formulation allows a flexible formulation where we can jointly estimate motion, geometry and semantics in a unified optimisation.

Estimating motion and surrounding geometry of a moving camera remains a challenging inference problem. From an information theoretic point of view, estimates should get better as more information is included, such as is done in dense SLAM, but this is strongly dependent on the validity of the underlying models. In the present paper, we use triangular meshes as both compact and dense geometry representation. To allow for simple and fast usage, we propose a view-based formulation for which we predict the in-plane vertex coordinates directly from images and then employ the remaining vertex depth components as free variables. Flexible and continuous integration of information is achieved through the use of a residual based inference technique. This so-called factor graph encodes all information as mapping from free variables to residuals, the squared sum of which is minimised during inference. We propose the use of different types of learnable residuals, which are trained end-to-end to increase their suitability as information bearing models and to enable accurate and reliable estimation. Detailed evaluation of all components is provided on both synthetic and real data which confirms the practicability of the presented approach.

Dense visual SLAM methods are able to estimate the 3D structure of an environment and locate the observer within them. They estimate the motion of a camera by matching visual information between consecutive frames, and are thus prone to failure under extreme motion conditions or when observing texture-poor regions. The integration of additional sensor modalities has shown great promise in improving the robustness and accuracy of such SLAM systems. In contrast to the popular use of inertial measurements we propose to tightly-couple a dense RGB-D SLAM system with kinematic and odometry measurements from a wheeled robot equipped with a manipulator. The system has real-time capability while running on GPU. It optimizes the camera pose by considering the geometric alignment of the map as well as kinematic and odometric data from the robot. Through experimentation in the real-world, we show that the system is more robust to challenging trajectories featuring fast and loopy motion than the equivalent system without the additional kinematic and odometric knowledge, whilst retaining comparable performance to the equivalent RGB-D only system on easy trajectories.

We propose a new multi-instance dynamic RGB-D SLAM system using an object-level octree-based volumetric representation. It can provide robust camera tracking in dynamic environments and at the same time, continuously estimate geometric, semantic, and motion properties for arbitrary objects in the scene. For each incoming frame, we perform instance segmentation to detect objects and refine mask boundaries using geometric and motion information. Meanwhile, we estimate the pose of each existing moving object using an object-oriented tracking method and robustly track the camera pose against the static scene. Based on the estimated camera pose and object poses, we associate segmented masks with existing models and incrementally fuse corresponding colour, depth, semantic, and foreground object probabilities into each object model. In contrast to existing approaches, our system is the first system to generate an object-level dynamic volumetric map from a single RGB-D camera, which can be used directly for robotic tasks. Our method can run at 2-3 Hz on a CPU, excluding the instance segmentation part. We demonstrate its effectiveness by quantitatively and qualitatively testing it on both synthetic and real-world sequences.

We propose an online object-level SLAM system which builds a persistent and accurate 3D graph map of arbitrary reconstructed objects. As an RGB-D camera browses a cluttered indoor scene, Mask-RCNN instance segmentations are used to initialise compact per-object Truncated Signed Distance Function (TSDF) reconstructions with object size-dependent resolutions and a novel 3D foreground mask. Reconstructed objects are stored in an optimisable 6DoF pose graph which is our only persistent map representation. Objects are incrementally refined via depth fusion, and are used for tracking, relocalisation and loop closure detection. Loop closures cause adjustments in the relative pose estimates of object instances, but no intra-object warping. Each object also carries semantic information which is refined over time and an existence probability to account for spurious instance predictions. We demonstrate our approach on a hand-held RGB-D sequence from a cluttered office scene with a large number and variety of object instances, highlighting how the system closes loops and makes good use of existing objects on repeated loops. We quantitatively evaluate the trajectory error of our system against a baseline approach on the RGB-D SLAM benchmark, and qualitatively compare reconstruction quality of discovered objects on the YCB video dataset. Performance evaluation shows our approach is highly memory efficient and runs online at 4-8Hz (excluding relocalisation) despite not being optimised at the software level.

The representation of geometry in real-time 3D perception systems continues to be a critical research issue. Dense maps capture complete surface shape and can be augmented with semantic labels, but their high dimensionality makes them computationally costly to store and process, and unsuitable for rigorous probabilistic inference. Sparse feature-based representations avoid these problems, but capture only partial scene information and are mainly useful for localisation only. We present a new compact but dense representation of scene geometry which is conditioned on the intensity data from a single image and generated from a code consisting of a small number of parameters. We are inspired by work both on learned depth from images, and auto-encoders. Our approach is suitable for use in a keyframe-based monocular dense SLAM system: While each keyframe with a code can produce a depth map, the code can be optimised efficiently jointly with pose variables and together with the codes of overlapping keyframes to attain global consistency. Conditioning the depth map on the image allows the code to only represent aspects of the local geometry which cannot directly be predicted from the image. We explain how to learn our code representation, and demonstrate its advantageous properties in monocular SLAM.

While dense visual SLAM methods are capable of estimating dense reconstructions of the environment, they suffer from a lack of robustness in their tracking step, especially when the optimisation is poorly initialised. Sparse visual SLAM systems have attained high levels of accuracy and robustness through the inclusion of inertial measurements in a tightly-coupled fusion. Inspired by this performance, we propose the first tightly-coupled dense RGB-D-inertial SLAM system. Our system has real-time capability while running on a GPU. It jointly optimises for the camera pose, velocity, IMU biases and gravity direction while building up a globally consistent, fully dense surfel-based 3D reconstruction of the environment. Through a series of experiments on both synthetic and real world datasets, we show that our dense visual-inertial SLAM system is more robust to fast motions and periods of low texture and low geometric variation than a related RGB-D-only SLAM system.

In this paper we present a new estimation algorithm that allows for the combination of information from any number of process and measurement models. This adds more flexibility to the design of the estimator and in our case avoids the need for state augmentation. We achieve this by adapting the maximum likelihood formulation of the Kalman Filter, and thereby represent all measurement models as residuals. Posing the problem in this form allows for the straightforward integration of any number of (nonlinear) constraints between two subsequent states. To solve the optimization we present a closed form recursive set of equations that directly marginalizes out information that is not required, this leads to an efficient and generic implementation. The new algorithm is applied to parameter estimation on MAVs which have two dynamic models, the MAV dynamic model and the IMU-driven model. We show the benefits and limitations of the new filtering approach on a simplified simulation example and on a real MAV system.

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.

Real-time dense mapping and pose estimation is essential for a wide range of navigation tasks in mobile robotic applications. We propose an odometry and mapping system that leverages the full photometric information from a stereo-vision system as well as inertial measurements in a probabilistic framework while running in real-time on a single low-power Intel CPU core. Instead of performing mapping and localization on a set of sparse image features, we use the complete dense image intensity information in our navigation system. By incorporating a probabilistic model of the stereo sensor and the IMU, we can robustly estimate the ego-motion as well as a dense 3D model of the environment in real-time. The probabilistic formulation of the joint odometry estimation and mapping process enables to efficiently reject temporal outliers in ego-motion estimation as well as spatial outliers in the mapping process. To underline the versatility of the proposed navigation system, we evaluate it in a set of experiments on a multi-rotor system as well as on a quadrupedal walking robot. We tightly integrate our framework into the stabilization-loop of the UAV and the mapping framework of the walking robot. It is shown that the dense framework exhibits good tracking and mapping performance in terms of accuracy as well as robustness in scenarios with highly dynamic motion patterns while retaining a relatively small computational footprint. This makes it an ideal candidate for control and navigation tasks in unstructured GPS-denied environments, for a wide range of robotic platforms with power and weight constraints. The proposed framework is released as an open-source ROS package.

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°.

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 introduces a framework for state estimation on a humanoid robot platform using only common proprioceptive sensors and knowledge of leg kinematics. The presented approach extends that detailed in prior work on a point-foot quadruped platform by adding the rotational constraints imposed by the humanoid's flat feet. As in previous work, the proposed Extended Kalman Filter accommodates contact switching and makes no assumptions about gait or terrain, making it applicable on any humanoid platform for use in any task. A nonlinear observability analysis is performed on both the point-foot and flat-foot filters and it is concluded that the addition of rotational constraints significantly simplifies singular cases and improves the observability characteristics of the system. Results on a simulated walking dataset demonstrate the performance gain of the flat-foot filter as well as confirm the results of the presented observability analysis.

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 presents a method for state estimation on a ballbot; i.e., a robot balancing on a single sphere. Within the framework of an extended Kalman filter and by utilizing a complete kinematic model of the robot, sensory information from different sources is combined and fused to obtain accurate estimates of the robot's attitude, velocity, and position. This information is to be used for state feedback control of the dynamically unstable system. Three incremental encoders (attached to the omniwheels that drive the ball of the robot) as well as three rate gyroscopes and accelerometers (attached to the robot's main body) are used as sensors. For the presented method, observability is proven analytically for all essential states in the system, and the algorithm is experimentally evaluated on the Ballbot Rezero.

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.

Within the research on Micro Aerial Vehicles (MAVs), the field on flight control and autonomous mission execution is one of the most active. A crucial point is the localization of the vehicle, which is especially difficult in unknown, GPS-denied environments. This paper presents a novel vision based approach, where the vehicle is localized using a downward looking monocular camera. A state-of-the-art visual SLAM algorithm tracks the pose of the camera, while, simultaneously, building an incremental map of the surrounding region. Based on this pose estimation a LQG/LTR based controller stabilizes the vehicle at a desired setpoint, making simple maneuvers possible like take-off, hovering, setpoint following or landing. Experimental data show that this approach efficiently controls a helicopter while navigating through an unknown and unstructured environment. To the best of our knowledge, this is the first work describing a micro aerial vehicle able to navigate through an unexplored environment (independently of any external aid like GPS or artificial beacons), which uses a single camera as only exteroceptive sensor.