Point cloud registration is a critical problem in computer vision and robotics, especially in the field of navigation. Current methods often fail when faced with high outlier rates or take a long time to converge to a suitable solution. In this work, we introduce a novel algorithm for point cloud registration called SANDRO11https://github.com/iit-DLSLab/SANDRO (Splitting strategy for point cloud Alignment using Non-convex anD Robust Optimization), which combines an Iteratively Reweighted Least Squares (IRLS) framework with a robust loss function with graduated non-convexity. This approach is further enhanced by a splitting strategy designed to handle high outlier rates and skewed distributions of outliers. SANDRO is capable of addressing important limitations of existing methods, as in challenging scenarios where the presence of high outlier rates and point cloud symmetries significantly hinder convergence. SANDRO achieves superior performance in terms of success rate when compared to the state-of-the-art methods, demonstrating a 20% improvement from the current state of the art when tested on the Redwood real dataset and 60% improvement when tested on synthetic data.

The capability of a quadruped robot to negotiate obstacles is tightly connected to its leg workspace and joint torque limits. When facing terrain where the height of obstacles is close to the leg length, the locomotion robustness and safety are reduced since more dynamic motions are required to traverse it. In this paper, we introduce a new mechanism called the Carpal-Claw, which enables quadruped robots to negotiate higher obstacles and adds safety to the locomotion by allowing the robot to negotiate obstacles under static and quasi-static locomotion and regular joint torque demands. The design of the mechanism is detailed, as well as the methodology to exploit the mechanism in the locomotion control framework. The Carpal-Claw functionality is validated through various experiments on a very high obstacle and stairs-like terrains using an Aliengo robot. We demonstrate how Aliengo can safely descend a step height of 40cm, which is 80% of its leg length. To the best knowledge of the authors, this is the first time a mechanism like the C-Claw is proposed for improving quadruped robot locomotion over high obstacles.

This paper presents a novel approach to enhance Model Predictive Control (MPC) for legged robots through Distributed Optimization. Our method focuses on decomposing the robot dynamics into smaller, parallelizable subsystems, and utilizing the Alternating Direction Method of Multipliers (ADMM) to ensure consensus among them. Each subsystem is managed by its own Optimal Control Problem, with ADMM facilitating consistency between their optimizations. This approach not only decreases the computational time but also allows for effective scaling with more complex robot configurations, facilitating the integration of additional subsystems such as articulated arms on a quadruped robot. We demonstrate, through numerical evaluations, the convergence of our approach on two systems with increasing complexity. In addition, we showcase that our approach converges towards the same solution when compared to a state-of-the-art centralized whole-body MPC implementation. Moreover, we quantitatively compare the computational efficiency of our method to the centralized approach, revealing up to a 75% reduction in computational time. Overall, our approach offers a promising avenue for accelerating MPC solutions for legged robots, paving the way for more effective utilization of the computational performance of modern hardware. Accompanying video at https://youtu.be/Yar4W-Vlh2A. The related code can be found at https://github.com/iit-DLSLab/DWMPC

Model-free reinforcement learning is a promising approach for autonomously solving challenging robotics control problems, but faces exploration difficulty without information about the robot’s morphology. The under-exploration of multiple modalities with symmetric states leads to behaviors that are often unnatural and sub-optimal. This issue becomes particularly pronounced in the context of robotic systems with morphological symmetries, such as legged robots for which the resulting asymmetric and aperiodic behaviors compromise performance, robustness, and transferability to real hardware. To mitigate this challenge, we can leverage symmetry to guide and improve the exploration in policy learning via equivariance / invariance constraints. We investigate the efficacy of two approaches to incorporate symmetry: modifying the network architectures to be strictly equivariant / invariant, and leveraging data augmentation to approximate equivariant / invariant actor-critics. We implement the methods on challenging loco-manipulation and bipedal locomotion tasks and compare with an unconstrained baseline. We find that the strictly equivariant policy consistently outperforms other methods in sample efficiency and task performance in simulation. Additionaly, symmetry-incorporated approaches exhibit better gait quality, higher robustness and can be deployed zero-shot to hardware.

Quadrupedal robots excel in mobility, navigating complex terrains with agility. However, their complex control systems present challenges that are still far from being fully addressed. In this paper, we introduce the use of Sample-Based Stochastic control strategies for quadrupedal robots, as an alternative to traditional optimal control laws. We show that Sample-Based Stochastic methods, supported by GPU acceleration, can be effectively applied to real quadruped robots. In particular, in this work, we focus on achieving gait frequency adaptation, a notable challenge in quadrupedal locomotion for gradient-based methods. To validate the effectiveness of Sample-Based Stochastic controllers we test two distinct approaches for quadrupedal robots and compare them against a conventional gradientbased Model Predictive Control system. Our findings, validated both in simulation and on a real 21Kg Aliengo quadruped, demonstrate that our method is on par with a traditional Model Predictive Control strategy when the robot is subject to zero or moderate disturbance, while it surpasses gradient-based methods in handling sustained external disturbances, thanks to the straightforward gait adaptation strategy that is possible to achieve within their formulation.

In this paper, we introduce the concept of using passive arm structures with intrinsic impedance for robot-robot and human-robot collaborative carrying with quadruped robots. The concept is meant for a leader-follower task and takes a minimalist approach that focuses on exploiting the robots’ payload capabilities and reducing energy consumption, without compromising the robot locomotion capabilities. We introduce a preliminary arm mechanical design and describe how to use its joint displacements to guide the robot’s motion. To control the robot’s locomotion, we propose a decentralized Model Predictive Controller that incorporates an approximation of the arm dynamics and the estimation of the external forces from the collaborative carrying. We validate the overall system experimentally by performing both robot-robot and human-robot collaborative carrying on a stair-like obstacle and on rough terrain.

We propose a control pipeline for SAG (Searching, Approaching, and Grasping) of objects, based on a decoupled arm kinematic chain and impedance control, which integrates image-based visual servoing (IBVS). The kinematic decoupling allows for fast end-effector motions and recovery that leads to robust visual servoing. The whole approach and pipeline can be generalized for any mobile platform (wheeled or tracked vehicles), but is most suitable for dynamically moving quadruped manipulators thanks to their reactivity against disturbances. The compliance of the impedance controller makes the robot safer for interactions with humans and the environment. We demonstrate the performance and robustness of the proposed approach with various experiments on our 140 kg HyQReal quadruped robot equipped with a 7-DoF manipulator arm. The experiments consider dynamic locomotion, tracking under external disturbances, and fast motions of the target object.

Legged robots are increasingly entering new domains and applications, including search and rescue, inspection, and logistics. However, for such a systems to be valuable in real-world scenarios, they must be able to autonomously and robustly navigate irregular terrains. In many cases, robots that are sold on the market do not provide such abilities, being able to perform only blind locomotion. Furthermore, their controller cannot be easily modified by the end-user, requiring a new and time-consuming control synthesis. In this work, we present a fast local motion planning pipeline that extends the capabilities of a black-box walking controller that is only able to track high-level reference velocities. More precisely, we learn a set of motion models for such a controller that maps high-level velocity commands to Center of Mass (CoM) and footstep motions. We then integrate these models with a variant of the$A$* algorithm to plan the CoM trajectory, footstep sequences, and corresponding high-level velocity commands based on visual information, allowing the quadruped to safely traverse irregular terrains at demand.

Developing feasible body trajectories for legged systems on arbitrary terrains is a challenging task. In this paper, we present a paradigm that allows to design feasible Center of Mass (CoM) and body trajectories in an efficient manner. In our previous work [1], we introduced the notion of the 2D feasible region, where static balance and the satisfaction of joint torque limits were guaranteed, whenever the projection of the CoM lied inside the proposed admissible region. In this work we propose a general formulation of the improved feasible region that guarantees dynamic balance alongside the satisfaction of both joint-torque and kinematic limits in an efficient manner. To incorporate the feasibility of the kinematic limits, we introduce an algorithm that computes the reachable region of the CoM. Furthermore, we propose an efficient planning strategy that utilizes the improved feasible region to design feasible CoM and body orientation trajectories. Finally, we validate the capabilities of the improved feasible region and the effectiveness of the proposed planning strategy, using simulations and experiments on the 90 kg Hydraulically actuated Quadruped (HyQ) and the 21 kg Aliengo robots.

This article focuses on vision-based planning strategies for legged robots that separate locomotion planning into foothold selection and pose adaptation. Current pose adaptation strategies optimize the robot's body pose relative togivenfootholds. If these footholds are not reached, the robot may end up in a state with no reachable safe footholds. Therefore, we present a vision-based terrain-aware locomotion (ViTAL) strategy that consists of novel pose adaptation and foothold selection algorithms. ViTAL introduces a different paradigm in pose adaptation that does not optimize the body pose relative to given footholds, but the body pose that maximizes the chances of the legs in reaching safe footholds. ViTAL plans footholds and poses based on skills that characterize the robot's capabilities and its terrain awareness. We use the 90-kg HyQ and 140-kg HyQReal quadruped robots to validate ViTAL and show that they are able to climb various obstacles, including stairs, gaps, and rough terrains, at different speeds and gaits. We compare ViTAL with a baseline strategy that selects the robot pose based on given selected footholds and show that ViTAL outperforms the baseline.

To traverse complex scenarios reliably a legged robot needs to move its base aided by the ground reaction forces, which can only be generated by the legs that are momentarily in contact with the ground. A proper selection of footholds is crucial for maintaining balance. In this paper, we propose a foothold evaluation criterion that considers the transition feasibility for both linear and angular dynamics to overcome complex scenarios. We devise convex and nonlinear formulations as a direct extension of [1] in a receding-horizon fashion to grant dynamic feasibility for future behaviours. The criterion is integrated with a Vision-based Foothold Adaptation (VFA) strategy that takes into account the robot kinematics, leg collisions and terrain morphology. We verify the validity of the selected footholds and the generated trajectories in simulation and experiments with the 90kg quadruped robot HyQ.

Quadrupedal manipulators require to be compliant when dealing with external forces during autonomous manipulation, tele-operation or physical human-robot interaction. This paper presents a whole-body controller that allows for the implementation of a Cartesian impedance control to coordinate tracking performance and desired compliance for the robot base and manipulator arm. The controller is formulated through an optimization problem using Quadratic Programming (QP) to impose a desired behavior for the system while satisfying friction cone constraints, unilateral force constraints, joint and torque limits. The presented strategy decouples the arm and the base of the platform, enforcing the behavior of a linear double-mass spring damper system, and allows to independently tune their inertia, stiffness and damping properties. The control architecture is validated through an extensive simulation study using the 90kg HyQ robot equipped with a 7-DoF manipulator arm. Simulation results show the impedance rendering performance when external forces are applied at the arm's end-effector. The paper presents results for full stance condition (all legs on the ground) and, for the first time, also shows how the impedance rendering is affected by the contact conditions during a dynamic gait.

Simplified models are useful to increase the computational efficiency of a motion planning algorithm, but their lack of accuracy have to be managed. We propose two feasibility constraints to be included in a Single Rigid Body Dynamics-based trajectory optimizer in order to obtain robust motions in challenging terrain. The first one finds an approximate relationship between joint-torque limits and admissible contact forces, without requiring the joint positions. The second one proposes a leg model to prevent leg collision with the environment. Such constraints have been included in a simplified nonlinear non-convex trajectory optimization problem. We demonstrate the feasibility of the resulting motion plans both in simulation and on the Hydraulically actuated Quadruped (HyQ) robot, considering experiments on an irregular terrain.

Advances in legged robotics are strongly rooted in animal observations. A clear illustration of this claim is the generalization of Central Pattern Generators (CPG), first identified in the cat spinal cord, to generate cyclic motion in robotic locomotion. Despite a global endorsement of this model, physiological and functional experiments in mammals have also indicated the presence of descending signals from the cerebellum, and reflex feedback from the lower limb sensory cells, that closely interact with CPGs. To this day, these interactions are not fully understood. In some studies, it was demonstrated that pure reflex-based locomotion in the absence of oscillatory signals could be achieved in realistic musculoskeletal simulation models or small compliant quadruped robots. At the same time, biological evidence has attested the functional role of the cerebellum for predictive control of balance and stance within mammals. In this paper, we promote both approaches and successfully apply reflex-based dynamic locomotion, coupled with a balance and gravity compensation mechanism, on the state-of-art HyQ robot. We discuss the importance of this stability module to ensure a correct foot lift-off and maintain a reliable gait. The robotic platform is further used to test two different architectural hypotheses inspired by the cerebellum. An analysis of experimental results demonstrates that the most biologically plausible alternative also leads to better results for robust locomotion.

We present a novel control strategy for dynamic legged locomotion in complex scenarios that considers information about the morphology of the terrain in contexts when only on-board mapping and computation are available. The strategy is built on top of two main elements: first a contact sequence task that provides safe foothold locations based on a convolutional neural network to perform fast and continuous evaluation of the terrain in search of safe foothold locations; then a model predictive controller that considers the foothold locations given by the contact sequence task to optimize target ground reaction forces. We assess the performance of our strategy through simulations of the hydraulically actuated quadruped robot HyQReal traversing rough terrain under realistic on-board sensing and computing conditions.

Estimation of a quadruped's state is fundamentally important to its operation. In this paper we develop a low-level state estimator for quadrupedal robots that includes attitude, odometry, ground reaction forces, and contact detection. The state estimator is divided into three parts. First, a nonlinear observer estimates attitude by fusing inertial measurements. The attitude estimator is globally exponentially stable and is able to initialize with large errors in the initial state estimates whereas a state-of-the-art EKF would diverge. This is practical for situations when the robot has fallen over and needs to start from its side. Second, leg odometry is calculated with encoders, force sensors, and torque sensors in the robot's joints. Lastly, the leg odometry and inertial measurements are fused to obtain linear position and velocity. We experimentally validate the state estimator using a novel dataset from the HyQ robot. For the entirety of the experiment the estimated attitude matched the ground truth data and had a root mean square error (RMSE) of [2 1 5] deg, the velocity estimates has a RMSE of [0.11 0.15 0.04] m/s, and the position estimates, which are unobservable, drifted on average [2 1 8] mm/s.

The ability of legged systems to traverse highly- constrained environments depends by and large on the performance of their motion and balance controllers. This paper presents a controller that excels in a scenario that most state- of-the-art balance controllers have not yet addressed: line walking, or walking on nearly null support regions. Our approach uses a low-dimensional virtual model (2-DoF) to generate balancing actions through a previously derived four- term balance controller and transforms them to the robot through a derived kinematic mapping. The capabilities of this controller are tested in simulation, where we show the 90kg quadruped robot HyQ crossing a bridge of only 6 cm width (compared to its 4 cm diameter spherical foot), by balancing on two feet at any time while moving along a line. Additional simulations are carried to test the performance of the controller and the effect of external disturbances. Lastly, we present our preliminary experimental results showing HyQ balancing on two legs while being disturbed.

Whole-Body Control (WBC) has emerged as an important framework in locomotion control for legged robots. However, most WBC frameworks fail to generalize beyond rigid terrains. Legged locomotion over soft terrain is difficult due to the presence of unmodeled contact dynamics that WBCs do not account for. This introduces uncertainty in locomotion and affects the stability and performance of the system. In this article, we propose a novel soft terrain adaptation algorithm called STANCE: Soft Terrain Adaptation and Compliance Estimation. STANCE consists of a WBC that exploits the knowledge of the terrain to generate an optimal solution that is contact consistent and an online terrain compliance estimator that provides the WBC with terrain knowledge. We validated STANCE both in simulation and experiment on the Hydraulically actuated Quadruped (HyQ) robot, and we compared it against the state-of-the-art WBC. We demonstrated the capabilities of STANCE with multiple terrains of different compliances, aggressive maneuvers, different forward velocities, and external disturbances. STANCE allowed HyQ to adapt online to terrains with different compliances (rigid and soft) without pretuning. HyQ was able to successfully deal with the transition between different terrains and showed the ability to differentiate between compliances under each foot.

Planning whole-body motions while taking into account the terrain conditions is a challenging problem for legged robots since the terrain model might produce many local minima. Our coupled planning method uses stochastic and derivatives-free search to plan both foothold locations and horizontal motions due to the local minima produced by the terrain model. It jointly optimizes body motion, step duration and foothold selection, and it models the terrain as a cost-map. Due to the novel attitude planning method, the horizontal motion plans can be applied to various terrain conditions. The attitude planner ensures the robot stability by imposing limits to the angular acceleration. Our whole-body controller tracks compliantly trunk motions while avoiding slippage, as well as kinematic and torque limits. Despite the use of a simplified model, which is restricted to flat terrain, our approach shows remarkable capability to deal with a wide range of noncoplanar terrains. The results are validated by experimental trials and comparative evaluations in a series of terrains of progressively increasing complexity.

In legged locomotion, the projection of the robot's Center of Mass (CoM) being inside the convex hull of the contact points is a commonly accepted sufficient condition to achieve static balancing. However, some of these configurations cannot be realized because the joint-torques required to sustain them would be above their limits (actuation limits). In this article, we rule out such configurations and define the feasible region, a revisited support region that guarantees both global static stability in the sense of tip-over and slippage avoidance and of existence of a set of joint-torques that are able to sustain the robot's body weight. We show that the feasible region can be employed for the online selection of feasible footholds and CoM trajectories to achieve statically stable locomotion on rough terrains, also in presence of load-intensive tasks. Key results of our approach include the efficiency in the computation of the feasible region using an Iterative Projection (IP) algorithm and the successful execution of hardware experiments on the HyQ robot, that was able to negotiate obstacles of moderate dimensions while carrying an extra 10-kg payload.

We present a trajectory optimization framework for legged locomotion on rough terrain. We jointly optimize the center of mass motion and the foothold locations, while considering terrain conditions. We use a terrain costmap to quantify the desirability of a foothold location. We increase the gait's adaptability to the terrain by optimizing the step phase duration and modulating the trunk attitude, resulting in motions with guaranteed stability. We show that the combination of parametric models, stochastic-based exploration and receding horizon planning allows us to handle the many local minima associated with different terrain conditions and walking patterns. This combination delivers robust motion plans without the need for warm-starting. Moreover, we use soft-constraints to allow for increased flexibility when searching in the cost landscape of our problem. We showcase the performance of our trajectory optimization framework on multiple terrain conditions and validate our method in realistic simulation scenarios and experimental trials on a hydraulic, torque controlled quadruped robot.

Autonomous legged robots will be required to handle a wide range of tasks in complex environments. While a lot of research has focused on developing their abilities for periodic locomotion tasks, less effort has been invested in devising generalized strategies for dynamic, non-periodic movements. Motion design approaches are frequently enlisted in the form of teleoperation or predefined heuristics in such scenarios. We employ a realistic simulation of the hydraulically actuated HyQ2Max quadrupedal system for investigations on two distinctive tasks: rearing and posture recovery. We present a whole-body optimization methodology for non-periodic tasks on quadrupedal systems. This approach delivers solutions involving multiple contacts without the need for predefined feet placements. The results obtained show the potential of optimization approaches for motion synthesis in the context of complex tasks.

We propose a reactive locomotion strategy, called height reflex, that is useful to address big elevation changes in the terrain (e.g. when a quadruped robot has to step down from a high platform). In these cases the swing leg can lose mobility creating issues in the subsequent steps. The height reflex is a foot trajectory replanning strategy that redistributes the swing motion (in a smart way) to the stance legs to “lower” the whole trunk and to aid the foothold searching motion. To spread the motion we exploit a massless link model of the robot with virtual dampers at the joints, which is used to replan the feet trajectories. The proposed approach is able to incorporate kinematic limits, it is easy-to-tune, computationally efficient and suitable for real-time implementations. The reflex is implemented and experimentally evaluated on the 80 kg hydraulic quadruped HyQ. With our approach we were able to address high steps, up to 24 cm which is 30% of HyQ leg length and 53% of its retractable leg range.

The identification of inertial parameters is crucial to achieve high-performance model-based control of legged robots. The inertial parameters of the legs are typically not altered during expeditions and therefore are best identified offline. On the other hand, the trunk parameters depend on the modules mounted on the robot, like a motor to provide the hydraulic power, or different sets of cameras for perception. This motivates the use of recursive approaches to identify online mass and the position of the Center of Mass (CoM) of the robot trunk, when a payload change occurs. We propose two such approaches and analyze their robustness in simulation. Furthermore, experimental trials on our 80-kg quadruped robot HyQ show the applicability of our strategies during locomotion to cope with large payload changes that would otherwise severely compromise the balance of the robot.

Most animal and human locomotion behaviors for solving complex tasks involve dynamic motions and rich contact interaction. In fact, complex maneuvers need to consider dynamic movement and contact events at the same time. We present a hierarchical trajectory optimization approach for planning dynamic movements with unscheduled contact sequences. We compute whole-body motions that achieve goals that cannot be reached in a kinematic fashion. First, we find a feasible CoM motion according to the centroidal dynamics of the robot. Then, we refine the solution by applying the robot's full-dynamics model, where the feasible CoM trajectory is used as a warm-start point. To accomplish the unscheduled contact behavior, we use complementarity constraints to describe the contact model, i.e. environment geometry and non-sliding active contacts. Both optimization phases are posed as Mathematical Program with Complementarity Constraints (MPCC). Experimental trials demonstrate the performance of our planning approach in a set of challenging tasks.

A common disadvantage of multi-legged robots is that they often lack the manipulation capability. To overcome this limitation, an arm can be added to the body of the multi-legged robot, to perform manipulation tasks and provide assistance for locomotion. First, we proposed an attachment configuration of the arm for a multi-legged robot that provide a uniform workspace in front, below and above the base robot trunk. Second, an integrated control framework promises to keep the mobility and the balance of the mobile platform and provides precise manipulation capability of the arm incorporating a payload estimation scheme. Finally, we verify an integrated control framework with experimental results of a static and walking mobile platform while moving the arm.

We present a framework for dynamic quadrupedal locomotion over challenging terrain, where the choice of appropriate footholds is crucial for the success of the behaviour. We build a model of the environment on-line and on-board using an efficient occupancy grid representation. We use Any-time-Repairing A* (ARA*) to search over a tree of possible actions, choose a rough body path and select the locally-best footholds accordingly. We run a n-step lookahead optimization of the body trajectory using a dynamic stability metric, the Zero Moment Point (ZMP), that generates natural dynamic whole-body motions. A combination of floating-base inverse dynamics and virtual model control accurately executes the desired motions on an actively compliant system. Experimental trials show that this framework allows us to traverse terrains at nearly 6 times the speed of our previous work, evaluated over the same set of trials.

Agile robot locomotion on rough terrain is highly dependent on the ability to perceive the environment. In this paper, we show how the interaction between a reactive control framework and an online mapping system can significantly improve the trotting performance on irregular terrain. In particular, this new locomotion controller increases the stability of the robot and reduces frontal leg and shin collisions with obstacles by correcting in realtime the foothold locations. The mapping system uses an RGB-D sensor and a motion capture system to build a three dimensional map of the surroundings of the robot. While the robot is trotting, the control framework requests in advance a local heightmap around the next nominal foothold position. Then, an optimized foot placement location is estimated by applying visual pattern classification on the acquired heightmaps, and the leg endpoint trajectory is modified accordingly. The foothold correction is performed independently for each leg. To show the effectiveness of our approach the controller was tested both in simulation and experimentally with our 80 kg hydraulic quadruped robot, HyQ. The results show that visual based reaction through pattern classification is a promising approach to increase locomotion robustness over challenging terrain.

Increasingly, robots are designed to interact with the environment, including humans and tools. Legged robots, in particular, have to deal with environmental contacts every time they take a step. To handle these interactions properly, it is desirable to be able to set the robot's dynamic behavior, i.e., its impedance. In this contribution, we investigate the most relevant theoretical and practical aspects in impedance control using hydraulic actuators, ranging from the force dynamics analysis and model-based controller design to the overall stability and performance assessment. We present results with one leg of the quadruped robot HyQ and also highlight the influence of hardware parameters, such as valve bandwidth and inertia, in the impedance and force tracking. In addition, we demonstrate the capabilities of HyQ's actively compliant leg by experimentally comparing it with a passively compliant version of the same leg. With such a broad spectrum of analyses and discussions, this paper aims to serve as a practical and comprehensive guide for implementing high-performance impedance control on highly dynamic hydraulic robots.

We present a framework for quadrupedal locomotion over highly challenging terrain where the choice of appropriate footholds is crucial for the success of the behaviour. We use a path planning approach which shares many similarities with the results of the DARPA Learning Locomotion challenge and extend it to allow more flexibility and increased robustness. During execution we incorporate an on-line force-based foothold adaptation mechanism that updates the planned motion according to the perceived state of the environment. This way we exploit the active compliance of our system to smoothly interact with the environment, even when this is inaccurately perceived or dynamically changing, and update the planned path on-the-fly. In tandem we use a virtual model controller that provides the feed-forward torques that allow increased accuracy together with highly compliant behaviour on an otherwise naturally very stiff robotic system. We leverage the full set of benefits that a high performance torque controlled quadruped robot can provide and demonstrate the flexibility and robustness of our approach on a set of experimental trials of increasing difficulty.

We propose a reactive controller framework for robust quadrupedal locomotion, designed to cope with terrain irregularities, trajectory tracking errors and poor state estimation. The framework comprises two main modules: One related to the generation of elliptic trajectories for the feet and the other for control of the stability of the whole robot. We propose a task space CPG-based trajectory generation that can be modulated according to terrain irregularities and the posture of the robot trunk. To improve the robot's stability, we implemented a null space based attitude control for the trunk and a push recovery algorithm based on the concept of capture points. Simulations and experimental results on the hydraulically actuated quadruped robot HyQ will be presented to demonstrate the effectiveness of our framework.

A legged robot has to deal with environmental contacts every time it takes a step. To properly handle these interactions, it is desirable to be able to set the foot compliance. For an actively-compliant legged robot, in order to ensure a stable contact with the environment the robot leg has to be passive at the contact point. In this work, we asses some passivity and stability issues of the actively-compliant leg of the quadruped robot HyQ, which employs a highperformance cascade compliance controller. We demonstrate that both the nested torque loop performance as well as the actuator bandwidth have a strong influence in the range of virtual impedances that can be passively rendered by the robot leg. Based on the stability analyses and experimental results, we propose a procedure for designing cascade compliance controllers. Furthermore, we experimentally demonstrate that the HyQ's actively-compliant leg is able to reproduce the compliant behavior presented by an identical but passively-compliant version of the same leg.

This paper presents a framework developed to increase the autonomy and versatility of a large (~75kg) hydraulically actuated quadrupedal robot. It combines onboard perception with two locomotion strategies, a dynamic trot and a static crawl gait. This way the robot can perceive its environment and arbitrate between the two behaviours according to the situation at hand. All computations are performed on-board and are carried out in two separate computers, one handles the high-level processes while the other is concerned with the low-level hard real-time control. The perception and subsequently the appropriate gait modifications are performed autonomously. We present outdoor experimental trials of the robot trotting over unknown terrain, perceiving a large obstacle, altering its behaviour to the cautious crawl gait and stepping onto the obstacle. This allows the robot to locomote quickly on relatively flat terrain and gives the robot the ability to overcome large irregular obstacles when required.

This paper presents a trajectory generator and an active compliance control scheme, unified in a framework to synthesize dynamic, feasible and compliant trot-walking locomotion cycles for a stiff-by-nature hydraulically actuated quadruped robot. At the outset, a CoP-based trajectory generator that is constructed using an analytical solution is implemented to obtain feasible and dynamically balanced motion references in a systematic manner. Initial conditions are uniquely determined for symmetrical motion patterns, enforcing that trajectories are seamlessly connected both in position, velocity and acceleration levels, regardless of the given support phase. The active compliance controller, used simultaneously, is responsible for sufficient joint position/force regulation. An admittance block is utilized to compute joint displacements that correspond to joint force errors. In addition to position feedback, these joint displacements are inserted to the position control loop as a secondary feedback term. In doing so, active compliance control is achieved, while the position/force trade-off is modulated via the virtual admittance parameters. Various trot-walking experiments are conducted with the proposed framework using HyQ, a ~ 75kg hydraulically actuated quadruped robot. We present results of repetitive, continuous, and dynamically equilibrated trot-walking locomotion cycles, both on level surface and uneven surface walking experiments.

Legged robots have the potential to serve as versatile and useful autonomous robotic platforms for use in unstructured environments such as disaster sites. They need to be both capable of fast dynamic locomotion and precise movements. However, there is a lack of platforms with suitable mechanical properties and adequate controllers to advance the research in this direction. In this paper we are presenting results on the novel research platform HyQ, a torque controlled hydraulic quadruped robot. We identify the requirements for versatile robotic legged locomotion and show that HyQ is fulfilling most of these specifications. We show that HyQ is able to do both static and dynamic movements and is able to cope with the mechanical requirements of dynamic movements and locomotion, such as jumping and trotting. The required control, both on hydraulic level (force/torque control) and whole body level (rigid model based control) is discussed.

Robots are frequently modeled as rigid body systems, having torques as input to their dynamics. A high-performance low-level torque source allows us to control the robot/environment interaction and to straightforwardly take advantage of many model-based control techniques. In this paper, we define a general 1-DOF framework, using basic physical principles, to show that there exists an intrinsic velocity feedback in the generalized force dynamics, independently of the actuation technology. We illustrate this phenomena using three different systems: a generic spring-mass system, a hydraulic actuator, and an electric motor. This analogy helps to clarify important common aspects regarding torque/force control that can be useful when designing and controlling a robot. We demonstrate, using simulations and experimental data, that it is possible to compensate for the load motion influence and to increase the torque tracking capabilities.

This paper is focussed on the modelling and control of a hydraulically-driven biologically-inspired robotic leg. The study is part of a larger project aiming at the development of an autonomous quadruped robot (hyQ) for outdoor operations. The leg has two hydraulically-actuated degrees of freedom (DOF), the hip and knee joints. The actuation system is composed of proportional valves and asymmetric cylinders. After a brief description of the prototype leg, the paper shows the development of a comprehensive model of the leg where critical parameters have been experimentally identified. Subsequently the leg control design is presented. The core of this work is the experimental assessment of the pros and cons of single-input single-output (SISO) vs. multiple-input multiple-output (MIMO) and linear vs. nonlinear control algorithms in this application (the leg is a coupled multivariable system driven by nonlinear actuators). The control schemes developed are a conventional PID (linear SISO), a Linear Quadratic Regulator (LQR) controller (linear MIMO) and a Feedback Linearisation (FL) controller (nonlinear MIMO). LQR performs well at low frequency but its behaviour worsens at higher frequencies. FL produces the fastest response in simulation, but when implemented is sensitive to parameters uncertainty and needs to be properly modified to achieve equally good performance also in the practical implementation.

This paper deals with a comparative study on using water and air as actuation means for the control of a fluidic muscle (designed for air) and assesses the performance, particularly from a dynamic and energetic point of view. A medium with higher bulk modulus such as oil/water is believed to increase pressure and force bandwidths and reduce sensitivity to load variations, as is the case with conventional hydraulic stiff actuation systems. However in this application the inherent flexibility of the muscle plays a major role. Water has been chosen because of its non-flammability, environmental friendliness and the low solubility of air in it. The operating pressure range of the pneumatic muscle is 0-6 bar (typical range of a pneumatic system) that is well below typical operating pressures of hydraulic systems (typically over 100 bar). At such low pressures the dynamic behaviour of water is less predictable because of the higher likelihood of entrapped air in the water which physically occurs when operating at low pressures. This can majorly affect water bulk modulus and hence its dynamic performance. Therefore, the behaviour of the system in this unconventional pressure range for a liquid must be more thoroughly investigated. Theoretical and experimental analyses on a dedicated test rig have been carried out to assess these assumptions.

This paper is concerned with the application of switching technology to hydraulic actuation. Over the last 50 years with advances in power electronics, faster and faster static switches have been developed and applied to the control of motors. Hydraulic technology evolved in the opposite direction: switching control was not considered, and more and more accurate proportional flow/pressure control devices (servovalves etc) were developed. However despite the sophistication of such valves, from an energetic viewpoint proportional control is dissipative and inefficient. Indeed, by analogy it can be seen as the equivalent of resistive (rheostatic) motor control. In robotic applications where high power density, ruggedness and reliability are key requirements hydraulic actuation can be a sensible choice. However, the low efficiency of proportional control can be a limitation and it is necessary to go beyond the paradigm of proportional flow/pressure control. One response to this challenge is to revisit traditional on-off hydraulic technology and develop "power hydraulic" devices that behave in analogous manner to their power electronic counterparts. "Power hydraulics" is a challenging and little explored technology due to the markedly non-linear behaviour of hydraulic systems and the need of components with dynamic specifications that are not readily available off-the-shelf. After an analysis of the real on-off characteristics of a valve, a prototype hydraulic switching converter, inspired by the electric DC-DC Buck converter, is presented and its performance in pressure control mode, relative to a classical proportional valve-controlled system, are assessed. An energy saving of 75% is achieved. Merits and limitations of the current design are identified.

This paper focuses on the design and experimental evaluation of a hydraulically actuated robot leg. The evaluation of the leg prototype is an important milestone in the development of HyQ, a Hydraulically actuated Quadruped robot. The prototype features two rotary joints actuated by hydraulic cylinders and has a mass of 4.5kg. We performed several experiments with the leg prototype attached to a vertical slider to tests the robustness of the mechanical design and the hydraulic actuation system. Besides the experimental evaluation of the hydraulic components, we also extensively studied the sensor data of the leg during periodic hopping. The results show that hydraulic actuation is suitable for legged robots because of its high power-to-weight ratio, fast response and ability to cope with high impact force peaks. Furthermore, we compare the cylinder force data obtained by the load cell with the calculated value based on the cylinder pressures to analyze if it is possible to eliminate this sensory system redundancy in the future. Through these studies, weaknesses of the design were identified and suggestions on how to improve them are presented.

Hydraulic actuators are characterized by fast dynamics, high power density, high stiffness, large output force/torque, and in recent years are becoming increasingly attractive in the field of robotics. This paper presents the study of a 3-way proportional valve controlled, spring assisted electro-hydraulic rotary actuator, which consists of a 3-way proportional valve, a linear cylinder and a reciprocal spring. The operating principle is presented and a mathematical model is developed. Comparison analysis is made between the new actuator and a traditional one with an application to a hydraulically actuated legged robot.

The MACCEPA (Mechanically Adjustable Compliance and Controllable Equilibrium Position Actuator) is an electric actuator of which the compliance and equilibrium position are fully independently controllable and both are set by a dedicated servomotor. In this paper an improvement of the actuator is proposed where the torque-angle curve and consequently the stiffness-angle curve can be modified by choosing an appropriate shape of a profile disk, which replaces the lever arm of the former design. The actuator has a large joint angle, torque and stiffness range and these properties can be made beneficial for safe human robot interaction and the construction of energy efficient walking, hopping and running robots. The ability to store and release energy is shown by simulations on a 1DOF hopping robot. Its hopping height is much higher compared to a configuration in which the same motor is used in a traditional stiff setup. The stiffness of the actuator has a stiffening characteristic so the leg stiffness resembles more a linear stiffness as found in humans.

The performance of highly dynamic robotic machines is directly associated with both the actuation means and the specific mechanical properties/configuration of the system. Hydraulic actuation demonstrates significant competitive advantages when minimum weight and volume, large forces and wide range of speeds are required and this makes it very suitable for systems such as legged robots. The geometry and design of leg mechanisms have great effect on the actuation system performance such as the required flow, which directly determines the size/weight and power density, in turn affecting the performance of the robot. This paper describes the mechanism and operation principle of two 2-DOF legs considered for HyQ, a hydraulically actuated quadruped robot. Numerical studies have been done to investigate the required flow, the pressure in the actuator chambers and the efficiency of the two leg mechanisms. The results show that the second leg design reduces the required flow significantly with less pressure-jump in the actuator and higher efficiency.