Legged locomotion over various terrains is challenging and requires precise perception of the robot and its surroundings from both proprioception and vision. However, learning directly from high-dimensional visual input is often data-inefficient and intricate. To address this issue, traditional methods attempt to learn a teacher policy with access to privileged information first and then learn a student policy to imitate the teacher's behavior with visual input. Despite some progress, this imitation framework prevents the student policy from achieving optimal performance due to the information gap between inputs. Furthermore, the learning process is unnatural since animals intuitively learn to traverse different terrains based on their understanding of the world without privileged knowledge. Inspired by this natural ability, we propose a simple yet effective method, World Model-based Perception (WMP), which builds a world model of the environment and learns a policy based on the world model. We illustrate that though completely trained in simulation, the world model can make accurate predictions of real-world trajectories, thus providing informative signals for the policy controller. Extensive simulated and real-world experiments demonstrate that WMP outperforms state-of-the-art baselines in traversability and robustness. Videos and Code are available at: https://wmp-loco.github.io/.
California Institute of Technology（加州理工学院）；ETH Zurich（苏黎世联邦理工学院）
Terrain-aware locomotion has become an emerging topic in legged robotics. However, it is hard to generate diverse, challenging, and realistic unstructured terrains in simulation, which limits the way researchers evaluate their locomotion policies. In this paper, we prototype the generation of a terrain dataset via terrain authoring and active learning, and the learned samplers can stably generate diverse high-quality terrains. We expect the generated dataset to make a terrain-robustness benchmark for legged locomotion. The dataset, the code implementation, and some policy evaluations are relea…
As both legged robots and embedded compute have become more capable, researchers have started to focus on field deployment of these robots. Robust autonomy in unstructured environments requires perception of the world around the robot in order to avoid hazards. However, incorporating perception online while maintaining agile motion is more challenging for legged robots than other mobile robots due to the complex planners and controllers required to handle the dynamics of locomotion. This report will compare three recent approaches for perceptive locomotion and discuss the different ways in whi…
In this paper, we study the regulation of the Ground Contact Forces (GRF) in thruster-assisted legged locomotion. We will employ Reference Governors (RGs) for enforcing GRF constraints in Harpy model which is a bipedal robot that is being developed at Northeastern University. Optimization-based methods and whole body control are widely used for enforcing the no-slip constraints in legged locomotion which can be very computationally expensive. In contrast, RGs can enforce these constraints by manipulating joint reference trajectories using Lyapunov stability arguments which can be computed much…
Deep reinforcement learning produces robust locomotion policies for legged robots over challenging terrains. To date, few studies have leveraged model-based methods to combine these locomotion skills with the precise control of manipulators. Here, we incorporate external dynamics plans into learning-based locomotion policies for mobile manipulation. We train the base policy by applying a random wrench sequence on the robot base in simulation and adding the noisified wrench sequence prediction to the policy observations. The policy then learns to counteract the partially-known future disturbanc…
Locomotion over soft terrain remains a challenging problem for legged robots. Most of the work done on state estimation for legged robots is designed for rigid contacts, and does not take into account the physical parameters of the terrain. That said, this letter answers the following questions: how and why does soft terrain affect state estimation for legged robots? To do so, we utilized a state estimator that fuses IMU measurements with leg odometry that is designed with rigid contact assumptions. We experimentally validated the state estimator with the HyQ robot trotting over both soft and …
Oxford Robotics Institute, University of Oxford（牛津大学牛津机器人研究所）
We present a unified model-based and data-driven approach for quadrupedal planning and control to achieve dynamic locomotion over uneven terrain. We utilize on-board proprioceptive and exteroceptive feedback to map sensory information and desired base velocity commands into footstep plans using a reinforcement learning (RL) policy. This RL policy is trained in simulation over a wide range of procedurally generated terrains. When ran online, the system tracks the generated footstep plans using a model-based motion controller. We evaluate the robustness of our method over a wide variety of compl…
Dynamic Quadrupedal Legged and Aerial Locomotion via Structure Repurposing
Department of Electrical and Computer Engineering, Northeastern University（电气与计算机工程系，东北大学）；Department of Aerospace Engineering, California Institute of Technology（航空航天工程系，加州理工学院）
Optimal control is a successful approach to generate motions for complex robots, in particular for legged locomotion. However, these techniques are often too slow to run in real time for model predictive control or one needs to drastically simplify the dynamics model. In this work, we present a method to learn to predict the gradient and hessian of the problem value function, enabling fast resolution of the predictive control problem with a one-step quadratic program. In addition, our method is able to satisfy constraints like friction cones and unilateral constraints, which are important for …
A Foot Resistive Force Model for Legged Locomotion on Muddy Terrains
Department of Mechanical and Aerospace Engineering, Rutgers University（罗格斯大学机械与航空航天工程系）；Department of Electrical and Biomedical Engineering, University of Nevada（内华达大学电气与生物医学工程系）
California Institute of Technology（加州理工学院）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Northeastern University（东北大学）
There have been several successful implementations of bio-inspired legged robots that can trot, walk, and hop robustly even in the presence of significant unplanned disturbances. Despite all of these accomplishments, practical control and high-level decision-making algorithms in multi-modal legged systems are overlooked. In nature, animals such as birds impressively showcase multiple modes of mobility including legged and aerial locomotion. They are capable of performing robust locomotion over large walls, tight spaces, and can recover from unpredictable situations such as sudden gusts or slip…
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；NVIDIA Research（英伟达研究）；Princeton University（普林斯顿大学）；Department of Mechanical Engineering, University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校机械工程系）
Legged robot locomotion on a dynamic rigid surface (i.e., a rigid surface moving in the inertial frame) involves complex full-order dynamics that is high-dimensional, nonlinear, and time-varying. Towards deriving an analytically tractable dynamic model, this study theoretically extends the reduced-order linear inverted pendulum (LIP) model from legged locomotion on a stationary surface to locomotion on a dynamic rigid surface (DRS). The resulting model is herein termed as DRS-LIP. Furthermore, this study introduces an approximate analytical solution of the proposed DRS-LIP that is computationa…
X2-N: A Transformable Wheel-legged Humanoid Robot with Dual-mode Locomotion and Manipulation
Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology（香港理工大学电子与计算机工程系）；X-lab Department, Agibot Innovation Company（阿吉博创新公司X实验室）
NVIDIA（英伟达）；Univ. of British Columbia（不列颠哥伦比亚大学）；Univ. of Washington（华盛顿大学）；Caltech（加州理工学院）；UT Austin（德克萨斯大学奥斯汀分校）；Univ. of Toronto（多伦多大学）；Vector Institute（向量学院）
We present a hierarchical framework that combines model-based control and reinforcement learning (RL) to synthesize robust controllers for a quadruped (the Unitree Laikago). The system consists of a high-level controller that learns to choose from a set of primitives in response to changes in the environment and a low-level controller that utilizes an established control method to robustly execute the primitives. Our framework learns a controller that can adapt to challenging environmental changes on the fly, including novel scenarios not seen during training. The learned controller is up to 8…
Mixture-of-Experts RL for Fault-Tolerant Legged Locomotion
Dynamic Legged Systems Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy（意大利技术研究院（IIT）动态腿足系统实验室，热那亚，意大利）；Dipartimento di Informatica, Bioingegneria, Robotica e Ingegneria dei Sistemi (DIBRIS), Universita di Genova, Genova, Italy（热那亚大学计算机科学、生物工程、机器人及系统工程系（DIBRIS），热那亚，意大利）
One Policy to Run Them All: an End-to-end Learning Approach to Multi-Embodiment Locomotion
Department of Computer Science, Technical University of Darmstadt（德累斯顿技术大学计算机科学系）；Institute of Robotics and Machine Intelligence, Poznan University of Technology（波兹南技术大学机器人与机器智能研究所）；German Research Center for AI (DFKI), Research Department: Systems AI for Robot Learning（德国人工智能研究中心（DFKI）系统AI for机器人学习研究部）；IDEAS NCBR, Warsaw, Poland（华沙波兰IDEAS NCBR）；Centre for Cognitive Science（认知科学中心）
Both legged locomotion and slithering motions typically utilize periodic gaits -- repeating cycles of body shape change that produce a net motion through the world. Legged locomotion can be viewed from the perspective of piece-wise contact constraint formation and removal. Slithering and low Reynolds number swimming operate under continuous constraints of force balance, wherein dissipation removes the ability to accumulate momentum. Here we discuss how to bridge the gap between these domains of motion, thereby, among other benefits, producing models for the space of legged locomotion with slip…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Muscle models and animal observations suggest that physical damping is beneficial for stabilization. Still, only a few implementations of mechanical damping exist in compliant robotic legged locomotion. It remains unclear how physical damping can be exploited for locomotion tasks, while its advantages as sensor-free, adaptive force- and negative work-producing actuators are promising. In a simplified numerical leg model, we studied the energy dissipation from viscous and Coulomb damping during vertical drops with ground-level perturbations. A parallel spring-damper is engaged between touch-dow…
We propose in this paper a motion planning method for legged robot locomotion based on Geometric Heat Flow framework. The motion planning task is challenging due to the hybrid nature of dynamics and contact constraints. We encode the hybrid dynamics and constraints into Riemannian inner product, and this inner product is defined so that short curves correspond to admissible motions for the system. We rely on the affine geometric heat flow to deform an arbitrary path connecting the desired initial and final states to this admissible motion. The method is able to automatically find the trajector…
We derive a hybrid feedback control law for the lateral leg spring (LLS) model so that the center of mass of a legged runner follows a curved path in horizontal plane. The control law enables the runner to change the placement and the elasticity of its legs to move in a desired direction. Stable motion along a curved path is achieved using curvature, bearing and relative distance between the runner and the curve as feedback. Constraints on leg parameters determine the class of curves that can be followed. We also derive an optimal control law that stabilizes the orientation of the runner's bod…
Politecnico di Milano（米兰理工大学）；Istituto Italiano di Tecnologia（意大利技术研究院）
Hybrid wheeled-legged locomotion is a navigation paradigm only recently opened up by novel robotic designs,e.g. the centaur-type humanoid CENTAURO [1] or the quadruped ANYmal [2] in its configuration featuring non-steerable wheels. The term Hybrid Locomotion is hereafter used to indicate a particular type of locomotion, achieved with simultaneous and coordinate use of legs and wheels,see Fig. 1. Such choice stems at the intersection between legged locomotion and the simpler wheeled navigation, in order to get the best from both techniques: agility and ability to traverse uneven terrains from t…
Istituto Italiano di Tecnologia（意大利理工学院）；University of Notre Dame（圣母大学）
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 targe…
Princeton University（普林斯顿大学）；Google Research（谷歌研究院）；Georgia Institute of Technology（佐治亚理工学院）
Designing control policies for legged locomotion is complex due to the under-actuated and non-continuous robot dynamics. Model-free reinforcement learning provides promising tools to tackle this challenge. However, a major bottleneck of applying model-free reinforcement learning in real world is safety. In this paper, we propose a safe reinforcement learning framework that switches between a safe recovery policy that prevents the robot from entering unsafe states, and a learner policy that is optimized to complete the task. The safe recovery policy takes over the control when the learner polic…
School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；Institute of Cyber-Systems and Control, Zhejiang University（浙江大学控制科学与工程学院 cyber-system 研究所）
Achieving versatile robot locomotion requires motor skills which can adapt to previously unseen situations. We propose a Multi-Expert Learning Architecture (MELA) that learns to generate adaptive skills from a group of representative expert skills. During training, MELA is first initialised by a distinct set of pre-trained experts, each in a separate deep neural network (DNN). Then by learning the combination of these DNNs using a Gating Neural Network (GNN), MELA can acquire more specialised experts and transitional skills across various locomotion modes. During runtime, MELA constantly blend…
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；Purdue University（普渡大学）；University of Rhode Island（罗德岛大学）
State estimation for legged locomotion over a dynamic rigid surface (DRS), which is a rigid surface moving in the world frame (e.g., ships, aircraft, and trains), remains an under-explored problem. This paper introduces an invariant extended Kalman filter that estimates the robot's pose and velocity during DRS locomotion by using common sensors of legged robots (e.g., inertial measurement units (IMU), joint encoders, and RDB-D camera). A key feature of the filter lies in that it explicitly addresses the nonstationary surface-foot contact point and the hybrid robot behaviors. Another key featur…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Maastricht University（马斯特里赫特大学）；Ghent University（根特大学）；Bielefeld University（比勒费尔德大学）
We present Oncilla robot, a novel mobile, quadruped legged locomotion machine. This large-cat sized, 5.1 robot is one of a kind of a recent, bioinspired legged robot class designed with the capability of model-free locomotion control. Animal legged locomotion in rough terrain is clearly shaped by sensor feedback systems. Results with Oncilla robot show that agile and versatile locomotion is possible without sensory signals to some extend, and tracking becomes robust when feedback control is added (Ajaoolleian 2015). By incorporating mechanical and control blueprints inspired from animals, and …
Multi-Loco: Unifying Multi-Embodiment Legged Locomotion via Reinforcement Learning Augmented Diffusion
Southern University of Science and Technology, China（南方科技大学）；University of Notre Dame, United States（Notre Dame 大学）；Zhejiang University-University of Illinois Urbana-Champaign Institute, China（浙江大学-伊利诺伊大学厄巴纳-香槟分校联合研究所）；LimX Dynamics, Shenzhen, China（LimX 动力学（深圳））
Tandon School of Engineering, New York University（纽约大学坦登工程学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Whole-body optimizers have been successful at automatically computing complex dynamic locomotion behaviors. However they are often limited to offline planning as they are computationally too expensive to replan with a high frequency. Simpler models are then typically used for online replanning. In this paper we present a method to generate whole body movements in real-time for locomotion tasks. Our approach consists in learning a centroidal neural network that predicts the desired centroidal motion given the current state of the robot and a desired contact plan. The network is trained using an…
Southern University of Science and Technology（南方科技大学）
This paper studies the problem of constructing polytopic representations of planar regions from depth camera readings. This problem is of great importance for terrain mapping in complicated environment and has great potentials in legged locomotion applications. To address the polytopic planar region characterization problem, we propose a two-stage solution scheme. At the first stage, the planar regions embedded within a sequence of depth images are extracted individually first and then merged to establish a terrain map containing only planar regions in a selected frame. To simplify the represe…
Robotic mobility in microgravity is necessary to expand human utilization and exploration of outer space. Bio-inspired multi-legged robots are a possible solution for safe and precise locomotion. However, a dynamic motion of a robot in microgravity can lead to failures due to gripper detachment caused by excessive motion reactions. We propose a novel Reaction-Aware Motion Planning (RAMP) to improve locomotion safety in microgravity, decreasing the risk of losing contact with the terrain surface by reducing the robot's momentum change. RAMP minimizes the swing momentum with a Low-Reaction Swing…
ETH Zürich（苏黎世联邦理工学院）；Delft University of Technology（代尔夫特理工大学）；Boston Dynamics（波士顿动力公司）
Wheeled-legged robots have the potential for highly agile and versatile locomotion. The combination of legs and wheels might be a solution for any real-world application requiring rapid, and long-distance mobility skills on challenging terrain. In this paper, we present an online trajectory optimization framework for wheeled quadrupedal robots capable of executing hybrid walking-driving locomotion strategies. By breaking down the optimization problem into a wheel and base trajectory planning, locomotion planning for high dimensional wheeled-legged robots becomes more tractable, can be solved i…
This work tries to contribute to the design of legged robots with capabilities boosted through thruster-assisted locomotion. Our long-term goal is the development of robots capable of negotiating unstructured environments, including land and air, by leveraging legs and thrusters collaboratively. These robots could be used in a broad number of applications including search and rescue operations, space exploration, automated package handling in residential spaces and digital agriculture, to name a few. In all of these examples, the unique capability of thruster-assisted mobility greatly broadens…
CTS: Concurrent Teacher-Student Reinforcement Learning for Legged Locomotion
School of System Design and Intelligent Manufacturing (SDIM), Southern University of Science and Technology（南方科技大学系统设计与智能制造学院）；LimX Dynamics（灵蜥动力）；Zhejiang University-University of Illinois Urbana-Champaign Institute (ZJUI)（浙江大学-伊利诺伊大学厄巴纳-香槟分校学院）
While quadruped robots usually have good stability and load capacity, bipedal robots offer a higher level of flexibility / adaptability to different tasks and environments. A multi-modal legged robot can take the best of both worlds. In this paper, we propose a multi-modal locomotion framework that is composed of a hand-crafted transition motion and a learning-based bipedal controller -- learnt by a novel algorithm called Automated Residual Reinforcement Learning. This framework aims to endow arbitrary quadruped robots with the ability to walk bipedally. In particular, we 1) design an addition…
Impressive animal locomotion capabilities are mediated by the co-evolution of the skeletal morphology and muscular properties. Legged robot performance would also likely benefit from the co-optimization of actuators and leg morphology. However, development of custom actuators for legged robots is often expensive and time consuming, which discourages roboticists from pursuing performance gains afforded by application-specific actuator optimization. This paper presents open-source designs for two quasi-direct-drive actuators with performance regimes appropriate for an 8--15 kg robot, built compl…
Real-time constraint satisfaction for robots can be quite challenging due to the high computational complexity that arises when accounting for the system dynamics and environmental interactions, often requiring simplification in modelling that might not necessarily account for all performance criteria. We instead propose an optimization-free approach where reference trajectories are manipulated to satisfy constraints brought on by ground contact as well as those prescribed for states and inputs. Unintended changes to trajectories especially ones optimized to produce periodic gaits can adversel…
Virginia Tech（弗吉尼亚理工大学）；California Institute of Technology（加州理工学院）
The aim of this work is to define a planner that enables robust legged locomotion for complex multi-agent systems consisting of several holonomically constrained quadrupeds. To this end, we employ a methodology based on behavioral systems theory to model the sophisticated and high-dimensional structure induced by the holonomic constraints. The resulting model is then used in tandem with distributed control techniques such that the computational burden is shared across agents while the coupling between agents is preserved. Finally, this distributed model is framed in the context of a predictive…
