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 body relative to the velocity of the runner's center of mass.
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 …
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）
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）
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）
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…
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…
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…
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…
Towards Standardized Disturbance Rejection Testing of Legged Robot Locomotion with Linear Impactor: A Preliminary Study, Observations, and Implications
Iowa State University（爱荷华州立大学）；The Ohio State University（俄亥俄州立大学）
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；KU Leuven（鲁汶大学）
Most legged robots are built with leg structures from serially mounted links and actuators and are controlled through complex controllers and sensor feedback. In comparison, animals developed multi-segment legs, mechanical coupling between joints, and multi-segmented feet. They run agile over all terrains, arguably with simpler locomotion control. Here we focus on developing foot mechanisms that resist slipping and sinking also in natural terrain. We present first results of multi-segment feet mounted to a bird-inspired robot leg with multi-joint mechanical tendon coupling. Our one- and two-se…
GPO: Growing Policy Optimization for Legged Robot Locomotion and Whole-Body Control
Beihang University, China（北京航空航天大学）；Department of Mechanical Engineering, National University of Singapore, Singapore（新加坡国立大学机械工程系）；Henan Univeristy, China（河南大学）
NASA Jet Propulsion Laboratory（NASA喷气推进实验室）；California Institute of Technology（加州理工学院）
This paper serves as one of the first efforts to enable large-scale and long-duration autonomy using the Boston Dynamics Spot robot. Motivated by exploring extreme environments, particularly those involved in the DARPA Subterranean Challenge, this paper pushes the boundaries of the state-of-practice in enabling legged robotic systems to accomplish real-world complex missions in relevant scenarios. In particular, we discuss the behaviors and capabilities which emerge from the integration of the autonomy architecture NeBula (Networked Belief-aware Perceptual Autonomy) with next-generation mobili…
MOVE: Multi-skill Omnidirectional Legged Locomotion with Limited View in 3D Environments
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）；State Key Laboratory of Industrial Control Technology（工业控制技术国家重点实验室）
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…
Much current study of legged locomotion has rightly focused on foot traction forces, including on granular media. Future legged millirobots will need to go through terrain, such as brush or other vegetation, where the body contact forces significantly affect locomotion. In this work, a (previously developed) low-cost 6-axis force/torque sensing shell is used to measure the interaction forces between a hexapedal millirobot and a set of compliant beams, which act as a surrogate for a densely cluttered environment. Experiments with a VelociRoACH robotic platform are used to measure lift and drag …
Collaborative Robotics and Intelligent Systems Institute, Oregon State University（俄勒冈州立大学协作机器人与智能系统研究所）
The complex dynamics of agile robotic legged locomotion requires motion planning to intelligently adjust footstep locations. Often, bipedal footstep and motion planning use mathematically simple models such as the linear inverted pendulum, instead of dynamically-rich models that do not have closed-form solutions. We propose a real-time optimization method to plan for dynamical models that do not have closed form solutions and experience irrecoverable failure. Our method uses a data-driven approximation of the step-to-step dynamics and of a failure margin function. This failure margin function …
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…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Middle East Technical University（中东技术大学）；METU Robotics and AI Technologies Application and Research Center（中东技术大学机器人与人工智能技术应用研究中心）
In this manuscript, we present a novel method for estimating the stochastic stability characteristics of metastable legged systems using the unscented transformation. Prior methods for stability analysis in such systems often required high-dimensional state space discretization and a broad set of initial conditions, resulting in significant computational complexity. Our approach aims to alleviate this issue by reducing the dimensionality of the system and utilizing the unscented transformation to estimate the output distribution. This technique allows us to account for multiple sources of unce…
Istituto Italiano di Tecnologia（意大利理工学院）；Politecnico di Torino（都灵理工大学）
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 Dynamicsbased 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 …
