Simultaneous Contact, Gait and Motion Planning for Robust Multi-Legged Locomotion via Mixed-Integer Convex Optimization
School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA（电气与计算机工程系，佐治亚理工学院，亚特兰大，GA 30332 USA）；Twentieth Century Fox, Springfield, USA（二十世纪福克斯，斯普林菲尔德，USA）；Starfleet Academy, San Francisco, CA 96678 USA（星际舰队学院，旧金山，CA 96678 USA）；Tyrell Inc., 123 Replicant Street, Los Angeles, CA 90210 USA（泰勒尔公司，123 复制人街，洛杉矶，CA 90210 USA）
Bernardo Aceituno-Cabezas, Carlos Mastalli, Hongkai Dai, Michele Focchi, Andreea Radulescu, Darwin G. Caldwell, Jose Cappelletto, Juan C. Grieco, Gerardo Fernan… 展开作者
Bernardo Aceituno-Cabezas, Carlos Mastalli, Hongkai Dai, Michele Focchi, Andreea Radulescu, Darwin G. Caldwell, Jose Cappelletto, Juan C. Grieco, Gerardo Fernandez-Lopez, Claudio Semini
Traditional motion planning approaches for multi-legged locomotion divide the problem into several stages, such as contact search and trajectory generation. However, reasoning about contacts and motions simultaneously is crucial for the generation of complex whole-body behaviors. Currently, coupling theses problems has required either the assumption of a fixed gait sequence and flat terrain condition, or non-convex optimization with intractable computation time. In this paper, we propose a mixed-integer convex formulation to plan simultaneously contact locations, gait transitions and motion, in a computationally efficient fashion. In contrast to previous works, our approach is not limited to flat terrain nor to a pre-specified gait sequence. Instead, we incorporate the friction cone stability margin, approximate the robot's torque limits, and plan the gait using mixed-integer convex constraints. We experimentally validated our approach on the HyQ robot by traversing different challenging terrains, where non-convexity and flat terrain assumptions might lead to sub-optimal or unstable plans. Our method increases the motion generality while keeping a low computation time.
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…
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…
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…
Learning controllers that reproduce legged locomotion in nature has been a long-time goal in robotics and computer graphics. While yielding promising results, recent approaches are not yet flexible enough to be applicable to legged systems of different morphologies. This is partly because they often rely on precise motion capture references or elaborate learning environments that ensure the naturality of the emergent locomotion gaits but prevent generalization. This work proposes a generic approach for ensuring realism in locomotion by guiding the learning process with the spring-loaded invert…
Sampling Strategy Design for Model Predictive Path Integral Control on Legged Robot Locomotion
School of Artificial Intelligence Shandong University Jinan, China；Department of Mechatronics；Robotics Xi'an Jiaotong-Liverpool University Suzhou, China；Robotics Xi'an Jiaotong-Liverpool University Suzhou, China University of Liverpool United Kingdom；Robotic Systems Xi'an Jiaotong-Liverpool University Suzhou, China
Korea Advanced Institute of Science and Technology（韩国科学技术院）；Istituto Italiano di Tecnologia（意大利理工学院）
In this work, a non-gaited framework for legged system locomotion is presented. The approach decouples the gait sequence optimization by considering the problem as a decision-making process. The redefined contact sequence problem is solved by utilizing a Monte Carlo Tree Search (MCTS) algorithm that exploits optimization-based simulations to evaluate the best search direction. The proposed scheme has proven to have a good trade-off between exploration and exploitation of the search space compared to the state-of-the-art Mixed-Integer Quadratic Programming (MIQP). The model predictive control (…
Legged locomotion is commonly studied and expressed as a discrete set of gait patterns, like walk, trot, gallop, which are usually treated as given and pre-programmed in legged robots for efficient locomotion at different speeds. However, fixing a set of pre-programmed gaits limits the generality of locomotion. Recent animal motor studies show that these conventional gaits are only prevalent in ideal flat terrain conditions while real-world locomotion is unstructured and more like bouts of intermittent steps. What principles could lead to both structured and unstructured patterns across mammal…
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…
Agile asymmetric multi-legged locomotion: contact planning via geometric mechanics and spin model duality
Department of Mechanical Engineering, Pennsylvania State University（宾夕法尼亚州立大学机械工程系）；MIT Improbable AI Lab, Maschusetts Institute of Technology（麻省理工学院Improbable AI实验室）；Department of Physics, Georgia Institute of Technology（佐治亚理工学院物理系）；Department of Physics, Tsinghua University（清华大学物理系）
This paper systematically decomposes a quadrupedal robot into bipeds to rapidly generate walking gaits and then recomposes these gaits to obtain quadrupedal locomotion. We begin by decomposing the full-order, nonlinear and hybrid dynamics of a three-dimensional quadrupedal robot, including its continuous and discrete dynamics, into two bipedal systems that are subject to external forces. Using the hybrid zero dynamics (HZD) framework, gaits for these bipedal robots can be rapidly generated (on the order of seconds) along with corresponding controllers. The decomposition is achieved in such a w…
IMT School for Advanced Studies Lucca（卢卡高等研究院）；Istituto Italiano di Tecnologia（意大利理工学院）；Università di Genova（热那亚大学）
Re-planning in legged locomotion is crucial to track the desired user velocity while adapting to the terrain and rejecting external disturbances. In this work, we propose and test in experiments a real-time Nonlinear Model Predictive Control (NMPC) tailored to a legged robot for achieving dynamic locomotion on a variety of terrains. We introduce a mobility-based criterion to define an NMPC cost that enhances the locomotion of quadruped robots while maximizing leg mobility and improves adaptation to the terrain features. Our NMPC is based on the real-time iteration scheme that allows us to re-p…
Trajectory optimization is becoming increasingly powerful in addressing motion planning problems of underactuated robotic systems. Numerous prior studies solve such a class of large non-convex optimal control problems in a hierarchical fashion. However, numerical accuracy issues are prone to occur when one uses a full-order model to track reference trajectories generated from a reduced-order model. This study investigates an approach of Alternating Direction Method of Multipliers (ADMM) and proposes a new splitting scheme for legged locomotion problems. Rigid body dynamics constraints and othe…
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…
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…
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）
The quest for the efficient adaptation of multilegged robotic systems to changing conditions is expected to render new insights into robotic control and locomotion. In this paper, we study the performance frontiers of the enumerative (factorial) encoding of hexapod gaits for fast recovery to conditions of leg failures. Our computational studies using five nature-inspired gradient-free optimization heuristics have shown that it is possible to render feasible recovery gait strategies that achieve minimal deviation to desired locomotion directives with a few evaluations (trials). For instance, it…
Zhejiang University（浙江大学）；ZJU-Hangzhou Global Scientific and Technological Innovation Center（浙江大学-杭州市全球科技创新中心）；State Key Laboratory of Fluid Power and Mechatronic System, Zhejiang University（浙江大学流体动力与机电系统国家重点实验室）；Institute of Applied Mechanics, Zhejiang University（浙江大学应用力学研究所）
Gaits and transitions are key components in legged locomotion. For legged robots, describing and reproducing gaits as well as transitions remain longstanding challenges. Reinforcement learning has become a powerful tool to formulate controllers for legged robots. Learning multiple gaits and transitions, nevertheless, is related to the multi-task learning problems. In this work, we present a novel framework for training a simple control policy for a quadruped robot to locomote in various gaits. Four independent phases are used as the interface between the gait generator and the control policy, …
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）
Non-Gaited Legged Locomotion with Monte-Carlo Tree Search and Supervised Learning
Dynamic Legged Systems Laboratory, Istituto Italiano di Tecnologia (IIT), Genova, Italy（动态腿系统实验室，意大利技术研究院（IIT），意大利热那亚）；D AI Laboratory, Technical University of Munich (TUM), Germany（3D人工智能实验室，慕尼黑技术大学（TUM），德国）；ATARI Laboratory, MIRMI, Technical University of Munich (TUM), Germany（ATARI实验室，MIRMI，慕尼黑技术大学（TUM），德国）
GenTe: Generative Real-world Terrains for General Legged Robot Locomotion Control
School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理工学院）；Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳市人工智能与机器人研究院）
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…
In this paper, we propose a locomotion training framework where a control policy and a state estimator are trained concurrently. The framework consists of a policy network which outputs the desired joint positions and a state estimation network which outputs estimates of the robot's states such as the base linear velocity, foot height, and contact probability. We exploit a fast simulation environment to train the networks and the trained networks are transferred to the real robot. The trained policy and state estimator are capable of traversing diverse terrains such as a hill, slippery plate, …
Robotic Systems Lab, ETH Zurich（苏黎世联邦理工学院机器人系统实验室）；Robotics and Artificial Intelligence Lab, KAIST（韩国科学技术院机器人与人工智能实验室）；Intelligent Systems Lab, Intel（英特尔智能系统实验室）
Some of the most challenging environments on our planet are accessible to quadrupedal animals but remain out of reach for autonomous machines. Legged locomotion can dramatically expand the operational domains of robotics. However, conventional controllers for legged locomotion are based on elaborate state machines that explicitly trigger the execution of motion primitives and reflexes. These designs have escalated in complexity while falling short of the generality and robustness of animal locomotion. Here we present a radically robust controller for legged locomotion in challenging natural en…
University of Washington（华盛顿大学）；Robotics at Google（Google机器人部门）
We focus on the problem of developing energy efficient controllers for quadrupedal robots. Animals can actively switch gaits at different speeds to lower their energy consumption. In this paper, we devise a hierarchical learning framework, in which distinctive locomotion gaits and natural gait transitions emerge automatically with a simple reward of energy minimization. We use evolutionary strategies (ES) to train a high-level gait policy that specifies gait patterns of each foot, while the low-level convex MPC controller optimizes the motor commands so that the robot can walk at a desired vel…
Institute for Infocomm Research, A*STAR（新加坡科技研究局资讯通信研究院）；University College London（伦敦大学学院）
This work developed a learning framework for perceptive legged locomotion that combines visual feedback, proprioceptive information, and active gait regulation of foot-ground contacts. The perception requires only one forward-facing camera to obtain the heightmap, and the active regulation of gait paces and traveling velocity are realized through our formulation of CPG-based high-level imitation of foot-ground contacts. Through this framework, an end-user has the ability to command task-level inputs to control different walking speeds and gait frequencies according to the traversal of differen…
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…
