We present a real-time framework for expressive legged locomotion that enables independent control over velocity and style. Unlike existing data-driven controllers, which typically require explicit style labels for training, our method efficiently leverages large-scale unstructured motion data and generalizes to unseen styles. We disentangle style from functional locomotion through a tailored sampling strategy used to train a style encoder whose output conditions an autoregressive diffusion model. During inference, the user provides a style reference clip and a joystick velocity command. The diffusion model then generates a kinematic reference tracked by a reinforcement learning controller. To improve user controllability and stylization strength, we propose an attention biasing mechanism and a velocity command correction strategy. We demonstrate our method on a physics-based humanoid character in simulation and on a physical robot, showcasing robust real-time control and continuous style modulation. The results can be best seen in our supplemental video (https://www.youtube.com/watch?v=roFnS6N7nJ4).
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…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Stanford University（斯坦福大学）
Whole-body control (WBC) is a generic task-oriented control method for feedback control of loco-manipulation behaviors in humanoid robots. The combination of WBC and model-based walking controllers has been widely utilized in various humanoid robots. However, to date, the WBC method has not been employed for unsupported passive-ankle dynamic locomotion. As such, in this paper, we devise a new WBC, dubbed whole-body locomotion controller (WBLC), that can achieve experimental dynamic walking on unsupported passive-ankle biped robots. A key aspect of WBLC is the relaxation of contact constraints …
In this paper, we propose a deep forward-backward stochastic differential equation (FBSDE) based control algorithm for locomotion tasks. We also include state constraints in the FBSDE formulation to impose stable walking solutions or other constraints that one may want to consider (e.g., energy). Our approach utilizes a deep neural network (i.e., LSTM) to solve, in general, high-dimensional Hamilton-Jacobi-Bellman (HJB) equation resulting from the stated optimal control problem. As compared to traditional methods, our proposed method provides a higher computational efficiency in real-time; thu…
Towards An Adaptive Locomotion Strategy For Quadruped Rovers: Quantifying When To Slide Or Walk On Planetary Slopes
Dynamic Legged Systems Lab, Istituto Italiano di Tecnologia (IIT)（动态腿系统实验室，意大利技术研究院）；Dipartimento di Ingegneria Elettrica Elettronica e Informatica, Università di Catania（电气电子与信息工程系，卡塔尼亚大学）
University of Massachusetts Lowell（马萨诸塞大学洛厄尔分校）；NVIDIA Research（英伟达研究院）；Princeton University（普林斯顿大学）；Purdue University（普渡大学）
This study introduces an analytically tractable and computationally efficient model of the legged robot dynamics associated with locomotion on a dynamic rigid surface (DRS), and develops a real-time motion planner based on the proposed model and its analytical solution. This study first theoretically extends the classical linear inverted pendulum (LIP) model from legged locomotion on a static surface to DRS locomotion, by relaxing the LIP's underlying assumption that the surface is static. The resulting model, which we call "DRS-LIP", is explicitly time-varying. After converting the DRS-LIP in…
Delft University of Technology（代尔夫特理工大学）；California Institute of Technology（加州理工学院）
Humans are able to negotiate downstep behaviors -- both planned and unplanned -- with remarkable agility and ease. The goal of this paper is to systematically study the translation of this human behavior to bipedal walking robots, even if the morphology is inherently different. Concretely, we begin with human data wherein planned and unplanned downsteps are taken. We analyze this data from the perspective of reduced-order modeling of the human, encoding the center of mass (CoM) kinematics and contact forces, which allows for the translation of these behaviors into the corresponding reduced-ord…
In this paper, previous works on the Model Predictive Control (MPC) and the Divergent Component of Motion (DCM) for bipedal walking control are extended. To this end, we employ a single MPC which uses a combination of Center of Pressure (CoP) manipulation, step adjustment, and Centroidal Moment Pivot (CMP) modulation to design a robust walking controller. Furthermore, we exploit the concept of time-varying DCM to generalize our walking controller for walking in uneven surfaces. Using our scheme, a general and robust walking controller is designed which can be implemented on robots with differe…
We describe a whole-body dynamic walking controller implemented as a convex quadratic program. The controller solves an optimal control problem using an approximate value function derived from a simple walking model while respecting the dynamic, input, and contact constraints of the full robot dynamics. By exploiting sparsity and temporal structure in the optimization with a custom active-set algorithm, we surpass the performance of the best available off-the-shelf solvers and achieve 1kHz control rates for a 34-DOF humanoid. We describe applications to balancing and walking tasks using the si…
Italian Institute of Technology（意大利技术研究院）；University of Manchester（曼彻斯特大学）；University of Genoa（热那亚大学）
The paper presents a planner to generate walking trajectories by using the centroidal dynamics and the full kinematics of a humanoid robot. The interaction between the robot and the walking surface is modeled explicitly via new conditions, the \emph{Dynamical Complementarity Constraints}. The approach does not require a predefined contact sequence and generates the footsteps automatically. We characterize the robot control objective via a set of tasks, and we address it by solving an optimal control problem. We show that it is possible to achieve walking motions automatically by specifying a m…
PolygMap: A Perceptive Locomotion Framework for Humanoid Robot Stair Climbing
The Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳人工智能与机器人社会研究院）；Electronic science and technology, Guangdong University of Technology（广东技术大学电子科学与技术学院）；Leju robotics（乐居机器人）
Locomotion of legged machines faces the problems of model complexity and computational costs. Algorithms based on complex models and/or reinforcement learning exist to solve the walking control task. In this project, we aim to develop a bipedal walking control system based on a simple model the Linear Inverted Pendulum model. In order to simplify the complex process of controlling legged locomotion, we make use of the technique of splitting the control into three parts as height control, forward velocity control and balance control. The forward velocity of the body has a linear relationship wi…
This study proposes an integrated task and motion planning method for dynamic locomotion in partially observable environments with multi-level safety guarantees. This layered planning framework is composed of a high-level symbolic task planner and a low-level phase-space motion planner. A belief abstraction at the task planning level enables belief estimation of dynamic obstacle locations and guarantees navigation safety with collision avoidance. The high-level task planner, i.e., a two-level navigation planner, employs linear temporal logic for a reactive game synthesis between the robot and …
IEETA / DETI University of Aveiro（阿威罗大学 IEETA / DETI）
Generating robust locomotion for a humanoid robot in the presence of disturbances is difficult because of its high number of degrees of freedom and its unstable nature. In this paper, we used the concept of Divergent Component of Motion~(DCM) and propose an optimal closed-loop controller based on Linear-Quadratic-Gaussian to generate a robust and stable walking for humanoid robots. The biped robot dynamics has been approximated using the Linear Inverted Pendulum Model~(LIPM). Moreover, we propose a controller to adjust the landing location of the swing leg to increase the withstanding level of…
ETH Zürich（苏黎世联邦理工学院）；California Institute of Technology（加州理工学院）
The ability to generate dynamic walking in real-time for bipedal robots with input constraints and underactuation has the potential to enable locomotion in dynamic, complex and unstructured environments. Yet, the high-dimensional nature of bipedal robots has limited the use of full-order rigid body dynamics to gaits which are synthesized offline and then tracked online. In this work we develop an online nonlinear model predictive control approach that leverages the full-order dynamics to realize diverse walking behaviors. Additionally, this approach can be coupled with gaits synthesized offlin…
Oregon State University（俄勒冈州立大学）；Collaborative Robotics and Intelligent Systems Institute（协作机器人与智能系统研究所）
In this paper, we describe an approach to achieve dynamic legged locomotion on physical robots which combines existing methods for control with reinforcement learning. Specifically, our goal is a control hierarchy in which highest-level behaviors are planned through reduced-order models, which describe the fundamental physics of legged locomotion, and lower level controllers utilize a learned policy that can bridge the gap between the idealized, simple model and the complex, full order robot. The high-level planner can use a model of the environment and be task specific, while the low-level le…
Nonlinear Model Predictive Control for Robust Bipedal Locomotion: Exploring Angular Momentum and CoM Height Changes
School of Power and Mechanical Engineering, Wuhan University（武汉大学动力与机械学院）；Shenzhen Institute of Artificial Intelligence and Robotics for Society（深圳人工智能与机器人研究院）；School of Mechanical Engineering, University of Leeds（利兹大学机械工程学院）；School of Informatics, The University of Edinburgh（爱丁堡大学信息学院）；Humanoid and Human Centered Mechatronics Research Line, Istituto Italiano di Tecnologia（意大利技术研究院人形与以人为中心的机电一体化研究线）
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…
Istituto Italiano di Tecnologia（意大利理工学院）；University of Genoa（热那亚大学）；University of Manchester（曼彻斯特大学）
This paper presents a Non-Linear Model Predictive Controller for humanoid robot locomotion with online step adjustment capabilities. The proposed controller considers the Centroidal Dynamics of the system to compute the desired contact forces and torques and contact locations. Differently from bipedal walking architectures based on simplified models, the presented approach considers the reduced centroidal model, thus allowing the robot to perform highly dynamic movements while keeping the control problem still treatable online. We show that the proposed controller can automatically adjust the …
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…
This work presents a teleoperated humanoid robot system that can imitate human motions, walk and turn. To capture human motions, a Microsoft Kinect Depth sensor is used. Unlike the cumbersome motion capture suits, the sensor makes the system more comfortable to interact with. The skeleton data is extracted from the Kinect which is processed to generate the robot's joint angles. Robot Operating System (ROS) is used for the communication between the various parts of the code to achieve minimal latency. Thus the robot imitates the human in real-time with negligible lag. Unlike most of the human m…
Walking motion planning based on Divergent Component of Motion (DCM) and Linear Inverted Pendulum Model (LIPM) is one of the alternatives that could be implemented to generate online humanoid robot gait trajectories. This algorithm requires different parameters to be adjusted. Herein, we developed a framework to attain optimal parameters to achieve a stable and energy-efficient trajectory for real robot's gait. To find the optimal trajectory, four cost functions representing energy consumption, the sum of joints velocity and applied torque at each lower limb joint of the robot, and a cost func…
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…
University of British Columbia（英属哥伦比亚大学）；Oregon State University（俄勒冈州立大学）
Deep reinforcement learning (DRL) is a promising approach for developing legged locomotion skills. However, the iterative design process that is inevitable in practice is poorly supported by the default methodology. It is difficult to predict the outcomes of changes made to the reward functions, policy architectures, and the set of tasks being trained on. In this paper, we propose a practical method that allows the reward function to be fully redefined on each successive design iteration while limiting the deviation from the previous iteration. We characterize policies via sets of Deterministi…
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…
The ability to realize nonlinear controllers with formal guarantees on dynamic robotic systems has the potential to enable more complex robotic behaviors -- yet, realizing these controllers is often practically challenging. To address this challenge, this paper presents the end-to-end realization of dynamic bipedal locomotion on an underactuated bipedal robot via hybrid zero dynamics and control Lyapunov functions. A compliant model of Cassie is represented as a hybrid system to set the stage for a trajectory optimization framework. With the goal of achieving a variety of walking speeds in all…
IEETA / DETI University of Aveiro（阿威罗大学IEETA / DETI）
Developing robust locomotion for humanoid robots is a complex task due to the unstable nature of these robots and also to the unpredictability of the terrain. A robust locomotion planner is one of the fundamental components for generating stable biped locomotion. This paper presents an optimal closed-loop biped locomotion planner which can plan reference trajectories even in challenging conditions. The proposed planner is designed based on a Time-Varying Model Predictive Control~(TVMPC) scheme to be able to consider some constraints in the states, inputs and outputs of the system and also mixe…
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…
Facebook（脸书）；Facebook AI Research（脸书人工智能研究院）；University of California, Berkeley（加州大学伯克利分校）
Learning to locomote to arbitrary goals on hardware remains a challenging problem for reinforcement learning. In this paper, we present a hierarchical learning framework that improves sample-efficiency and generalizability of locomotion skills on real-world robots. Our approach divides the problem of goal-oriented locomotion into two sub-problems: learning diverse primitives skills, and using model-based planning to sequence these skills. We parametrize our primitives as cyclic movements, improving sample-efficiency of learning on a 18 degrees of freedom robot. Then, we learn coarse dynamics m…
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…
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…
Stabilizing legged robot locomotion on a dynamic rigid surface (DRS) (i.e., rigid surface that moves in the inertial frame) is a complex planning and control problem. The complexity arises due to the hybrid nonlinear walking dynamics subject to explicitly time-varying holonomic constraints caused by the surface movement. The first main contribution of this study is the extension of the capture point from walking on a static surface to locomotion on a DRS as well as the use of the resulting capture point for online motion planning. The second main contribution is a quadratic-programming (QP) ba…
Locomotion is a crucial challenge for legged robots that is addressed "effortlessly" by biological networks abundant in nature, named central pattern generators (CPG). The multitude of CPG network models that have so far become biomimetic robotic controllers is not applicable to the emerging neuromorphic hardware, depriving mobile robots of a robust walking mechanism that would result in inherently energy-efficient systems. Here, we propose a brain-morphic CPG controler based on a comprehensive spiking neural-astrocytic network that generates two gait patterns for a hexapod robot. Building on …
In this paper, we propose a novel framework on force-and-moment-based Model Predictive Control (MPC) for dynamic legged robots. Specifically, we present a formulation of MPC designed for 10 degree-of-freedom (DoF) bipedal robots using simplified rigid body dynamics with input forces and moments. This MPC controller will calculate the optimal inputs applied to the robot, including 3-D forces and 2-D moments at each foot. These desired inputs will then be generated by mapping these forces and moments to motor torques of 5 actuators on each leg. We evaluate our proposed control design on physical…
Idiap Research Institute（Idiap研究所）；EPFL（洛桑联邦理工学院）；LAAS-CNRS（法国国家科学研究中心自动化系统实验室）
In this paper, we propose a framework to build a memory of motion for warm-starting an optimal control solver for the locomotion task of a humanoid robot. We use HPP Loco3D, a versatile locomotion planner, to generate offline a set of dynamically consistent whole-body trajectory to be stored as the memory of motion. The learning problem is formulated as a regression problem to predict a single-step motion given the desired contact locations, which is used as a building block for producing multi-step motions. The predicted motion is then used as a warm-start for the fast optimal control solver …
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；University of Trento（特伦托大学）；New York University（纽约大学）
Linear Model Predictive Control (MPC) has been successfully used for generating feasible walking motions for humanoid robots. However, the effect of uncertainties on constraints satisfaction has only been studied using Robust MPC (RMPC) approaches, which account for the worst-case realization of bounded disturbances at each time instant. In this letter, we propose for the first time to use linear stochastic MPC (SMPC) to account for uncertainties in bipedal walking. We show that SMPC offers more flexibility to the user (or a high level decision maker) by tolerating small (user-defined) probabi…
Beijing University of Aeronautics and Astronautics（北京航空航天大学）；Bernstein Center for Computational Neuroscience（伯恩斯坦计算神经科学中心）；Georg-August-Universität Göttingen（哥廷根大学）；University of Southern Denmark（南丹麦大学）
An originally chaotic system can be controlled into various periodic dynamics. When it is implemented into a legged robot's locomotion control as a central pattern generator (CPG), sophisticated gait patterns arise so that the robot can perform various walking behaviors. However, such a single chaotic CPG controller has difficulties dealing with leg malfunction. Specifically, in the scenarios presented here, its movement permanently deviates from the desired trajectory. To address this problem, we extend the single chaotic CPG to multiple CPGs with learning. The learning mechanism is based on …
The design of gaits for robot locomotion can be a daunting process which requires significant expert knowledge and engineering. This process is even more challenging for robots that do not have an accurate physical model, such as compliant or micro-scale robots. Data-driven gait optimization provides an automated alternative to analytical gait design. In this paper, we propose a novel approach to efficiently learn a wide range of locomotion tasks with walking robots. This approach formalizes locomotion as a contextual policy search task to collect data, and subsequently uses that data to learn…
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…
University of Michigan（密歇根大学）；University of Texas at Dallas（得克萨斯大学达拉斯分校）；Shirley Ryan AbilityLab（雪莉瑞安能力实验室）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；Northwestern University（西北大学）
Human locomotion involves continuously variable activities including walking, running, and stair climbing over a range of speeds and inclinations as well as sit-stand, walk-run, and walk-stairs transitions. Understanding the kinematics and kinetics of the lower limbs during continuously varying locomotion is fundamental to developing robotic prostheses and exoskeletons that assist in community ambulation. However, available datasets on human locomotion neglect transitions between activities and/or continuous variations in speed and inclination during these activities. This data paper reports a…
