Biped robots are inherently unstable because of their complex kinematics as well as dynamics. Despite the many research efforts in developing biped locomotion, the performance of biped locomotion is still far from the expectations. This paper proposes a model-based framework to generate stable biped locomotion. The core of this framework is an abstract dynamics model which is composed of three masses to consider the dynamics of stance leg, torso and swing leg for minimizing the tracking problems. According to this dynamics model, we propose a modular walking reference trajectories planner which takes into account obstacles to plan all the references. Moreover, this dynamics model is used to formulate the controller as a Model Predictive Control (MPC) scheme which can consider some constraints in the states of the system, inputs, outputs and also mixed input-output. The performance and the robustness of the proposed framework are validated by performing several numerical simulations using MATLAB. Moreover, the framework is deployed on a simulated torque-controlled humanoid to verify its performance and robustness. The simulation results show that the proposed framework is capable of generating biped locomotion robustly.
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…
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 …
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…
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）；Agility Robotics
Recent work has demonstrated the success of reinforcement learning (RL) for training bipedal locomotion policies for real robots. This prior work, however, has focused on learning joint-coordination controllers based on an objective of following joint trajectories produced by already available controllers. As such, it is difficult to train these approaches to achieve higher-level goals of legged locomotion, such as simply specifying the desired end-effector foot movement or ground reaction forces. In this work, we propose an approach for integrating knowledge of the robot system into RL to all…
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…
Beijing Research Institute of UBTECH Robotics（优必选机器人北京研究院）；Tsinghua University（清华大学）
The planning of whole-body motion and step time for bipedal locomotion is constructed as a model predictive control (MPC) problem, in which a sequence of optimization problems needs to be solved online. While directly solving these problems is extremely time-consuming, we propose a predictive gait synthesizer to offer immediate solutions. Based on the full-dimensional model, a library of gaits with different speeds and periods is first constructed offline. Then the proposed gait synthesizer generates real-time gaits at 1kHz by synthesizing the gait library based on the online prediction of cen…
State-of-the-art approaches to legged locomotion are widely dependent on the use of models like the linear inverted pendulum (LIP) and the spring-loaded inverted pendulum (SLIP), popular because their simplicity enables a wide array of tools for planning, control, and analysis. However, they inevitably limit the ability to execute complex tasks or agile maneuvers. In this work, we aim to automatically synthesize models that remain low-dimensional but retain the capabilities of the high-dimensional system. For example, if one were to restore a small degree of complexity to LIP, SLIP, or a simil…
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…
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…
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…
Learning Terrain Aware Bipedal Locomotion via Reduced Dimensional Perceptual Representations
Electrical and Computer Engineering, The Ohio State University（电气与计算机工程系，俄亥俄州立大学）；Mechanical and Aerospace Engineering, The Ohio State University（机械与航空航天工程系，俄亥俄州立大学）
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）
Wheeled-legged robots combine the efficiency of wheeled robots when driving on suitably flat surfaces and versatility of legged robots when stepping over or around obstacles. This paper introduces a planning and control framework to realise dynamic locomotion for wheeled biped robots. We propose the Cart-Linear Inverted Pendulum Model (Cart-LIPM) as a template model for the rolling motion and the under-actuated LIPM for contact changes while walking. The generated motion is then tracked by an inverse dynamic whole-body controller which coordinates all joints, including the wheels. The framewor…
Waseda University（早稻田大学）；Waseda Institute for Advanced Study（早稻田大学高等研究所）；Humanoid Robotics Institute (HRI)（仿人机器人研究所）
In this paper we tackle the problem of visually predicting surface friction for environments with diverse surfaces, and integrating this knowledge into biped robot locomotion planning. The problem is essential for autonomous robot locomotion since diverse surfaces with varying friction abound in the real world, from wood to ceramic tiles, grass or ice, which may cause difficulties or huge energy costs for robot locomotion if not considered. We propose to estimate friction and its uncertainty from visual estimation of material classes using convolutional neural networks, together with probabili…
Despite the extensive presence of the legged locomotion in animals, it is extremely challenging to be reproduced with robots. Legged locomotion is an dynamic task which benefits from a planning that takes advantage of the gravitational pull on the system. However, the computational cost of such optimization rapidly increases with the complexity of kinematic structures, rendering impossible real-time deployment in unstructured environments. This paper proposes a simplified method that can generate desired centre of mass and feet trajectory for quadrupeds. The model describes a quadruped as two …
Enforcing safety in the presence of stochastic uncertainty is a challenging problem. Traditionally, researchers have proposed safety in the statistical mean as a safety measure in this case. However, ensuring safety in the statistical mean is only reasonable if system's safe behavior in the large number of runs is of interest, which precludes the use of mean safety in practical scenarios. In this paper, we propose a risk sensitive notion of safety called conditional-value-at-risk (CVaR) safety, which is concerned with safe performance in the worst case realizations. We introduce CVaR barrier f…
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…
Real-time Whole-body Model Predictive Control for Bipedal Locomotion with a Novel Kino-dynamic Model and Warm-start Method
Department of Intelligence and Information, Graduate School of Convergence Science and Technology, Seoul National University（智能信息系，融合科学与技术研究生院，首尔国立大学）；Advanced Institutes of Convergence Technology(AICT)（融合技术先进研究院）
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…
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…
Model-Based Reinforcement Learning Exploits Passive Body Dynamics for High-Performance Biped Robot Locomotion
Department of Mechanical Science and Bioengineering, Graduate School of Engineering and Science, The University of Osaka（大阪大学机械科学与生物工程学系）；Department of Electrical and Mechanical Engineering, Nagoya Institute of Technology（名古屋工业大学电气机械学系）
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…
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…
Teaching an anthropomorphic robot from human example offers the opportunity to impart humanlike qualities on its movement. In this work we present a reinforcement learning based method for teaching a real world bipedal robot to perform movements directly from human motion capture data. Our method seamlessly transitions from training in a simulation environment to executing on a physical robot without requiring any real world training iterations or offline steps. To overcome the disparity in joint configurations between the robot and the motion capture actor, our method incorporates motion re-t…
This paper presents a gait controller for bipedal robots to achieve highly agile walking over various terrains given local slope and friction cone information. Without these considerations, untimely impacts can cause a robot to trip and inadequate tangential reaction forces at the stance foot can cause slippages. We address these challenges by combining, in a novel manner, a model based on an Angular Momentum Linear Inverted Pendulum (ALIP) and a Model Predictive Control (MPC) foot placement planner that is executed by the method of virtual constraints. The process starts with abstracting from…
Waseda University（早稻田大学）；Waseda Institute for Advanced Study（早稻田高等研究所）；Humanoid Robotics Institute（人形机器人研究所）
Trajectory optimization and posture generation are hard problems in robot locomotion, which can be non-convex and have multiple local optima. Progress on these problems is further hindered by a lack of open benchmarks, since comparisons of different solutions are difficult to make. In this paper we introduce a new benchmark for trajectory optimization and posture generation of legged robots, using a pre-defined scenario, robot and constraints, as well as evaluation criteria. We evaluate state-of-the-art trajectory optimization algorithms based on sequential quadratic programming (SQP) on the b…
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…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Technical University of Munich（慕尼黑工业大学）
Legged locomotion in humans is governed by natural dynamics of the human body and neural control. One mechanism that is assumed to contribute to the high efficiency of human walking is the impulsive ankle push-off, which potentially powers the swing leg catapult. However, the mechanics of the human lower leg with its complex muscle-tendon units spanning over single and multiple joints is not yet understood. Legged robots allow testing the interaction between complex leg mechanics, control, and environment in real-world walking gait. We developed a 0.49m tall, 2.2kg anthropomorphic bipedal robo…
Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）；Amirkabir University of Technology（阿米尔卡比尔理工大学）；Tandon School of Engineering, New York University（纽约大学坦登工程学院）
In this paper, we present a novel two-level variable Horizon Model Predictive Control (VH-MPC) framework for bipedal locomotion. In this framework, the higher level computes the landing location and timing (horizon length) of the swing foot to stabilize the unstable part of the center of mass (CoM) dynamics, using feedback from the CoM states. The lower level takes into account the swing foot dynamics and generates dynamically consistent trajectories for landing at the desired time as close as possible to the desired location. To do that, we use a simplified model of the robot dynamics project…
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…
California Institute of Technology（加州理工学院）；Technion - Israel Institute of Technology（以色列理工学院）
Dynamic bipedal robot locomotion has achieved remarkable success due in part to recent advances in trajectory generation and nonlinear control for stabilization. A key assumption utilized in both theory and experiments is that the robot's stance foot always makes no-slip contact with the ground, including at impacts. This assumption breaks down on slippery low-friction surfaces, as commonly encountered in outdoor terrains, leading to failure and loss of stability. In this work, we extend the theoretical analysis and trajectory optimization to account for stick-slip transitions at point foot co…
Task-Space Riccati Feedback based Whole Body Control for Underactuated Legged Locomotion
School of System Design and Intelligent Manufacturing, Southern University of Science and Technology（南方科技大学系统设计与智能制造学院）；Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology（香港科技大学土木与环境工程系）；Department of Aerospace and Mechanical Engineering, University of Notre Dame（圣母大学航空航天与机械工程系）
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）
