In this paper, we will report our efforts in designing closed-loop feedback for the thruster-assisted walking of bipedal robots. We will assume for well-tuned supervisory controllers and will focus on fine-tuning the joints desired trajectories to satisfy the performance being sought. In doing this, we will devise an intermediary filter based on reference governors that guarantees the satisfaction of performance-related constraints. Since these modifications and impact events lead to deviations from the desired periodic orbits, we will guarantee hybrid invariance in a robust way by applying predictive schemes withing a very short time envelope during the gait cycle. To achieve the hybrid invariance, we will leverage the unique features in our model, that is, the thrusters. The merit of our approach is that unlike existing optimization-based nonlinear control methods, satisfying performance-related constraints during the single support phase does not rely on expensive numeric approaches. In addition, the overall structure of the proposed thruster-assisted gait control allows for exploiting performance and robustness enhancing capabilities during specific parts of the gait cycle, which is unusual and not reported before.
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…
Northeastern University（东北大学）；University of Alabama（阿拉巴马大学）
We will report our efforts in designing feedback for the thruster-assisted walking of a bipedal robot. We will assume for well-tuned supervisory controllers and will focus on fine-tuning the desired joint trajectories to satisfy the performance being sought. In doing this, we will devise an intermediary filter based on the emerging idea of reference governors. Since these modifications and impact events lead to deviations from the desired periodic orbits, we will guarantee hybrid invariance in a robust fashion by applying predictive schemes within a short time envelope during the double suppor…
In the control of bipedal locomotion, linear velocity of the center of mass has been widely accepted as a primary variable for summarizing a robot's state vector. The ubiquitous massless-legged linear inverted pendulum (LIP) model is based on it. In this paper, we argue that angular momentum about the contact point has several properties that make it superior to linear velocity for feedback control. So as not to confuse the benefits of angular momentum with any other control design decisions, we first reformulate the standard LIP controller in terms of angular momentum. We then implement the r…
A Framework for Planning and Controlling Non-Periodic Bipedal Locomotion
Human Centered Robotics Laboratory, The University of Texas at Austin, TX, USA（以人为中心的机器人实验室，德克萨斯大学奥斯汀分校）；Neuro-Engineering Research and Development Laboratory, The University of Texas at Austin, TX, USA（神经工程研究与开发实验室，德克萨斯大学奥斯汀分校）
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…
Robust Optimal Planning and Control of Non-Periodic Bipedal Locomotion with A Centroidal Momentum Model
Human Centered Robotics Laboratory, The University of Texas at Austin, TX, USA（以人为本的机器人实验室，德克萨斯大学奥斯汀分校）；Neuro-Engineering Research and Development Laboratory, The University of Texas at Austin, TX, USA（神经工程研究与开发实验室，德克萨斯大学奥斯汀分校）
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…
Developing robust walking controllers for bipedal robots is a challenging endeavor. Traditional model-based locomotion controllers require simplifying assumptions and careful modelling; any small errors can result in unstable control. To address these challenges for bipedal locomotion, we present a model-free reinforcement learning framework for training robust locomotion policies in simulation, which can then be transferred to a real bipedal Cassie robot. To facilitate sim-to-real transfer, domain randomization is used to encourage the policies to learn behaviors that are robust across variat…
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…
Descriptive Model-based Learning and Control for Bipedal Locomotion
Robert Bosch Centre for Cyber Physical Systems, Indian Institute of Science（罗伯特·博世中心，印度科学研究院）；U R Rao Satellite Center, Bengaluru, KA, India（U R Rao卫星中心，印度班加罗尔）；Visiting Faculty, Indian Institute of Science,Bengaluru and Plaksha University, Mohali（印度科学研究院访问教职，班加罗尔和Plaksha大学，莫哈利）；Cornell University, USA（康奈尔大学，美国）
In this paper, we propose a multi-domain control parameter learning framework that combines Bayesian Optimization (BO) and Hybrid Zero Dynamics (HZD) for locomotion control of bipedal robots. We leverage BO to learn the control parameters used in the HZD-based controller. The learning process is firstly deployed in simulation to optimize different control parameters for a large repertoire of gaits. Next, to tackle the discrepancy between the simulation and the real world, the learning process is applied on the physical robot to learn for corrections to the control parameters learned in simulat…
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…
Adaptive Step Duration for Accurate Foot Placement: Achieving Robust Bipedal Locomotion on Terrains with Restricted Footholds
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）；Electrical and Computer Engineering, The Ohio State University（电气与计算机工程系，俄亥俄州立大学）
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…
Stable Walking for Bipedal Locomotion under Foot-Slip via Virtual Nonholonomic Constraints
Centre for Automation and Robotics (CSIC-UPM)（自动化与机器人中心（CSIC-UPM））；Comillas Pontifical University（科米利亚斯主教大学）；IE University（IE大学）；University of Michigan（密歇根大学）
Low-dimensional models are ubiquitous in the bipedal robotics literature. On the one hand is the community of researchers that bases feedback control design on pendulum models selected to capture the center of mass dynamics of the robot during walking. On the other hand is the community that bases feedback control design on virtual constraints, which induce an exact low-dimensional model in the closed-loop system. In the first case, the low-dimensional model is valued for its physical insight and analytical tractability. In the second case, the low-dimensional model is integral to a rigorous a…
This paper combines episodic learning and control barrier functions in the setting of bipedal locomotion. The safety guarantees that control barrier functions provide are only valid with perfect model knowledge; however, this assumption cannot be met on hardware platforms. To address this, we utilize the notion of projection-to-state safety paired with a machine learning framework in an attempt to learn the model uncertainty as it affects the barrier functions. The proposed approach is demonstrated both in simulation and on hardware for the AMBER-3M bipedal robot in the context of the stepping…
Robust and energy-efficient bipedal locomotion in robotics is still a challenging topic. In order to address issues in this field, we can take inspiration from nature, by studying human locomotion. The Spring-Loaded Inverted Pendulum (SLIP) model has shown to be a good model for this purpose. However, the human musculoskeletal system enables us to actively modulate leg stiffness, for example when walking in rough terrain with irregular and unexpected height variations of the walking surface. This ability of varying leg stiffness is not considered in conventional SLIP-based models, and therefor…
This paper introduces a new approach to studying bipedal locomotion. The approach is based on magnetically actuated miniature robots. Building prototypes of bipedal locomotion machines has been very costly and overly complicated. We demonstrate that a magnetically actuated 0.3~gm robot, we call Big Foot, can be used to test fundamental ideas without necessitating very complex and expensive bipedal machines. We explore analytically and experimentally two age old questions in bipedal locomotion: 1. Can such robots be driven with pure hip actuation. 2. Is it better to use continuous or impulsive …
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…
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）
Recent work on sim-to-real learning for bipedal locomotion has demonstrated new levels of robustness and agility over a variety of terrains. However, that work, and most prior bipedal locomotion work, have not considered locomotion under a variety of external loads that can significantly influence the overall system dynamics. In many applications, robots will need to maintain robust locomotion under a wide range of potential dynamic loads, such as pulling a cart or carrying a large container of sloshing liquid, ideally without requiring additional load-sensing capabilities. In this work, we ex…
Indian Institute of Technology (BHU) Varanasi（印度理工学院（巴纳拉斯印度教大学）瓦拉纳西分校）；Indian Institute of Technology Roorkee（印度理工学院鲁尔基分校）；Ohio State University（俄亥俄州立大学）；Indian Institute of Science（印度科学学院）
In this paper, with a view toward deployment of light-weight control frameworks for bipedal walking robots, we realize end-foot trajectories that are shaped by a single linear feedback policy. We learn this policy via a model-free and a gradient-free learning algorithm, Augmented Random Search (ARS), in the two robot platforms Rabbit and Digit. Our contributions are two-fold: a) By using torso and support plane orientation as inputs, we achieve robust walking on slopes of up to 20 degrees in simulation. b) We demonstrate additional behaviors like walking backwards, stepping-in-place, and recov…
University of Zurich（苏黎世大学）；Ghent University（根特大学）；Fondazione Santa Lucia（圣卢西亚基金会）
Bipedal locomotion is a phenomenon that still eludes a fundamental and concise mathematical understanding. Conceptual models that capture some relevant aspects of the process exist but their full explanatory power is not yet exhausted. In the current study, we introduce the robustness criterion which defines the conditions for stable locomotion when steps are taken with imprecise angle of attack. Intuitively, the necessity of a higher precision indicates the difficulty to continue moving with a given gait. We show that the spring-loaded inverted pendulum model, under the robustness criterion, …
MOBIUS: A Multi-Modal Bipedal Robot that can Walk, Crawl, Climb, and Roll
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）；Robotic Systems Lab（机器人系统实验室）；Robotics and Mechanisms Laboratory（机器人与机构实验室）；Department of Mechanical and Aerospace Engineering, University of California, Los Angeles（加州大学洛杉矶分校机械与航空航天工程系）
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…
TOLEBI: Learning Fault-Tolerant Bipedal Locomotion via Online Status Estimation and Fallibility Rewards
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）；Artificial Intelligence Institute (AIIS), Seoul National University（人工智能研究院（AIIS），首尔国立大学）；Advanced Institutes of Convergence Technology (AICT), Suwon（融合技术高级研究院（AICT），Suwon）
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…
