We study the problem of realizing the full spectrum of bipedal locomotion on a real robot with sim-to-real reinforcement learning (RL). A key challenge of learning legged locomotion is describing different gaits, via reward functions, in a way that is intuitive for the designer and specific enough to reliably learn the gait across different initial random seeds or hyperparameters. A common approach is to use reference motions (e.g. trajectories of joint positions) to guide learning. However, finding high-quality reference motions can be difficult and the trajectories themselves narrowly constrain the space of learned motion. At the other extreme, reference-free reward functions are often underspecified (e.g. move forward) leading to massive variance in policy behavior, or are the product of significant reward-shaping via trial-and-error, making them exclusive to specific gaits. In this work, we propose a reward-specification framework based on composing simple probabilistic periodic costs on basic forces and velocities. We instantiate this framework to define a parametric reward function with intuitive settings for all common bipedal gaits - standing, walking, hopping, running, and skipping. Using this function we demonstrate successful sim-to-real transfer of the learned gaits to the bipedal robot Cassie, as well as a generic policy that can transition between all of the two-beat gaits.
Bipedal walking is one of the most difficult but exciting challenges in robotics. The difficulties arise from the complexity of high-dimensional dynamics, sensing and actuation limitations combined with real-time and computational constraints. Deep Reinforcement Learning (DRL) holds the promise to address these issues by fully exploiting the robot dynamics with minimal craftsmanship. In this paper, we propose a novel DRL approach that enables an agent to learn omnidirectional locomotion for humanoid (bipedal) robots. Notably, the locomotion behaviors are accomplished by a single control policy…
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（Agility Robotics（敏捷机器人公司））
Recently, work on reinforcement learning (RL) for bipedal robots has successfully learned controllers for a variety of dynamic gaits with robust sim-to-real demonstrations. In order to maintain balance, the learned controllers have full freedom of where to place the feet, resulting in highly robust gaits. In the real world however, the environment will often impose constraints on the feasible footstep locations, typically identified by perception systems. Unfortunately, most demonstrated RL controllers on bipedal robots do not allow for specifying and responding to such constraints. This missi…
Sun Yat-sen University（中山大学）；University of Oxford（牛津大学）
Controlling a non-statically bipedal robot is challenging due to the complex dynamics and multi-criterion optimization involved. Recent works have demonstrated the effectiveness of deep reinforcement learning (DRL) for simulation and physical robots. In these methods, the rewards from different criteria are normally summed to learn a single value function. However, this may cause the loss of dependency information between hybrid rewards and lead to a sub-optimal policy. In this work, we propose a novel reward-adaptive reinforcement learning for biped locomotion, allowing the control policy to …
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…
Ohio State University（俄亥俄州立大学）；Southern University of Science and Technology (SUSTech)（南方科技大学）
In this paper, a hierarchical and robust framework for learning bipedal locomotion is presented and successfully implemented on the 3D biped robot Digit built by Agility Robotics. We propose a cascade-structure controller that combines the learning process with intuitive feedback regulations. This design allows the framework to realize robust and stable walking with a reduced-dimension state and action spaces of the policy, significantly simplifying the design and reducing the sampling efficiency of the learning method. The inclusion of feedback regulation into the framework improves the robus…
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）
For legged robots to match the athletic capabilities of humans and animals, they must not only produce robust periodic walking and running, but also seamlessly switch between nominal locomotion gaits and more specialized transient maneuvers. Despite recent advancements in controls of bipedal robots, there has been little focus on producing highly dynamic behaviors. Recent work utilizing reinforcement learning to produce policies for control of legged robots have demonstrated success in producing robust walking behaviors. However, these learned policies have difficulty expressing a multitude of…
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）
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）
In this work, we propose a method to generate reduced-order model reference trajectories for general classes of highly dynamic maneuvers for bipedal robots for use in sim-to-real reinforcement learning. Our approach is to utilize a single rigid-body model (SRBM) to optimize libraries of trajectories offline to be used as expert references in the reward function of a learned policy. This method translates the model's dynamically rich rotational and translational behaviour to a full-order robot model and successfully transfers to real hardware. The SRBM's simplicity allows for fast iteration and…
The ability to generate robust walking gaits on bipedal robots is key to their successful realization on hardware. To this end, this work extends the method of Hybrid Zero Dynamics (HZD) -- which traditionally only accounts for locomotive stability via periodicity constraints under perfect impact events -- through the inclusion of the saltation matrix with a view toward synthesizing robust walking gaits. By jointly minimizing the norm of the extended saltation matrix and the torque of the robot directly in the gait generation process, we demonstrate that the synthesized gaits are more robust t…
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…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Laban/Bartenieff Institute of Movement Studies（拉班/芭特妮芙动作研究学院）
Humans are efficient, yet expressive in their motion. Human walking behaviors can be used to walk across a great variety of surfaces without falling and to communicate internal state to other humans through variable gait styles. This provides inspiration for creating similarly expressive bipedal robots. To this end, a framework is presented for stylistic gait generation in a compass-like under-actuated planar biped model. The gait design is done using model-based trajectory optimization with variable constraints. For a finite range of optimization parameters, a large set of 360 gaits can be ge…
National Institute of Applied Sciences and Technology（国立应用科学与技术学院）
In this paper, a simple trajectory generation method for biped walking is proposed. The dynamic model of the five link bipedal robot is first reduced using several biologically inspired assumptions. A sinusoidal curve is then imposed to the ankle of the swing leg's trajectory. The reduced model is finally obtained and solved: it is an homogeneous second order differential equations with constant coefficients. The algebraic solution obtained ensures a stable rhythmic gait for the bipedal robot. It's continuous in the defined time interval, easy to implement when the boundary conditions are well…
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…
CoRIS Institute, Oregon State University（俄勒冈州立大学CoRIS研究所）；Agility Robotics（敏捷机器人公司）
Accurate and precise terrain estimation is a difficult problem for robot locomotion in real-world environments. Thus, it is useful to have systems that do not depend on accurate estimation to the point of fragility. In this paper, we explore the limits of such an approach by investigating the problem of traversing stair-like terrain without any external perception or terrain models on a bipedal robot. For such blind bipedal platforms, the problem appears difficult (even for humans) due to the surprise elevation changes. Our main contribution is to show that sim-to-real reinforcement learning (…
University of Oslo（奥斯陆大学）；Norwegian Defence Research Institute（挪威国防研究所）
Legged robots promise higher versatility and the ability to traverse much more difficult terrains than their wheeled counterparts. Even though the use of legged robots have increased drastically in the last few years, they are still not close to the performance seen from legged animals in nature. Robotic legs are typically fairly simple mechanically, and few feature an ankle joint, even though most land mammals have one. The ankle could be a key to better performance and stability for legged robots, and in this paper we investigate how the use of an ankle in a bipedal robot could improve its p…
This work presents Neural Gaits, a method for learning dynamic walking gaits through the enforcement of set invariance that can be refined episodically using experimental data from the robot. We frame walking as a set invariance problem enforceable via control barrier functions (CBFs) defined on the reduced-order dynamics quantifying the underactuated component of the robot: the zero dynamics. Our approach contains two learning modules: one for learning a policy that satisfies the CBF condition, and another for learning a residual dynamics model to refine imperfections of the nominal model. Im…
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…
Walking controllers often require parametrization which must be tuned according to some cost function. To estimate these parameters, simulations can be performed which are cheap but do not fully represent reality. Real-robot experiments, on the other hand, are more expensive and lead to hardware wear-off. In this paper, we propose an approach for combining simulations and real experiments to learn gait stabilization parameters. We use a Bayesian optimization method which selects the most informative points in parameter space to evaluate based on the entropy of the cost function to optimize. Ex…
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, …
University of São Paulo（圣保罗大学）；University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
In bipedal gait design literature, one of the common ways of generating stable 3D walking gait is by designing the frontal and sagittal controllers as decoupled dynamics. The study of the decoupled frontal dynamics is, however, still understudied if compared with the sagittal dynamics. In this paper it is presented a formal approach to the problem of frontal dynamics stabilization by extending the hybrid zero dynamics framework to deal with the frontal gait design problem.
In this paper, we holistically present a Hybrid-Linear Inverted Pendulum (H-LIP) based approach for synthesizing and stabilizing 3D foot-underactuated bipedal walking, with an emphasis on thorough hardware realization. The H-LIP is proposed to capture the essential components of the underactuated and actuated part of the robotic walking. The robot walking gait is then directly synthesized based on the H-LIP. We comprehensively characterize the periodic orbits of the H-LIP and provably derive the stepping stabilization via its step-to-step (S2S) dynamics, which is then utilized to approximate t…
Laboratoire des Sciences du Numérique de Nantes (LS2N)（南特数字科学实验室）；CNRS（法国国家科学研究中心）；Ecole Centrale de Nantes（南特中央理工学院）；Université de Nantes（南特大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）；University of Michigan（密歇根大学）
This paper seeks insight into stabilization mechanisms for periodic walking gaits in 3D bipedal robots. Based on this insight, a control strategy based on virtual constraints, which imposes coordination between joints rather than a temporal evolution, will be proposed for achieving asymptotic convergence toward a periodic motion. For planar bipeds with one degree of underactuation, it is known that a vertical displacement of the center of mass---with downward velocity at the step transition---induces stability of a walking gait. This paper concerns the qualitative extension of this type of pro…
Tsinghua University（清华大学）；Technical University of Munich（慕尼黑工业大学）
Not until recently, robust bipedal locomotion has been achieved through reinforcement learning. However, existing implementations rely heavily on insights and efforts from human experts, which is costly for the iterative design of robot systems. Also, styles of the learned motion are strictly limited to that of the reference. In this paper, we propose a new way to learn bipedal locomotion from a simple sine wave as the reference for foot heights. With the naive human insight that the two feet should be lifted up alternatively and periodically, we experimentally demonstrate on the Cassie robot …
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…
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 algorithms for the feedback-stabilised walking of bipedal humanoid robotic platforms, along with the underlying theoretical and sensorimotor frameworks required to achieve it. Bipedal walking is inherently complex and difficult to control due to the high level of nonlinearity and significant number of degrees of freedom of the concerned robots, the limited observability and controllability of the corresponding states, and the combination of imperfect actuation with less-than-ideal sensing. The presented methods deal with these issues in a multitude of ways, ranging from the …
Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院）；Technische Universität Ilmenau（伊尔默瑙工业大学）
The hybrid zero dynamics control concept for bipedal walking is extended to include a non-instantaneous double support phase. A symmetric robot that consists of five rigid body segments which are connected by four actuated revolute joints is considered. Periodic walking gaits with a constant average walking speed consists of alternating single (SSP) and double support phases (DSP). Hybrid zero dynamics control designs usually assume an instantaneous DSP, which is a severe limitation. The proposed controllers use continuous SSPs and DSPs. Transitions between both phases are modeled as instantan…
An omnidirectional closed-loop gait based on the direct feedback of orientation deviation estimates is presented in this paper. At the core of the gait is an open-loop central pattern generator. The orientation feedback is derived from a 3D nonlinear attitude estimator, and split into the relevant angular deviations in the sagittal and lateral planes using the concept of fused angles. These angular deviations from expected are used by a number of independent feedback mechanisms, including one that controls timing, to perform stabilising corrective actions. The tuning of the feedback mechanisms…
Robust Humanoid Walking on Compliant and Uneven Terrain with Deep Reinforcement Learning
CNRS-AIST JRL (Joint Robotics Laboratory) IRL, National Institute of Advanced Industrial Science and Technology (AIST), Japan（日本国家先进工业科学与技术研究院（AIST））；University of Tsukuba（筑波大学）；Department of Computer Science, Stanford University（斯坦福大学计算机科学系）
The present research as described in this paper tries to impart how imitation based learning for behavior-based programming can be used to teach the robot. This development is a big step in way to prove that push recovery is a software engineering problem and not hardware engineering problem. The walking algorithm used here aims to select a subset of push recovery problem i.e. disturbance from environment. We applied the physics at each joint of Halo with some degree of freedom. The proposed model, Halo is different from other models as previously developed model were inconsistent with data fo…
This paper presents a framework that leverages both control theory and machine learning to obtain stable and robust bipedal locomotion without the need for manual parameter tuning. Traditionally, gaits are generated through trajectory optimization methods and then realized experimentally -- a process that often requires extensive tuning due to differences between the models and hardware. In this work, the process of gait realization via hybrid zero dynamics (HZD) based optimization is formally combined with preference-based learning to systematically realize dynamically stable walking. Importa…
In this research article, we have reported periodic cellular automata rules for different gait state prediction and classification of the gait data using extreme machine Leaning (ELM). This research is the first attempt to use cellular automaton to understand the complexity of bipedal walk. Due to nonlinearity, varying configurations throughout the gait cycle and the passive joint located at the unilateral foot-ground contact in bipedal walk resulting variation of dynamic descriptions and control laws from phase to phase for human gait is making difficult to predict the bipedal walk states. We…
The Indirect Method for Generating Libraries of Optimal Periodic Trajectories and Its Application to Economical Bipedal Walking
Institute for Adaptive Mechanical Systems, University of Stuttgart（斯图加特大学自适应机械系统研究所）；Systems Modeling and Simulation, Saarland University（萨尔大学系统建模与仿真研究所）
Dynamic walking on bipedal robots has evolved from an idea in science fiction to a practical reality. This is due to continued progress in three key areas: a mathematical understanding of locomotion, the computational ability to encode this mathematics through optimization, and the hardware capable of realizing this understanding in practice. In this context, this review article outlines the end-to-end process of methods which have proven effective in the literature for achieving dynamic walking on bipedal robots. We begin by introducing mathematical models of locomotion, from reduced order mo…
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Department of Physics, Harvard University（哈佛大学物理系）；Department of Organismic and Evolutionary Biology, Harvard University（哈佛大学有机与进化生物学系）
Walking is a common bipedal and quadrupedal gait and is often associated with terrestrial and aquatic organisms. Inspired by recent evidence of the neural underpinnings of primitive aquatic walking in the little skate Leucoraja erinacea, we introduce a theoretical model of aquatic walking that reveals robust and efficient gaits with modest requirements for body morphology and control. The model predicts undulatory behavior of the system body with a regular foot placement pattern which is also observed in the animal, and additionally predicts the existence of gait bistability between two states…
This paper presents a novel Adaptive-frequency MPC framework for bipedal locomotion over terrain with uneven stepping stones. In detail, we intend to achieve adaptive foot placement and gait period for bipedal periodic walking gait with this MPC, in order to traverse terrain with discontinuities without slowing down. We pair this adaptive-frequency MPC with a kino-dynamics trajectory optimization for optimal gait periods, center of mass (CoM) trajectory, and foot placements. We use whole-body control (WBC) along with adaptive-frequency MPC to track the optimal trajectories from the offline opt…
State-of-the-art reinforcement learning is now able to learn versatile locomotion, balancing and push-recovery capabilities for bipedal robots in simulation. Yet, the reality gap has mostly been overlooked and the simulated results hardly transfer to real hardware. Either it is unsuccessful in practice because the physics is over-simplified and hardware limitations are ignored, or regularity is not guaranteed, and unexpected hazardous motions can occur. This paper presents a reinforcement learning framework capable of learning robust standing push recovery for bipedal robots that smoothly tran…
CNRS（法国国家科学研究中心）；IRCCyN（南特中央理工学院机器人研究中心）；Nantes Atlantic University（南特大西洋大学）；University of Michigan（密歇根大学）；National Taiwan University of Science and Technology（台湾科技大学）
This paper presents three feedback controllers that achieve an asymptotically stable, periodic, and fast walking gait for a 3D (spatial) bipedal robot consisting of a torso, two legs, and passive (unactuated) point feet. The contact between the robot and the walking surface is assumed to inhibit yaw rotation. The studied robot has 8 DOF in the single support phase and 6 actuators. The interest of studying robots with point feet is that the robot's natural dynamics must be explicitly taken into account to achieve balance while walking. We use an extension of the method of virtual constraints an…
Hybrid systems, such as bipedal walkers, are challenging to control because of discontinuities in their nonlinear dynamics. Little can be predicted about the systems' evolution without modeling the guard conditions that govern transitions between hybrid modes, so even systems with reliable state sensing can be difficult to control. We propose an algorithm that allows for determining the hybrid mode of a system in real-time using data-driven analysis. The algorithm is used with data-driven dynamics identification to enable model predictive control based entirely on data. Two examples---a simula…
Ohio State University（俄亥俄州立大学）；Ottonomy Inc.（Ottonomy公司）
The popularity of mobile robots has been steadily growing, with these robots being increasingly utilized to execute tasks previously completed by human workers. For bipedal robots to see this same success, robust autonomous navigation systems need to be developed that can execute in real-time and respond to dynamic environments. These systems can be divided into three stages: perception, planning, and control. A holistic navigation framework for bipedal robots must successfully integrate all three components of the autonomous navigation problem to enable robust real-world navigation. In this p…
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 pr…
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…
Extended Hybrid Zero Dynamics for Bipedal Walking of the Knee-less Robot SLIDER
Robot Intelligence Lab, Dyson School of Design Engineering, Imperial College London, UK（机器人智能实验室，设计工程学院，伦敦帝国理工学院，英国）；Department of Aeronautics, Imperial College London, UK（航空系，伦敦帝国理工学院，英国）
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…
