Humanoid Balancing Behavior Featured by Underactuated Foot Motion

A novel control synthesis is proposed for humanoids to demonstrate unique foot-tilting behaviors that are comparable to humans in balance recovery. Our study of model-based behaviors explains the underlying mechanism and the significance of foot tilting well. Our main algorithms are composed of impedance control at the center of mass, virtual stoppers that prevent overtilting of the feet, and postural control for the torso. The proof of concept focuses on the sagittal scenario and the proposed control is effective to produce human-like balancing behaviors characterized by active foot tilting. The successful replication of this behavior on a real humanoid proves the feasibility of deliberately controlled underactuation. The experimental validation was rigorously performed, and the data from the submodules and the entire control were presented and analyzed

Emergence of Human-comparable Balancing Behaviors by Deep Reinforcement Learning

This paper presents a hierarchical framework based on deep reinforcement learning that learns a diversity of policies for humanoid balance control. Conventional zero moment point based controllers perform limited actions during under-actuation, whereas the proposed framework can perform human-like balancing behaviors such as active push-off of ankles. The learning is done through the design of an explainable reward based on physical constraints. The simulated results are presented and analyzed. The successful emergence of human-like behaviors through deep reinforcement learning proves the feasibility of using an AI-based approach for learning humanoid balancing control in a unified framework

Dynamic and Versatile Humanoid Walking via Embedding 3D Actuated SLIP Model with Hybrid LIP Based Stepping

In this paper, we propose an efficient approach to generate dynamic and versatile humanoid walking with non-constant center of mass (COM) height. We exploit the benefits of using reduced order models (ROMs) and stepping control to generate dynamic and versatile walking motion. Specifically, we apply the stepping controller based on the Hybrid Linear Inverted Pendulum Model (H-LIP) to perturb a periodic walking motion of a 3D actuated Spring Loaded Inverted Pendulum (3D-aSLIP), which yields versatile walking behaviors of the 3D-aSLIP, including various 3D periodic walking, fixed location tracking, and global trajectory tracking. The 3D-aSLIP walking is then embedded on the fully-actuated humanoid via the task space control on the COM dynamics and ground reaction forces. The proposed approach is realized on the robot model of Atlas in simulation, wherein versatile dynamic motions are generated.Comment: 8 pages, 8 figures; To appear in Robotics and Automation Letter

Dynamic Walking: Toward Agile and Efficient Bipedal Robots

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 models that capture essential walking behaviors to hybrid dynamical systems that encode the full order continuous dynamics along with discrete footstrike dynamics. These models form the basis for gait generation via (nonlinear) optimization problems. Finally, models and their generated gaits merge in the context of real-time control, wherein walking behaviors are translated to hardware. The concepts presented are illustrated throughout in simulation, and experimental instantiation on multiple walking platforms are highlighted to demonstrate the ability to realize dynamic walking on bipedal robots that is agile and efficient

Dynamic and Versatile Humanoid Walking via Embedding 3D Actuated SLIP Model with Hybrid LIP Based Stepping

In this letter, we propose an efficient approach to generate dynamic and versatile humanoid walking with non-constant center of mass (COM) height. We exploit the benefits of using reduced order models (ROMs) and stepping control to generate dynamic and versatile walking motion. Specifically, we apply the stepping controller based on the Hybrid Linear Inverted Pendulum Model (H-LIP) to perturb a periodic walking motion of a 3D actuated Spring Loaded Inverted Pendulum (3D-aSLIP), which yields versatile walking behaviors of the 3D-aSLIP, including various 3D periodic walking, fixed location tracking, and global trajectory tracking. The 3D-aSLIP walking is then embedded on the fully-actuated humanoid via the task space control on the COM dynamics and ground reaction forces. The proposed approach is realized on the robot model of Atlas in simulation, wherein versatile dynamic motions are generated

Control Implementation of Dynamic Locomotion on Compliant, Underactuated, Force-Controlled Legged Robots with Non-Anthropomorphic Design

The control of locomotion on legged robots traditionally involves a robot that takes a standard legged form, such as the anthropomorphic humanoid, the dog-like quadruped, or the bird-like biped. Additionally, these systems will often be actuated with position-controlled servos or series-elastic actuators that are connected through rigid links. This work investigates the control implementation of dynamic, force-controlled locomotion on a family of legged systems that significantly deviate from these classic paradigms by incorporating modern, state-of-the-art proprioceptive actuators on uniquely configured compliant legs that do not closely resemble those found in nature. The results of this work can be used to better inform how to implement controllers on legged systems without stiff, position-controlled actuators, and also provide insight on how intelligently designed mechanical features can potentially simplify the control of complex, nonlinear dynamical systems like legged robots. To this end, this work presents the approach to control for a family of non-anthropomorphic bipedal robotic systems which are developed both in simulation and with physical hardware. The first is the Non-Anthropomorphic Biped, Version 1 (NABi-1) that features position-controlled joints along with a compliant foot element on a minimally actuated leg, and is controlled using simple open-loop trajectories based on the Zero Moment Point. The second system is the second version of the non-anthropomorphic biped (NABi-2) which utilizes the proprioceptive Back-drivable Electromagnetic Actuator for Robotics (BEAR) modules for actuation and fully realizes feedback-based force controlled locomotion. These systems are used to highlight both the strengths and weaknesses of utilizing proprioceptive actuation in systems, and suggest the tradeoffs that are made when using force control for dynamic locomotion. These systems also present case studies for different approaches to system design when it comes to bipedal legged robots

Reactive Stepping for Humanoid Robots using Reinforcement Learning: Application to Standing Push Recovery on the Exoskeleton Atalante

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 transfer to reality, providing only instantaneous proprioceptive observations. By combining original termination conditions and policy smoothness conditioning, we achieve stable learning, sim-to-real transfer and safety using a policy without memory nor explicit history. Reward engineering is then used to give insights into how to keep balance. We demonstrate its performance in reality on the lower-limb medical exoskeleton Atalante

Dynamic Bipedal Locomotion: From Hybrid Zero Dynamics to Control Lyapunov Functions via Experimentally Realizable Methods

Robotic bipedal locomotion has become a rapidly growing field of research as humans increasingly look to augment their natural environments with intelligent machines. In order for these robotic systems to navigate the often unstructured environments of the world and perform tasks, they must first have the capability to dynamically, reliably, and efficiently locomote. Due to the inherently hybrid and underactuated nature of dynamic bipedal walking, the greatest experimental successes in the field have often been achieved by considering all aspects of the problem; with explicit consideration of the interplay between modeling, trajectory planning, and feedback control. The methodology and developments presented in this thesis begin with the modeling and design of dynamic walking gaits on bipedal robots through hybrid zero dynamics (HZD), a mathematical framework that utilizes hybrid system models coupled with nonlinear controllers that results in stable locomotion. This will form the first half of the thesis, and will be used to develop a solid foundation of HZD trajectory optimization tools and algorithms for efficient synthesis of accurate hybrid motion plans for locomotion on two underactuated and compliant 3D bipeds. While HZD and the associated trajectory optimization are an existing framework, the resulting behaviors shown in these preliminary experiments will extend the limits of what HZD has demonstrated is possible thus far in the literature. Specifically, the core results of this thesis demonstrate the first experimental multi-contact humanoid walking with HZD on the DURUS robot and then through the first compliant HZD motion library for walking over a continuum of walking speeds on the Cassie robot. On the theoretical front, a novel formulation of an optimization-based control framework is introduced that couples convergence constraints from control Lyapunov functions (CLF)s with desirable formulations existing in other areas of the bipedal locomotion field that have proven successful in practice, such as inverse dynamics control and quadratic programming approaches. The theoretical analysis and experimental validation of this controller thus forms the second half of this thesis. First, a theoretical analysis is developed which demonstrates several useful properties of the approach for tuning and implementation, and the stability of the controller for HZD locomotion is proven. This is then extended to a relaxed version of the CLF controller, which removes a convergence inequality constraint in lieu of a conservative CLF cost within a quadratic program to achieve tracking. It is then explored how this new CLF formulation can fully leverage the planned HZD walking gaits to achieve the target performance on physical hardware. Towards this goal, an experimental implementation of the CLF controller is derived for the Cassie robot, with the resulting experiments demonstrating the first successful realization of a CLF controller for a 3D biped on hardware in the literature. The accuracy of the robot model and synthesized HZD motion library allow the real-time control implementation to regularize the CLF optimization cost about the nominal walking gait. This drives the controller to choose smooth input torques and anticipated spring torques, as well as regulate an optimal distribution of feasible ground reaction forces on hardware while reliably tracking the planned virtual constraints. These final results demonstrate how each component of this thesis were brought together to form an effective end-to-end implementation of a nonlinear control framework for underactuated locomotion on a bipedal robot through modeling, trajectory optimization, and then ultimately real-time control.</p