Ryan W. Sinnet

3D Bipedal Robotic Walking: Models, Feedback Control, and Open Problems

Abstract The fields of control and robotics are contributing to the development of bipedal robots that can realize walking motions with the stability and agility of a human being. Dynamic models for bipeds are hybrid in nature. They contain both continuous and discrete elements, with switching events that are spatially driven by unilateral constraints at ground contact and impulse-like forces that occur at foot touchdown. Control laws for these machines must be hybrid as well. The goals of this paper are threefold: highlight certain properties of the models which greatly influence the control law design; present two control design approaches; and indicate some of the many open problems.

Models, feedback control, and open problems of 3D bipedal robotic walking

The fields of control and robotics are working toward the development of bipedal robots that can realize walking motions with the stability and agility of a human being. Dynamic models for bipeds are hybrid in nature. They contain both continuous and discrete elements, with switching events that are governed by a combination of unilateral constraints and impulse-like forces that occur at foot touchdown. Control laws for these machines must be hybrid as well. The goals of this paper are fourfold: highlight certain properties of the models which greatly influence the control law design; overview the literature; present two control design approaches in depth; and indicate some of the many open problems.

Valkyrie: NASA's First Bipedal Humanoid Robot

In December 2013, 16 teams from around the world gathered at Homestead Speedway near Miami, FL to participate in the DARPA Robotics Challenge DRC Trials, an aggressive robotics competition partly inspired by the aftermath of the Fukushima Daiichi reactor incident. While the focus of the DRC Trials is to advance robotics for use in austere and inhospitable environments, the objectives of the DRC are to progress the areas of supervised autonomy and mobile manipulation for everyday robotics. NASAs Johnson Space Center led a team comprised of numerous partners to develop Valkyrie, NASAs first bipedal humanoid robot. Valkyrie is a 44 degree-of-freedom, series elastic actuator-based robot that draws upon over 18 years of humanoid robotics design heritage. Valkyries application intent is aimed at not only responding to events like Fukushima, but also advancing human spaceflight endeavors in extraterrestrial planetary settings. This paper presents a brief system overview, detailing Valkyries mechatronic subsystems, followed by a summarization of the inverse kinematics-based walking algorithm employed at the Trials. Next, the software and control architectures are highlighted along with a description of the operator interface tools. Finally, some closing remarks are given about the competition, and a vision of future work is provided.

Three-Dimensional Kneed Bipedal Walking: A Hybrid Geometric Approach

A 3D biped with knees and a hip is naturally modeled as a nontrivial hybrid system; impacts occur when the knee strikes and when the foot impacts the ground causing a switch in the dynamics governing the system. Through a variant of geometric reduction--termed functional Routhian reduction --we can reduce the dynamics on each domain of this hybrid system to obtain a planar equivalent biped. Using preexisting techniques for obtaining walking gaits for 2D bipeds, and utilizing the decoupling effect afforded by the reduction process, we design control strategies that result in stable walking gaits for the 3D biped. That is, the main result of this paper is a control law that results in 3D bipedal walking obtained through stable walking gaits for the equivalent 2D biped.

A Human-Inspired Hybrid Control Approach to Bipedal Robotic Walking

Abstract A human-inspired method for achieving bipedal robotic walking is proposed in which a hybrid model of a human is used in conjunction with experimental walking data to obtain a multi-domain hybrid system. Walking data were collected for nine test subjects; these data are analyzed in terms of the kinematics of walking. In bipedal walking, certain points on the body are constrained for various intervals throughout the gait; this phenomenon is used to formally break the gait into walking phases. The results indicate that all of the nine subjects had the same breakdown with similar times spent in each phase; in other words, this specific breakdown likely represents a canonical human model. Using this canonical breakdown, a controller is designed for a robotic model which mimics human kinematics behaviors by tracking functions of the kinematics—this controller is applied in simulation, resulting in stable walking which is remarkably humanlike in nature.

3D bipedal walking with knees and feet: A hybrid geometric approach

Motivated by the goal of obtaining more-anthropomorphic walking in bipedal robots, this paper considers a hybrid model of a 3D hipped biped with feet and locking knees. The main observation of this paper is that functional Routhian Reduction can be used to extend two-dimensional walking to three dimensions—even in the presence of periods of underactuation—by decoupling the sagittal and coronal dynamics of the 3D biped. Specifically, we assume the existence of a control law that yields stable walking for the 2D sagittal component of the 3D biped. The main result of the paper is that utilizing this controller together with “reduction control laws” yields walking in three dimensions. This result is supported through simulation.

2D bipedal walking with knees and feet: A hybrid control approach

In this paper, we consider an anthropomorphically-inspired hybrid model of a bipedal robot with locking knees and feet in order to develop a control law that results in human-like walking. The presence of feet results in periods of full actuation and periods of underactuation during the course of a step. Properties of each of these phases of walking are utilized in order to achieve a stable walking gait. In particular, we will show that using controlled symmetries in the fully-actuated domains coupled with “partial” controlled symmetries and local ankle control laws in the underactuated domains yields stable walking; this result is possible due to the amount of time which the biped spends in the fully-actuated domains. The paper concludes with simulation results along with a comparison of these results to human walking data.

Compass gait revisited: A human data perspective with extensions to three dimensions

To better understand human walking, three bipedal robotic models—starting with the compass gait biped and increasing in complexity to a 3D kneed biped—are studied with controllers of human-inspired design; these controllers are derived from experimental data measuring the kinematics of human test subjects. The collected data are examined in an attempt to classify some of the most fundamental behaviors underlying human walking; it is found that a subset of functions on the kinematics of humans can be represented as a single class of functions. The control scheme uses feedback linearization to track the human output functions on a robot. A state-based parameterization for time is introduced to make these human functions time-invariant. Simulation results indicate the existence of locally exponentially stable periodic orbits for each model of interest; these orbits represent stable, steady-state walking gaits. The application of the human-inspired control approach results in “humanlike” walking as supported by agreement between the outputs of the robot models and humans.

Bio-Inspired Feedback Control of Three-Dimensional Humanlike Bipedal Robots

Bridging contemporary techniques in bio-inspired control affords a unique perspective into human locomotion where the interplay between sagittal and coronal dynamics is understood and exploited to simplify control design. Functional Routhian reduction is particularly useful on bipeds as it decouples these dynamics, allowing for control design on a sagittallyrestricted model while providing coronal stabilization. 2D sagittal walking is designed using Human-Inspired Control which produces humanlike walking with good stability properties. This walking is then easily translated to 3D via reduction. The proposed control scheme, which is based on a fundamental understanding of human walking, is validated in both simulation and experiment.

A human-inspired framework for bipedal robotic walking design

This work seeks virtual constraints, or outputs, that are intrinsic to human walking and utilises these outputs to construct controllers which produce human-like bipedal robotic walking. Beginning with experimental human walking data, human outputs are sought, i.e., functions of the kinematics of the human over time, which provides a low-dimensional representation of human walking. It will be shown that, for these outputs, humans act like linear mass-spring-dampers; this yields a time representation of the human outputs through canonical walking functions. Combining these formulations leads to human-inspired controllers that, when utilised in an optimisation problem, provably result in robotic walking that is as ‘human-like’ as possible. This human-inspired approach is applied to multiple human output combinations, from which it is determined which output combination results in the most human-like walking for a robotic model with mean human parameters.