Matthew J. Powell

Dynamically stable bipedal robotic walking with NAO via human-inspired hybrid zero dynamics

This paper demonstrates the process of utilizing human locomotion data to formally design controllers that yield provably stable robotic walking and experimentally realizing these formal methods to achieve dynamically stable bipedal robotic walking on the NAO robot. Beginning with walking data, outputs---or functions of the kinematics---are determined that result in a low-dimensional representation of human locomotion. These same outputs can be considered on a robot, and human-inspired control is used to drive the outputs of the robot to the outputs of the human. An optimization problem is presented that determines the parameters of this controller that provide the best fit of the human data while simultaneously ensuring partial hybrid zero dynamics. The main formal result of this paper is a proof that these same parameters result in a stable hybrid periodic orbit with a fixed point that can be computed in closed form. Thus, starting with only human data we obtain a stable walking gait for the bipedal robot model. These formal results are validated through experimentation: implementing the stable walking found in simulation on NAO results in dynamically stable robotic walking that shows excellent agreement with the simulated behavior from which it was derived.

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.

Towards the Unification of Locomotion and Manipulation through Control Lyapunov Functions and Quadratic Programs

This paper presents the first steps toward unifying locomotion controllers and algorithms with whole-body control and manipulation. A theoretical framework for this unification will be given based upon quadratic programs utilizing control Lyapunov functions. In particular, we will first consider output based feedback linearization strategies for locomotion together with whole-body control methods for manipulation. We will show that these two traditionally disjoint methods are equivalent through the correct choice of controller. We will then present a method for unifying these two methodologies through the use of control Lyapunov functions presented in the form of a quadratic program. In addition, it will be shown that these controllers can be combined with force-based control to achieve locomotion and force-based manipulation in a single framework. Finally, simulation results will be presented demonstrating the validity of the proposed framework.

Sufficient conditions for the Lipschitz continuity of QP-based multi-objective control of humanoid robots

In this paper we analyze the continuity properties of feedback controllers that are formulated as state-dependent quadratic programs (QP), with specific application to motion control for humanoid robots. With a desire to achieve multiple simultaneous goals in locomotion and manipulation, we develop a generalized QP-based control law through the use of multiple control Lyapunov functions (CLFs). Motivated by simulation studies showing cases where QP-based control loses Lipschitz continuity, the main result of this paper is a set of sufficient conditions under which such continuity properties will hold. This result provides conditions under which any number of tasks encoded as CLFs can be simultaneously exponentially stabilized. Finally, these results are demonstrated in a simulation of a simple humanoid robot climbing a vertical ladder.

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.

Motion primitives for human-inspired bipedal robotic locomotion: walking and stair climbing

This paper presents an approach to the development of bipedal robotic control techniques for multiple locomotion behaviors. Insight into the fundamental behaviors of human locomotion is obtained through the examination of experimental human data for walking on flat ground, upstairs and downstairs. Specifically, it is shown that certain outputs of the human, independent of locomotion terrain, can be characterized by a single function, termed the extended canonical human function. Optimized functions of this form are tracked via feedback linearization in simulations of a planar robotic biped walking on flat ground, upstairs and downstairs - these three modes of locomotion are termed “motion primitives.” A second optimization is presented, which yields controllers that evolve the robot from one motion primitive to another - these modes of locomotion are termed “motion transitions.” A final simulation is given, which shows the controlled evolution of a robotic biped as it transitions through each mode of locomotion over a pyramidal staircase.

Planar multi-contact bipedal walking using hybrid zero dynamics

This paper presents a method for achieving planar multi-phase, multi-contact robotic walking using human inspired control and optimization. The walking presented contains phases with differing degrees of actuation including over-actuated double support, fully-actuated single support, and under-actuated single support via heel lift. An optimization methodology for generating walking gaits using partial hybrid zero dynamics will be presented. It will be shown that this method yields periodic, multi-contact locomotion. Simulation results for the three domain walking under standard Input-Output Linearization control will be presented.

Speed regulation in 3D robotic walking through motion transitions between Human-Inspired partial hybrid zero dynamics

This paper employs the Human-Inspired Control framework in the formal design, optimization and implementation of controllers for 3D bipedal robotic walking. In this framework, controllers drive the robot to a low-dimensional representation, termed the partial hybrid zero dynamics, which is shaped by the parameters of the outputs describing human locomotion data. The main result of this paper is the use of partial hybrid zero dynamics in an optimization problem to compute physical constraints on the robot, without integrating the dynamics of the system, and while simultaneously yielding provably stable walking controllers for a 3D robot model. Controllers corresponding to various walking speeds are obtained through a second speed regulation optimization, and formal methods are presented which provide smooth transitions between walking speeds. These formal results are demonstrated through simulation and utilized to obtain 3D walking experimentally with the NAO robot.

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.

Model predictive control of underactuated bipedal robotic walking

This paper addresses the problem of controlling underactuated bipedal walking robots in the presence of actuator torque saturation. The proposed method synthesizes elements of the Human-Inspired Control (HIC) approach for generating provably-stable walking controllers, rapidly exponentially stabilizing control Lyapunov functions (RES-CLFs) and standard model predictive control (MPC). Specifically, the proposed controller uses feedback linearization to construct a linear control system describing the dynamics of the walking outputs. The input to this linear system is designed to be the solution of a MPC-based Quadratic Program which minimizes the sum of the values of a RES-CLF-describing the walking control objectives-over a finite-time horizon. Future values of the torque constraints are mapped into the linear control system using the Hybrid Zero Dynamics property of HIC and subsequently incorporated in the Quadratic Program. The proposed method is implemented in a rigid-body dynamics simulation and initial experiments with the Durus robot.