Huihua Zhao

Human-Inspired Multi-Contact Locomotion with AMBER2

This paper presents a methodology for translating a key feature encoded in human locomotion - multi-contact behavior - to a physical 2D bipedal robot, AMBER2, by leveraging novel controller design, optimization methods, and software structures for the translation to hardware. This paper begins with the analysis of human locomotion data and uses it to motivate the construction of a hybrid system model representing a multi-contact robotic walking gait. By again looking to human data for inspiration, human-inspired controllers are developed and used in the formulation of an optimization problem that yields stable human-like multi-domain walking in simulation. These formal results are translated to hardware implementation via a novel dynamic trajectory generation strategy. Finally, the specific software structures utilized to translate these trajectories to hardware are presented. The end result is experimentally realized stable robotic walking with remarkably human-like multi-contact foot behaviors.

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.

Learning impedance controller parameters for lower-limb prostheses

Impedance control is a common framework for control of lower-limb prosthetic devices. This approach requires choosing many impedance controller parameters. In this paper, we show how to learn these parameters for lower-limb prostheses by observation of unimpaired human walkers. We validate our approach in simulation of a transfemoral amputee, and we demonstrate the performance of the learned parameters in a preliminary experiment with a lower-limb prosthetic device.

Human-inspired walking via unified PD and impedance control.

This paper describes a torque control scheme unifying feedback PD control and feed-forward impedance control to realize human-inspired walking on a novel planar footed bipedal robot: AMBER2. It starts with high fidelity modeling of the robot including nonlinear dynamics, motor model, and impact dynamics. Human data is then used by an optimization algorithm to produce a human-like gait that can be implemented on the robot. To realize the bipedal walking, first a PD controller is utilized to track the optimized trajectory. Next, impedance control parameters are estimated from the experimental data. Finally, the unified PD, impedance torque control law is experimentally realized on the bipedal robot AMBER2. Through the evidence of sustainable and unsupported walking on AMBER2 showing high consistency with the simulated gait, the feasibility of AMBER2 walking scheme will be verified.

Quadratic programming and impedance control for transfemoral prosthesis.

This paper presents a novel optimal control strategy combining control Lyapunov function (CLF) based quadratic programs with impedance control, with the goal of improving both tracking performance and the stability of controllers implemented on transfemoral prosthesis. CLF based quadratic programs have the inherent capacity to optimally track a desired trajectory. This property is used in congruence with impedance control - implemented as a feedforward term - to realize significantly small tracking errors, while simultaneously yielding bipedal walking that is both stable and robust to disturbances. Moreover, instead of experimentally validating this on human subjects, a virtual prosthesis is attached to a robotic testbed, AMBER. The authors claim that the walking of AMBER is human like and therefore form a suitable substitute to human subjects on which a prosthetic control can be tested. Based on this idea, the proposed controller was first verified in simulation, then tested on the physical robot AMBER. The results indicate improved tracking performance, stability, and robustness to unknown disturbances.

Outputs of human walking for bipedal robotic controller design

This paper presents a method to determine outputs associated with human walking data that can be used to design controllers that achieve human-like robotic walking. We consider a collection of human outputs, i.e., functions of the kinematics computed from experimental human data, that satisfy criteria necessary for human-inspired bipedal robot control construction. These human outputs are described in a form amendable to controller design through a special class of time based functions - termed canonical walking functions. An optimization problem is presented to determine the parameters of this controller that yields the best fit to the human data that simultaneously produces stable robotic walking. The optimal value of the cost function is used as a metric to determine which human outputs result in the most “human-like” robotic walking. The human-like nature of the resulting robotic walking is verified through simulation.

Realization of nonlinear real-time optimization based controllers on self-contained transfemoral prosthesis

Lower-limb prosthesis provide a prime example of cyber-physical systems (CPSs) that interact with humans in a safety critical fashion, and therefore require the synergistic development of sensing, algorithms and controllers. With a view towards better understanding CPSs of this form, this paper presents a methodology for successfully translating nonlinear real-time optimization based controllers from bipedal robots to a novel custom built self-contained powered transfemoral prosthesis: AMPRO. To achieve this goal, we begin by collecting reference human locomotion data via Inertial measurement Units (IMUs). This data forms the basis for an optimization problem that generates virtual constraints, i.e., parametrized trajectories, for the prosthesis that provably yields walking in simulation. Leveraging methods that have proven successful in generating stable robotic locomotion, control Lyapunov function (CLF) based Quadratic Programs (QPs) are utilized to optimally track the resulting desired trajectories. The parameterization of the trajectories is determined through a combination of on-board sensing on the prosthesis together with IMU data, thereby coupling the actions of the user with the controller. Finally, impedance control is integrated into the QP yielding an optimization based control law that displays remarkable tracking and robustness, outperforming traditional PD and impedance control strategies. This is demonstrated experimentally on AMPRO through the implementation of the holistic sensing, algorithm and control framework, with the end result being stable and human-like walking.

Multi-Contact Bipedal Robotic Locomotion

This paper presents a formal framework for achieving multi-contact bipedal robotic walking, and realizes this methodology experimentally on two robotic platforms: AMBER2 and Assume The Robot Is A Sphere (ATRIAS). Inspired by the key feature encoded in human walking—multi-contact behavior—this approach begins with the analysis of human locomotion and uses it to motivate the construction of a hybrid system model representing a multi-contact robotic walking gait. Human-inspired outputs are extracted from reference locomotion data to characterize the human model or the spring-loaded invert pendulum (SLIP) model, and then employed to develop the human-inspired control and an optimization problem that yields stable multi-domain walking. Through a trajectory reconstruction strategy motivated by the process that generates the walking gait, the mathematical constructions are successfully translated to the two physical robots experimentally.

First steps toward translating robotic walking to prostheses: a nonlinear optimization based control approach

This paper presents the first steps toward successfully translating nonlinear real-time optimization based controllers from bipedal walking robots to a self-contained powered transfemoral prosthesis: AMPRO, with the goal of improving both the tracking performance and the energy efficiency of prostheses control. To achieve this goal, a novel optimization-based optimal control strategy combining control Lyapunov function based quadratic programs with impedance control is proposed. This optimization-based optimal controller is first verified on a human-like bipedal robot platform, AMBER. The results indicate improved (compared to variable impedance control) tracking performance, stability and robustness to unknown disturbances. To translate this complete methodology to a prosthetic device with an amputee, we begin by collecting reference locomotion data from a healthy subject via inertial measurement units (IMUs). This data forms the basis for an optimization problem that generates virtual constraints, i.e., parameterized trajectories, specifically for the amputee . A online optimization based controller is utilized to optimally track the resulting desired trajectories. An autonomous, state based parameterization of the trajectories is implemented through a combination of on-board sensing coupled with IMU data, thereby linking the gait progression with the actions of the user. Importantly, the proposed control law displays remarkable tracking and improved energy efficiency, outperforming PD and impedance control strategies. This is demonstrated experimentally on the prosthesis AMPRO through the implementation of a holistic sensing, algorithm and control framework, resulting in dynamic and stable prosthetic walking with a transfemoral amputee.

Multicontact Locomotion on Transfemoral Prostheses via Hybrid System Models and Optimization-Based Control

Lower-limb prostheses provide a prime example of cyber-physical systems (CPSs) requiring the synergistic development of sensing, algorithms, and controllers. With a view towards better understanding CPSs of this form, this paper presents a systematic methodology using multidomain hybrid system models and optimization-based controllers to achieve human-like multicontact prosthetic walking on a custom-built prosthesis: AMPRO. To achieve this goal, unimpaired human locomotion data is collected and the nominal multicontact human gait is studied. Inspired by previous work which realized multicontact locomotion on the bipedal robot AMBER2, a hybrid system-based optimization problem utilizing the collected reference human gait as reference is utilized to formally design stable multicontact prosthetic gaits that can be implemented on the prosthesis directly. Leveraging control methods that stabilize bipedal walking robots-control Lyapunov function-based quadratic programs coupled with variable impedance control-an online optimization-based controller is formulated to realize the designed gait in both simulation and experimentally on AMPRO. Improved tracking and energy efficiency are seen when this methodology is implemented experimentally. Importantly, the resulting multicontact prosthetic walking captures the essentials of natural human walking both kinematically and kinetically. Note to Practitioners- Variable impedance control, as one of the most popular prosthetic controllers, has been used widely on powered prostheses with notable success. However, due to the passivity of this controller, heuristic feedback is required to adjust the control parameters for different subjects and motion modes. The end result is extensive testing time for users, coupled with non-optimal performance of prostheses. Motivated by the shortcomings in the current state-of-the-art, this work proposes a novel systematic methodology-including gait generation and optimization-based control based on a multidomain hybrid system-to achieve prosthetic walking for a given subject. This method also aims to improve control optimality and efficiency while potentially reducing clinical tuning. The overarching technology utilized in this paper is the use of nominal human trajectories coupled with formal models and controllers that circumvent the need for excessive hand-tuning. In particular, rather than using a prerecorded trajectory (as is common), this work takes a different approach by using a human-inspired optimization problem to design a human-like gait for the amputee automatically. The proposed optimization framework uses the trajectory of a healthy subject as the reference and is subject to specific constraints (to ensure smooth transitions, torque and angle limitations) such that the output gait is applicable for implementation on the prosthetic device directly. The results of the offline optimization are then utilized to synthesize an online real-time optimization-based feedback controller that allows for pointwise optimal tracking on the prosthesis, thereby improving overall efficiency. The experimental results in this work suggest that this approach is able to achieve stable human-like multicontact prosthetic walking and also guarantees a more balanced performance compared to other traditional controllers (such as PD).