Input to State Stability of Bipedal Walking Robots: Application to DURUS

Bipedal robots are a prime example of systems which exhibit highly nonlinear dynamics, underactuation, and undergo complex dissipative impacts. This paper discusses methods used to overcome a wide variety of uncertainties, with the end result being stable bipedal walking. The principal contribution of this paper is to establish sufficiency conditions for yielding input to state stable (ISS) hybrid periodic orbits, i.e., stable walking gaits under model-based and phase-based uncertainties. In particular, it will be shown formally that exponential input to state stabilization (e-ISS) of the continuous dynamics, and hybrid invariance conditions are enough to realize stable walking in the 23-DOF bipedal robot DURUS. This main result will be supported through successful and sustained walking of the bipedal robot DURUS in a laboratory environment.Comment: 16 pages, 10 figure

Dynamic Walking with Compliance on a Cassie Bipedal Robot

The control of bipedal robotic walking remains a challenging problem in the domains of computation and experiment, due to the multi-body dynamics and various sources of uncertainty. In recent years, there has been a rising trend towards model reduction and the design of intuitive controllers to overcome the gap between assumed model and reality. Despite its viability in practical implementation, this local representation of true dynamics naturally indicate limited scalibility towards more dynamical behaviors. With the goal of moving towards increasingly dynamic behaviors, we leverage the detailed full body dynamics to generate controllers for the robotic system which utilizes compliant elements in the passive dynamics. In this process, we present a feasible computation method that yields walking trajectories for a highly complex robotic system. Direct implementation of these results on physical hardware is also performed with minimal tuning and heuristics. We validate the suggested method by applying a consistent control scheme across simulation, optimization and experiment, the result is that the bipedal robot Cassie walks over a variety of indoor and outdoor terrains reliably

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

Realizing Dynamic and Efficient Bipedal Locomotion on the Humanoid Robot DURUS

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.DOI: 10.1109/ICRA.2016.7487325This paper presents the methodology used to achieve efficient and dynamic walking behaviors on the prototype humanoid robotics platform, DURUS. As a means of providing a hardware platform capable of these behaviors, the design of DURUS combines highly efficient electromechanical components with “control in the loop” design of the leg morphology. Utilizing the final design of DURUS, a formal framework for the generation of dynamic walking gaits which maximizes efficiency by exploiting the full body dynamics of the robot, including the interplay between the passive and active elements, is developed. The gaits generated through this methodology form the basis of the control implementation experimentally realized on DURUS; in particular, the trajectories generated through the formal framework yield a feedforward control input which is modulated by feedback in the form of regulators that compensate for discrepancies between the model and physical system. The end result of the unified approach to control-informed mechanical design, formal gait design and regulator-based feedback control implementation is efficient and dynamic locomotion on the humanoid robot DURUS. In particular, DURUS was able to demonstrate dynamic locomotion at the DRC Finals Endurance Test, walking for just under five hours in a single day, traveling 3.9 km with a mean cost of transport of 1.61-the lowest reported cost of transport achieved on a bipedal humanoid robot

Input to State Stabilizing Control Lyapunov Functions for Robust Bipedal Robotic Locomotion

This paper analyzes the input to state stability properties of controllers which stabilize hybrid periodic orbits. Systems that are input to state stable tend to be robust to modeling and sensing uncertainties. The main contribution of this paper is in the construction of control Lyapunov functions that do not just stabilize, but also input to state stabilize a given hybrid system. Bipedal robotic walking, which can be naturally modeled as a hybrid system, is analyzed under this class of controllers. Specifically, we will select a class of controllers via rapidly exponentially stabilizing control Lyapunov functions that stabilize bipedal robotic walking; typically modeled as hybrid periodic orbits. We will show with simulation results that given the control Lyapunov functions and the associated set of stabilizing controllers, there exist input to state stabilizing control Lyapunov functions and the associated set of controllers that input to state stabilize the given periodic orbit

Input to State Stabilizing Control Lyapunov Functions for Robust Bipedal Robotic Locomotion

This paper analyzes the input to state stability properties of controllers which stabilize hybrid periodic orbits. Systems that are input to state stable tend to be robust to modeling and sensing uncertainties. The main contribution of this paper is in the construction of control Lyapunov functions that do not just stabilize, but also input to state stabilize a given hybrid system. Bipedal robotic walking, which can be naturally modeled as a hybrid system, is analyzed under this class of controllers. Specifically, we will select a class of controllers via rapidly exponentially stabilizing control Lyapunov functions that stabilize bipedal robotic walking; typically modeled as hybrid periodic orbits. We will show with simulation results that given the control Lyapunov functions and the associated set of stabilizing controllers, there exist input to state stabilizing control Lyapunov functions and the associated set of controllers that input to state stabilize the given periodic orbit

A hybrid systems and optimization-based control approach to realizing multi-contact locomotion on transfemoral prostheses

This paper presents a systematic methodology utilizing multi-domain hybrid system models and optimization based controllers to achieve human-like multi-contact prosthetic walking experimentally on a custom-built prosthesis: AMPRO. Inspired by previous work that realized multi-contact locomotion on a bipedal robot AMBER2, a hybrid system based optimization problem is proposed leveraging the framework of multi-domain hybrid systems. Utilizing a reference human gait coupled with physical constraints, the end result of this optimization problem is stable multi-contact prosthetic gaits that can be implemented on the prostheses 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. Additionally, the resulting multi-contact prosthetic walking captures the essentials of natural human walking both kinematically and kinetically

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

© 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.DOI: 10.1109/TASE.2016.2524528Lower-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 multi-domain hybrid system models and optimization-based controllers to achieve human-like multi-contact prosthetic walking on a custom-built prosthesis: AMPRO. To achieve this goal, unimpaired human locomotion data is collected and the nominal multi-contact human gait is studied. Inspired by previous work which realized multi-contact locomotion on a bipedal robot AMBER2, a hybrid system based optimization problem utilizing the collected reference human gait as reference is utilized to formally design stable multi-contact 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 multi-contact prosthetic walking captures the essentials of natural human walking both kinematically and kinetically

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