Separable Control Lyapunov Functions with Application to Prostheses

This letter extends bipedal trajectory tracking methods to prostheses to enable construction of a class of model-dependent prosthesis controllers using locally available sensor information. The rapidly exponentially stabilizing control Lyapunov functions (RES-CLFs) developed for bipedal robots guarantee stability of the hybrid zero dynamics in the presence of impacts that occur in walking. These methods cannot be directly applied to prostheses because of the unknown human dynamics. We overcome this challenge with two RES-CLFs, one for the prosthesis subsystem and another for the remaining human system. Further, we outline a method to construct these RES-CLFs for this type of separable system by first constructing separable CLFs for partially feedback linearizable systems. This letter develops a class of separable subsystem controllers that rely only on local information but provide formal guarantees of stability for the full hybrid system with zero dynamics

Separable Control Lyapunov Functions with Application to Prostheses

This letter extends bipedal trajectory tracking methods to prostheses to enable construction of a class of model-dependent prosthesis controllers using locally available sensor information. The rapidly exponentially stabilizing control Lyapunov functions (RES-CLFs) developed for bipedal robots guarantee stability of the hybrid zero dynamics in the presence of impacts that occur in walking. These methods cannot be directly applied to prostheses because of the unknown human dynamics. We overcome this challenge with two RES-CLFs, one for the prosthesis subsystem and another for the remaining human system. Further, we outline a method to construct these RES-CLFs for this type of separable system by first constructing separable CLFs for partially feedback linearizable systems. This letter develops a class of separable subsystem controllers that rely only on local information but provide formal guarantees of stability for the full hybrid system with zero dynamics

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

Torque Saturation in Bipedal Robotic Walking through Control Lyapunov Function Based Quadratic Programs

This paper presents a novel method for directly incorporating user-defined control input saturations into the calculation of a control Lyapunov function (CLF)-based walking controller for a biped robot. Previous work by the authors has demonstrated the effectiveness of CLF controllers for stabilizing periodic gaits for biped walkers, and the current work expands on those results by providing a more effective means for handling control saturations. The new approach, based on a convex optimization routine running at a 1 kHz control update rate, is useful not only for handling torque saturations but also for incorporating a whole family of user-defined constraints into the online computation of a CLF controller. The paper concludes with an experimental implementation of the main results on the bipedal robot MABEL

Constructions of Strict Lyapunov Functions for Discrete Time and Hybrid Time-Varying Systems

We provide explicit closed form expressions for strict Lyapunov functions for time-varying discrete time systems. Our Lyapunov functions are expressed in terms of known nonstrict Lyapunov functions for the dynamics and finite sums of persistency of excitation parameters. This provides a discrete time analog of our previous continuous time Lyapunov function constructions. We also construct explicit strict Lyapunov functions for systems satisfying nonstrict discrete time analogs of the conditions from Matrosov's Theorem. We use our methods to build strict Lyapunov functions for time-varying hybrid systems that contain mixtures of continuous and discrete time evolutions.Comment: 14 pages. Accepted for publication in Nonlinear Analysis: Hybrid Systems and Applications on September 6, 200

Global Exponential Attitude Tracking Controls on SO(3)

This paper presents four types of tracking control systems for the attitude dynamics of a rigid body. First, a smooth control system is constructed to track a given desired attitude trajectory, while guaranteeing almost semi-global exponential stability. It is extended to achieve global exponential stability by using a hybrid control scheme based on multiple configuration error functions. They are further extended to obtain robustness with respect to a fixed disturbance using an integral term. The resulting robust, global exponential stability for attitude tracking is the unique contribution of this paper, and these are developed directly on the special orthogonal group to avoid singularities of local coordinates, or ambiguities associated with quaternions. The desirable features are illustrated by numerical examples