Reachability Analysis for Robustness Evaluation of the Sit-To-Stand Movement for Powered Lower Limb Orthoses

TL;DR

This paper presents a sensitivity-based method to compute over-approximations of reachable states in a powered lower limb orthosis system, enabling robustness evaluation of control strategies during the Sit-To-Stand movement.

Contribution

It introduces a novel sensitivity-based approach for reachability analysis of nonlinear systems with parameter uncertainties, applied to a robotic orthosis model.

Findings

Over-approximations effectively capture worst-case trajectories.

The method assesses the robustness of LQR control during Sit-To-Stand.

Results demonstrate the approach's utility for safety and performance evaluation.

Abstract

A sensitivity-based approach for computing over-approximations of reachable sets, in the presence of constant parameter uncertainties and a single initial state, is used to analyze a three-link planar robot modeling a Powered Lower Limb Orthosis and its user. Given the nature of the mappings relating the state and parameters of the system with the inputs, and outputs describing the trajectories of its Center of Mass, reachable sets for their respective spaces can be obtained relying on the sensitivities of the nonlinear closed-loop dynamics in the state space. These over-approximations are used to evaluate the worst-case performances of a finite time horizon linear-quadratic regulator (LQR) for controlling the ascending phase of the Sit-To-Stand movement.