Robust observer-based tracking control under actuator constraints for power-assisted wheelchairs

Abstract

Power-assisted wheelchairs (PWA) is an important growing market. The goal is to provide electrical assistive kits that are able to cope with a large family of disabled people and to equip a large variety of wheelchairs. This work is made in collaboration with Autonomad Mobility, a company that designs the hardware and sells Power-Assistance kits for wheelchairs. Several crucial issues arise, e.g. how to assist any Person with Reduced Mobility (PRM)? How to detect user’s intentions? how to cope with the lack of system information due to excessive sensor costs. Effectively, due to the variety of wheelchairs and the different unknown PRM characteristics (mass, height, force, etc.) and pathologies, it is unrealistic to provide a solution using a precise modeling of the whole system including the wheelchair, the PRM and the ground conditions. However, proposing a safe and secure solution is obviously mandatory for this application. In particular, an on-the-market solution should be also smooth and friendly for the end-user. Estimation of the human torques is a first key point to achieve such a solution, which has been already studied in our previous works. This paper exploits these estimation results to propose a robust control law for PWA systems under saturation constraints. These constraints are unavoidable due to regulations on maximum authorized speed. From a control point of view, it resumes to an output feedback control with partially unknown references (desired speed, direction), unknown parameters (wheelchair and PRM masses, available force, ground characteristics) and input constraints. Finding an effective solution for this constrained output feedback tracking control still remains open. In this paper, we propose a two-step control design using quasi Linear Parameter Varying (q-LPV) formulation to solve this challenging control problem, i.e., first design an observer for state and unknown input estimation, and second propose a robust control scheme under parameter variations and input saturations. The control procedure is reformulated as convex optimization problems involving linear matrix inequality (LMI) constraints that can be efficiently solved with standard numerical solvers. Simulations and real-time experiments are proposed to show the effectiveness of the solution.