Design computed torque control for Stewart platform with uncertainty to the rehabilitation of patients with leg disabilities

Abstract

Physiotherapy is a treatment that may be required permanently by many patients. As a result, a robot that can execute physiotherapy exercises for the legs like a professional therapist with adequate performance and acceptable safety may be efficient and widely used. In this study, a robust control system for a Stewart platform with six degrees of freedom is provided. First, the Newton-Euler approach is used in conjunction with a methodology and some simplification tools to achieve explicit dynamics formulation for the Stewart platform. For the primary application of this research, which is to follow the specified trajectory of ankle rehabilitation, computed torque control law (CTCL) and polynomial chaos expansion (PCE) were used to examine and consider any uncertainty in geometric and physical parameters. In fact, this strategy integrated the uncertainties with CTCL using PCE. The suggested PCE-based CTCL eliminates the system’s nonlinearity by applying feedback linearization to evaluate generalized driving forces; hence, the nondeterministic multi-body system follows the desired direction. Uncertainties in the patient’s foot as well as the main diameter parameters of the moment of inertia of the upper platform of the Stewart robot with various uniform, beta, and normal distributions, have been analyzed. The PCE technique’s results were compared to the Monte Carlo method’s outcomes, and the strengths and weaknesses of each method were investigated. In brief, the PCE method operated far better than the Monte Carlo (MC) method in speed, accuracy, and numerical volume.