Wheelchairs are broadly accepted and are widespread because of the assistance they provide to people with limited mobility. The design of a good controller generally involves the formulation of a comprehensive wheelchair model. Most dynamic models in the literature presume non-inclined planer surfaces within-doors, and therefore fail to take the combined effects of both gravitational forces and rolling friction on the usable-traction into consideration. Wheel-slip situations are also commonly neglected. This paper contributes to wheelchair modeling by proposing and formulating a dynamic model that considers the effects of rolling friction and gravitational potential on the wheelchair’s road-load force, on both inclined and non-inclined surfaces. The dynamic model is derived through the Euler Lagrange procedure, and wheel slip is determined by an approach that reduces the convectional number of slip-detection encoders. In the closed-loop model, the input-output feedback controller is proposed for tracking the user inputs by torque compensation. The optimality of the resulting minimum-phase closed-loop system is then ensured through the performance index of the non-linear continuous-time generalized predictive control with good simulation results.
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