Optimal Functional Electrical Stimulation patterns synthesis for knee joint control

The work presented in this paper concerns the synthesis of Functional Electrical Stimulation (FES) patterns to generate movements of paralysed limbs for spinal cord injured patients. We propose an approach based on a nonlinear optimization formulation that may encounter physiological and technological constraints. The study considers a biomechanical knee model and the associated agonist/antagonist muscles. The goal of this method is to synthesize optimal patterns which minimize the muscular activities and/or tracking trajectory errors in order to reduce the muscular fatigue while achieving a desired movement. Different tests have been performed and the results compared with regard to the energetic balance. The approach is illustrated in simulation with: 1) sinusoidal desired knee joint trajectory, 2) optimal reference knee joint trajectory and 3) without explicit reference knee joint trajectory. The simulations have been performed with model parameters estimated from real subject data. We show that the trajectory tracking presents high energy consumption which demonstrates the inappropriateness of classical robotics methods for musculoskeletal system. Instead, minimization of muscle activation only gives better results with regard to energy consumption, still with a reasonnable trajectory tracking error.