Gain scheduling control of functional electrical stimulation for assisted standing up and sitting down in paraplegia: a simulation study

This paper reports on a simulation study that concerns the design of a non-linear controller for the standing up and the sitting down of a paraplegic patient by means of functional electrical stimulation. The simulations refer to a specific experimental device developed at the Fondazione Don Gnocchi (Italy). This is a seesaw, with the patient on one side and a weight on the other side. The patient is seated so that its posture can be fully known in real-time by continuously monitoring the knee joint angle. By delivering a suitable electrical stimulation to the quadriceps muscles groups, the patient can be raised and made to sit via smooth movements. Hitherto, the only feedback control law, which has been implemented in this area, is based on a PID controller and usually provides poor tracking performances. Hence, in this work, a non-linear gain scheduling controller has been designed and tested in a series of simulation experiments. The controller is tuned following a gain scheduling strategy: a set of local linear quadratic controllers is designed using a set of linear tangent models. A global non-linear gain scheduled controller is then obtained via interpolation. The gain- scheduled controller is implemented following an advanced strategy that guarantees that the so-called linearization property holds.