In restoring motor functions of paralyzed extremities by functional electrical stimulation (FES), determination of stimulus intensities of many muscles in multichannel control is an ill-posed problem because of redundancy in the input (stimulus intensity)-output (joint angle) relationship of the musculoskeletal system. In this paper, we use a multi-input and multi-output PID controller and propose a parameter determination method for the controller, which can solve the ill-posed problem in closed-loop control. In the parameter determination process, the stimulus intensity-joint angle characteristics of all muscles controlled were measured first. The elements of the matrix that transforms stimulus intensities into joint angles were determined by linear approximation of the measured characteristics. Then a generalized inverse matrix of the transformation matrix was calculated. The generalized inverse matrix and an expanded CHR method were used to determine the parameters of the PID controller. The PID controller was examined in tracking control on several trajectories of two-degree-of-freedom movement of the wrist joint with neurologically intact subjects. Electrical stimulation was applied to four muscles relating to the wrist joint movements through surface electrodes. The tracking control was achieved generally with good performance under different conditions of the gravitational effect. The new method proposed in this paper was found to provide a solution of the ill-posed problem. Multichannel closed-loop FES control of the wrist joint could be realized with this method.
- Closed-loop control
- Functional electrical stimulation
- Ill-posed problem
- PID control