Using Repetitive Control with Force Feedback to Reduce Impedance of Exoskeletons for Gait Training

Transparent interaction, or the reduction of human-robot interaction forces, is an important quality of gait training exoskeletons. In this paper, we investigate the feasibility of using a repetitive controller for reducing impedance of gait training exoskeletons using force feedback. We used a two-mass spring damper model system, and simulated the application of repetitive force controllers with the objective of reducing the end-point impedance of the distal mass. We designed and applied three repetitive controllers: a 1st order, a 2nd order designed for random signal period error, and a 2nd order designed for constant signal period error. We compared these three repetitive controllers subject to plant model parameter error, random signal period error, and constant signal period error. Numerical simulations under nominal conditions show that via repetitive force control, it is possible to reduce the endpoint impedance to the targeted magnitude and RMSE force below the limit achievable with force controllers while guaranteeing passivity. Furthermore, we established that the application of a 2nd order repetitive controller designed for random period error is highly robust to random period error - exceeding the performance of the passive proportional controller up to 30% error of nominal frequency. Furthermore, this 2nd order repetitive controller designed for random period error maintains a 100% convergence rate through 60% plant parameter error.