Using Repetitive Control to Enhance Force Control During Human–Robot Interaction in Quasi-Periodic Tasks

We investigated the use of repetitive control (RC) to enhance force control during human-robot interaction in quasi-periodic tasks. We first developed a two-mass spring damper model and formulated three different RCs under force control: a nth 1 order RC (RC-1), a nth 3 order RC designed for random period error (RC-RPE), and a nth 3 order RC designed for constant period error (RC-RPE). Then, we quantified the performance of these three RCs through simulations and experiments conducted on a bench top linear platform, subject to nominal cyclical inputs (input signal and RC frequency: 0.5 Hz), and subject to inputs with random and constant period errors. During evaluation, we compared the performance achieved with the RCs with the one achievable with a passive proportional controller (PPC), subject to known theoretical limits for passivity and coupled stability. In nominal simulation conditions, the RC-1 reduced force error most effectively to 0.7% of the error measured with PPC. In real-world nominal experiments the RC-RPE most effectively reduced force error to 17% of the error achieved with the PPC. Subject to inputs with constant period errors, the three RCs performed similarly and better than PPC for period error values below 0.02 Hz, with the RC-CPE performing the best above 0.02 Hz period error. Subject to inputs with random period errors, all RCs performed better than PPC up to 0.09 Hz of period error, with RC-1 significantly outperforming the two other RCs. Our results indicate that RC can be successfully integrated into force control schemes to improve performance beyond the one achievable with a PPC, in the range of period variability expected in applications such as assistance or rehabilitation of cyclical human movements.