Learning compliant dynamical system from human demonstrations for stable force control in unknown environments

Force control in unknown environments poses a significant challenge in robotics due to the necessity of adjusting impedance to accommodate environmental uncertainties. One potential solution is to transfer human variable impedance skills for delicate force control to robots. However, due to the short duration and small displacement of the contact transients, it is difficult to collect demonstration data and learn the control strategy used by human. This paper focuses on learning a stable force control policy from human demonstration during contact transients. We first propose a human-in-the-loop method for transferring human variable impedance skills during contact transient in unknown environments. Then, we analyze human demonstration data and conclude two observations: (1) Demonstrators adjust the end-effector velocity of the robot according to the force error, such that the velocity magnitude reduces nonlinearly as the force error decreases; (2) Demonstrators modify the slope of the velocity-force error curve according to environmental stiffnesses, such that the slope magnitude decreases as environmental stiffness increases. Finally, based on these observations, we proposed a novel human-inspired force control strategy called compliant dynamical system (CDS), which requires only actual contact force and rough estimation of environmental stiffness to achieve desired force control in contact tasks. The stability of the proposed CDS is rigorously proved using Lyapunov stability theory to guarantee accurate force control performance. The effectiveness of the proposed method is validated by simulation and real-world experiments involving single-arm contact with unknown environments and dual-arm cooperative transportation of an object.