Adaptive Power-Shaping-Signal Variable Impedance Control of Articulated-Soft Robots for Compliant Interaction

Articulated-soft robots (ASRs) offer a promising framework for achieving safe and adaptable physical human–robot interaction. However, their intrinsic underactuation and complex coupled dynamics pose major challenges for control design, particularly when high-order derivatives or full dynamic models are required, which is often the case. This article presents a novel adaptive power-shaping-signal control strategy that achieves accurate and safe trajectory tracking without the need for complex dynamic modeling. The proposed approach relies solely on estimates of the gravitational torque, motor damping, and inertia base parameters, thereby eliminating dependence on the most error-prone terms—namely, link inertia and Coriolis/centrifugal dynamics—and substantially simplifying implementation. This method further permits stable modulation of the sliding vector gains, effectively enabling joint-level variable impedance control. For the first time, a noncollocated (link-side) sliding vector and direct gravity compensation are both stably incorporated in the motor-side torque input, enhancing tracking robustness and interaction performance. By omitting high-order terms, the proposed scheme improves safety and computational tractability, while maintaining strong global asymptotical stability guarantees. Experimental results procured from an ASR (Baxter) reveal that not only does the proposed scheme improve interactional performance, but that it also leads to a gradual diminution of the link-position tracking error/s.