Relaxed state-independent stability constraints for the desired variable impedance model

Variable impedance control (VIC) improves robotic performance in complex tasks, but time-varying impedance parameters may destabilize the system. This paper investigates stability constraints for the desired variable impedance model (DVIM). By leveraging an invariance-like theorem for non-autonomous systems, two relaxed state-independent global uniform exponential stability (GUES) constraints are derived for the DVIM under zero external force. Compared with existing results, the proposed constraints are less conservative and are applicable to general impedance matrices. The first constraint allows non-strict inequalities, whereas the second admits damping that is neither positive definite nor differentiable and does not impose an upper bound on the stiffness rate of variation. Based on an input-to-state stability (ISS) framework, the proposed constraints guarantee bounded DVIM states under bounded external forces. Robustness of the VIC framework enforcing state-independent stability constraints is further established in the presence of bounded trajectory tracking errors and bounded external force measurement errors. Simulation and experimental results validate the proposed findings.