Virtual Contact Loop: Performance-Oriented Cartesian Impedance Synthesis for Robotic Manipulators

Abstract Cartesian impedance control is widely used to regulate physical interaction between robots and their environments. However, the configuration-dependent inertia and strong coupling of Cartesian dynamics make the systematic design of damping and stiffness matrices challenging. This paper proposes a performance-oriented Cartesian impedance synthesis method based on a virtual contact loop, termed VCL-IS. The virtual loop tracks the theoretical response of a desired impedance over a prescribed frequency range, converting impedance design into a weighted generalized-plant optimization problem. The synthesis objective combines weighted $\mathcal H_2$ and $\mathcal H_\infty$ performance with the negative spectral abscissa to balance compliance, aggregate robustness, and asymptotic convergence. Two- and six-dimensional simulations demonstrate that VCL-IS exploits dynamic coupling to achieve larger compliant displacements with low overshoot at comparable response speeds. The optimized damping and stiffness matrices exhibit interpretable modal relationships with the target bandwidth. For configuration-dependent inertia, a common quadratic Lyapunov analysis yields a sufficient admissible interval for time-varying modal frequencies, which is enforced in an SAC-based adaptation policy. Physical-robot experiments further show closer agreement between theoretical and measured six-dimensional responses than the baseline methods. These results support VCL-IS as an interpretable framework for performance-oriented synthesis and time-varying extension of coupled Cartesian impedance.