MDIR: A Task-Manifold Impedance Retargeting Method for Contact-Rich Teleoperation

Abstract

Fixed Cartesian impedance makes contact-rich teleoperation demonstrations practical, but gains that secure progress and contact support also determine impact and force variability. We study single-demonstration controller-to-controller impedance retargeting. Given one fixed Cartesian impedance command sequence {K0, D0, xcmd}, Manifold-Decomposed Impedance Retargeting (MDIR) deterministically reparameterizes the recorded controller into an executable task-channel variable-impedance command. MDIR targets this local retargeting problem by preserving projected task-channel responses near the demonstrated trajectory. It represents the source response in operational work, exertion, and support channels with a passive residual complement under a control-chain metric, computes an executable Cartesian-to-Manifold Retargeting (C2M) baseline, and applies Manifold-Constrained Parameter Optimization (MPO) to select a feasible representative with lower wrist-force peaks, impulse, force variability, and nominal controller power. Across planar wiping, pick-and-place, and pushing on a Franka Panda, the full MDIR controller passes Task Check in all 15 closed-loop executions and reduces all four aggressiveness metrics relative to the fixed-impedance demonstrations.