Wrench-Guided and Velocity-Field-Based Geometric Impedance Control*

Abstract

Taking inspiration from the principle of locality in the field theories of physics [1], we aim to generate an impedance-related velocity field on SE(3) that characterizes the local interaction behaviors associated with specific tasks. Thanks to its locality, the desired impedance at each point of SE(3) can be effectively rendered by following the velocity field, without invoking the geometrical inconsistency of active stiffness [3].First, we will introduce a nonlinear impedance equipped with a guided wrench and a velocity output to portray the global interaction behaviors. The guided wrench will be conceived to ensure that the velocity output at each point of SE(3) accurately reflect the local interaction behaviors. Next, we will employ model-matching approaches to regulate the robot’s end-effector based on the velocity output. Finally, we will conduct a case study on the Peg-in-Hole (PiH) task to demonstrate this impedance control technique.