Automated Off-Line Generation of Stable Variable Impedance Controllers According to Performance Specifications

In this letter, we propose a novel methodology for off-line generating stable Variable Impedance Controllers considering any parameter modulation law in function of exogenous signals to the robot, as e.g. the exerted force by the human in a collaborative task. The aim is to find the optimal controller according to a desired trade-off between accuracy and control effort. Each controller is formulated as a polytopic Linear Parameter Varying system consisting in a set of vertex systems at the limit operation points. Then, the stability and operating properties can be assessed through Linear Matrix Inequalities, from which an optimality index can be obtained. This index is used by a genetic optimisation algorithm to iteratively generate new controller solutions towards the best one. To exemplify our method we choose a case study of modulation laws for tasks that require a physical interaction between human and robot. Generated solutions for different trade-offs are evaluated on a object handover scenario using a 7-DoF WAM robotic manipulator.