Condition-based Design of Variable Impedance Controllers from User Demonstrations

This paper presents an approach to ensure conditions on Variable Impedance Controllers through the off-line tuning of the parameters involved in its description. In particular, we prove its application to term modulations defined by a Learning from Demonstration technique. This is performed through the assessment of conditions regarding safety and performance, which encompass heuristics and constraints in the form of Linear Matrix Inequalities. Latter ones allow to define a convex optimisation problem to analyse their fulfilment, and require a polytopic description of the VIC, in this case, obtained from its formulation as a discrete-time Linear Parameter Varying system. With respect to the current state-of-art, this approach only limits the term definition obtained by the Learning from Demonstration technique to be continuous and function of exogenous signals, i.e. external variables to the robot. Therefore, using a solution-search method, the most suitable set of parameters according to assessment criteria can be obtained. Using a 7-DoF KINOVAGEN3 manipulator, validation and comparison against solutions with relaxed conditions are performed. The method is applied to generate Variable Impedance Controllers for a pulley belt looping task, inspired by the Assembly Challenge for Industrial Robotics in World Robot Summit 2018, to reduce the exerted force with respect to a standard (constant) Impedance Controller. These controllers fulfil a set of safety constraints, namely stability, bounds on task variables and maximum response overshooting; and their performance is determined by the User Preference heuristic, which allows to intuitively define the desired compliant behaviour along the task. In the context of the task, this is used to generate new controllers for one-off modifications of the nominal belt looping task setup without new demonstrations.