LMI-based Variable Impedance Controller design from User Demonstrations and Preferences

Alberto San-Miguel, Guillem Alenyà and Vicenç Puig

Abstract - In this paper, we introduce a new off-line method to find suitable parameters of a Variable Impedance Control using the Learning from Demonstrations paradigm, fulfilling stability and performance constraints while taking into account user's task intuition. Considering a compliance profile obtained from human demonstrations, a Linear Parameter Varying Parameter description of the VIC is given, which allows to state the design problem including stability and performance constraints as Linear Matrix Inequalities. Therefore, using a solution-search method, we find the optimal solutions in terms of performance according to user preferences on the desired behaviour for the task. Design problem is validated by comparing the execution from the obtained controller against solutions from designs with relaxed conditions for different user preference sets in a 2-D trajectory tracking task. A pulley looping task is presented as a case study to evaluate the performance of the variable impedance controller against a constant one and its agility and leanness on two one-off modifications of the setup using the user preference mechanism. All the experiments have been performed using a 7-DoF \textsc{KINOVA Gen3} manipulator.

Keywords- Variable Impedance Control (VIC); Learning from Demonstrations (LfD); Linear Parameter Varying (LPV); Linear Matrix Inequalities (LMI)

Code- LMI VIC Toolbox

Extra- Implementation details