Stable-by-Design Kinematic Control Based on Optimization

Abstract

This article presents a new kinematic control paradigm for redundant robots based on optimization. The general approach takes into account convex objective functions with inequality constraints and a specific equality constraint resulting from a Lyapunov function, which ensures closed-loop stability by design. Furthermore, we tackle an important particular case by using a convex combination of quadratic and l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm objective functions, making possible for the designer to choose different degrees of sparseness and smoothness in the control inputs. We provide a pseudoanalytical solution to this optimization problem and validate the approach by controlling the center of mass of the humanoid robot HOAP3.