Stable-by-Design Kinematic Control Based on Optimization

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 l1-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.