On Weight-Prioritized Multi-Task Control of Humanoid Robots

We propose a formal analysis with some theoretical properties of weight-prioritized multi-task inverse-dynamics-like control of humanoid robots, being a case of redundant “manipulators” with a non-actuated free-floating base and multiple unilateral frictional contacts with the environment. The controller builds on a weighted sum scalarization of a multiobjective optimization problem under equality and inequality constraints, which appears as a straightforward solution to account for state and control input viability constraints characteristic of humanoid robots that were usually absent from early existing pseudo-inverse and null-space projection-based prioritized multitask approaches. We argue that our formulation is indeed well founded and justified from a theoretical standpoint, and we propose an analysis of some stability properties of the approach: Lyapunov stability is demonstrated for the closed-loop dynamical system that we analytically derive in the unconstrained multiobjective optimization case. Stability in terms of solution existence, uniqueness, continuity, and robustness to perturbations, is then formally demonstrated for the constrained quadratic program.