Abstract
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 " ma-nipulators " 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 multi-task 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 multiob-jective optimization case. Stability in terms of solution existence, uniqueness, continuity, and robustness to perturbations, is then formally demonstrated for the constrained quadratic program.