On Weight-Prioritized Multi-Task Control of Humanoid Robots
Résumé
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 systems, such as Coulomb friction cone and sustained unilateral contact constraints, torque saturation... 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 propose an analysis of some stability properties of the resulting closed-loop dynamical system based on the Lyapunov linearization method.
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