Optimal contact force distribution for compliant humanoid robots in whole-body loco-manipulation tasks

The term whole-body loco-manipulation refers to the case in which a humanoid robot exploits contacts with the environment, both with the end-effectors and with its internal limbs, in order to balance, move and/or manipulate the environment. In such a situation, high degree of redundancy may not be sufficient to completely control the robot movements and/or the forces applied on the environment. This problem is tackled in this work by means of quasi-static analysis tools. The reduction of mobility and manipulability is studied introducing the Fundamental Loco-Manipulation Matrix (FLMM) and its canonical form (cFLMM). Relevant information on the system can be extracted from those, obtaining, e.g., the space of the controllable contact forces, and the controllable displacements of the center of mass. Furthermore, the best contact force distribution able to meet the friction cone constraints is demonstrated to be the solution of a convex optimization problem. The validity of the proposed methods is verified in two numerical examples, where internal contacts affects the controllability of both forces and displacements. Numerical results show that is crucial to consider the correlations between contact forces in order to exert target actions on the environment while coping with friction limits on the whole set of contacts.