Center of Mass Wrench Constraints in Presence of Spatially Distributed Contacts

Motion planning starts by planning the trajectory of the center of mass. With the increasing capabilities of humanoid robots, the case when contacts are spatially distributed should be considered. This paper shows the existence of contact configurations in which any acceleration of the center of mass is feasible. The procedure for identifying such configurations is presented. On the other hand, for the configurations in which the constraint on center of mass movement exists, it will be shown how to find that linear constraint, which defines the space of feasible motion. The proposed algorithm has low complexity. Additionally, it will be shown that the whole procedure needs to be run only once when the contact configuration changes.