The DCM generalized inverse: efficient body-wrench distribution in multi-contact balance control

A computationally efficient solution of the body- wrench distribution problem for bipeds and multi-legged robots is introduced. The method is based on a weighted generalized inverse, the weights being determined from relationships pertinent to the divergent component of motion (DCM), base-of-support (BoS) geometry, friction constraints and center of pressure allocation. The user (or the robot) specifies appropriate weights only indirectly, by setting the desired contact transition boundaries within the net BoS. It is shown that the proposed weighted generalized inverse ensures body- wrench distribution in a way consistent with both the static and dynamic states. The dependency on the DCM yields an important advantage when the method is applied to reactive balance control in response to unknown disturbances. An admittance-type stabilizer is obtained by setting the reference DCM at the current center of mass position. This stabilizer does not require reference values for the centers of pressures and the contact wrenches. The method is implemented with a whole-body, torque-based balance controller. Its performance is examined through simulations with planar and non-coplanar contacts, during proactive and reactive tasks.