New approach for testing dynamic balance and motion feasibility of humanoids in presence of multiple spatial contacts*

Besides the contacts between the feet and the ground, in some cases motion of humanoids may require additional contacts with environment. When spatial distribution of contacts is needed in order to perform planned motion, decision where the next contact will be established may be of fundamental importance. To ensure that planned motion will be feasible and dynamically balanced, all contacts with environment should remain sustained. However, the main indicator of dynamical balance, the ZMP, is only applicable to the robots walking on flat horizontal surfaces. For that reason, method for testing dynamical balance when contacts are distributed spatially will be presented. To do so, constraints on all contact wrenches are written in the form of Composite Dynamic Balance Matrix. Based on that, condition which can tell if desired motion is feasible or not, is derived. Those conditions are in form of inequalities and maintaining them satisfied is of highest importance. For synthesizing whole body motion where robot has to fulfill several tasks (in form of equalities and inequalities), generalized task prioritization framework could be used.