US Patent 8737692 Contact state estimating apparatus and trajectory generation apparatus

A state where at least a part of the virtual object (e.g., a foot of a robot) enters into the actual object (e.g., floor), i.e., a state where at least a part of a plurality of virtual points located on the surface of the virtual object is inside the actual object, can be assumed. At each of the inside and the outside of the actual object, as a virtual point is located at a deeper position inside and away from the surface or the skin part of the actual object and as a coordinate value difference ΔZi is larger, a higher value is calculated for the cost Ei as well. The combination Z^ of coordinate values of virtual points, bringing the total cost E=ΣiEi closer to an absolute minimum or a local minimum, can be searched.