An optimal control model unifying holonomic and nonholonomic walking

In this paper we explore the underlying principles of natural locomotion path generation of human beings. The knowledge of these principles is useful to implement biologically inspired path planning algorithms on a humanoid robot. The key is to formulate the path planning problem as optimal control problem. We propose a single dynamic model valid for all situations, unifying nonholonomic and holonomic parts of the motion, as well as a carefully designed unified objective function. The choice between holonomic and nonholonomic behavior appears, along with the optimal path, as result of the optimization by powerful numerical techniques. The proposed model and objective function are successfully tested in six different locomotion scenarios. The resulting paths are implemented on the HRP2 robot in the simulation environment OpenHRP as well as in the experiment on the real robot.