Nonholonomic motion planning based on optimal control for flight phases of planar bipedal running

Presented is a novel approach for online trajectory modification of joint motions to transfer a free open kinematic chain, undergoing flight phase, from a specified initial configuration to a specified final configuration. Formally, it is assumed that a nominal trajectory, computed offline, can reorient the kinematic chain (reconfiguration problem) for a given angular momentum on a time interval. A modification algorithm of body joints, based on optimal control, is developed such that for different angular momentums and time intervals, the same reconfiguration problem can be solved online. This approach can be utilised for space robotics applications and online computation of planar running trajectories during flight phases.