Optimal motion planning based on path length minimisation

In this paper, the path planning problem for a single autonomous robot treading on a static terrain is solved using optimal control theory. The performance measure selected for the optimal control formulation is the path length between a predefined initial and final position on an inertial frame of reference. The terrain features are assumed to be known a priori and is represented using a b-spline surface. The terrain tractability constraint is decoupled from the dynamic stability equation of the robot and absorbed as a terrain feature. The results indicate that the target is reached optimally and the trajectory is smooth. The smoothness of the trajectory eliminates the need for post processing for trajectory tracking. This formulation can be applied to path planning problems related to aerial and ground vehicles with minimum modifications to take care of the real time requirements.