ON MINIMAL ENERGY TRAJECTORIES

Among all trajectories in the plane that have a given location and direction of endpoints, the one that minimizes the integral of the squared curvature is defined as the minimal energy trajectory. Plane trajectories minimizing a length-normalized and thus scale-invariant energy measure are discussed along with algorithms for obtaining them. It is shown that a scale-invariant measure is more natural for the design of interpolation and shape completion curves, and with this measure, circular arcs are optimal in a large number of situations. A simple numerical procedure is proposed for computing piecewise linear approximations of optimal trajectories as a solution of discrete two-point boundary value problems. Such trajectories are useful in computer graphics, geometric design, and motion planning of robots. © 1990.