Path planning for mobile and hyper-redundant robots using Pythagorean hodograph curves

Pythagorean hodograph curves (PH curves) have a number of advantages over other splines commonly used in planar robot path planning: (1) the integral of curvature is small; (2) the curve, its length, curvature and total “bending energy” are known in closed-form; (3) start and end positions and directions are straightforwardly usable as boundary conditions; and (4) length can be traded off against curvature quite easily. These facts make PH curves especially interesting for the planning of car-like mobile robot paths, as well as for the calculation of the “backbone curve” in the inverse kinematics of hyper-redundant robots