Path planning with obstacle avoidance by G1G1 PH quintic splines

•A two-step approach to design planar smooth collision-free paths is presented.•The construction of piecewise linear paths with angle-based criteria is investigated.•The smooth path is based on PH spline interpolation schemes with tension parameters.•A selection of test cases demonstrates the quality of the new motion planning scheme.

We propose a two-step approach for the construction of planar smooth collision-free navigation paths. Obstacle avoidance techniques that rely on classical data structures are initially considered for the identification of piecewise linear paths having no intersection with the obstacles of a given scenario. Variations of the shortest piecewise linear path with angle-based criteria are proposed and discussed. In the second part of the scheme we rely on spline interpolation algorithms with tension parameters to provide a smooth planar control strategy. In particular, we consider the class of curves with Pythagorean structures, because they provide an exact computation of fundamental geometric quantities. A selection of test cases demonstrates the quality of the new motion planning scheme.