Motion planning in the presence of directional and obstacle avoidance constraints using nonlinear, anisotropic, harmonic potential fields

Recently, the authors suggested a new class of Intelligent Motion Controllers that are called Evolutionary, Hybrid, PDEODE Controllers (EHPCs) [33]. A controller of such a class is designed for the special task of guiding an agent in a fully unknown environment to a target set along an obstacle-free trajectory. In a short compaion paper, the authors briefly described an extension that would allow an EHPC to jointly condition a motion trajectory with both directional and region avoidance constraints. In this paper, an indepth investigation of the proposed extension is provided. Also, mathematical proofs of both convergence, and the ability to enforce directional and region avoidance constraints are supplied.