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

The authors (1998) suggested a new class of intelligent motion controllers, called evolutionary, hybrid PDE-ODE controllers (EHPCs). 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. 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 in-depth 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