Optimal Trajectory Design for Vehicles Navigating around Obstacles Using Pontryagin Neural Networks

A vehicle flying in 3D often encounters obstacles to avoid while navigating to an objective in an optimal way. Optimality implies expending the least control effort which can be essential for drones with limited energy sources whether chemical or battery. We show how the Pontryagin Neural Network may be applied to find a path that minimizes control effort and intersects the objective at a prescribed time. Additional constraints such as final incidence angle, final glideslope, ground avoidance, and zero thrust may be easily enforced using this technique. In this paper, we show examples for up to four inequality constraints with both fixed and free final time.