Abstract
Navigation in a dynamic environment requires reactive actions to avoid collision and navigate safely. This paper deals with optimal and reactive motion planning for unmanned air vehicles in a dynamic world. A virtual space representation is used to formulate and solve the problem and derive real time optimal trajectories. This formulation allows for the construction of different control subspaces from which optimal control laws for the speed, the flight path angle, and the heading angle are derived. The safety margins are translated to the control subspaces as speed and orientation margins. Closed-form reactive optimal solutions are calculated to achieve reactive motion and avoid collision in each subspace. The dynamic and kinematic constraints are taken into account when planning motion in the control subspaces. Simulation results show the effectiveness of the proposed methods.