Combined Bernstein Polynomial Optimal Reciprocal Collision Avoidance Differential Dynamic Programming for Trajectory Replanning and Collision Avoidance for UAM Vehicles

This paper presents an integration of differential dynamic programming (DDP) with the optimal reciprocal collision avoidance (ORCA) algorithm as the basis for a new algorithm, titled combined Bernstein polynomial optimal reciprocal collision avoidance DDP (COBRA DDP), for trajectory replanning and collision avoidance for urban air mobility (UAM) vehicles. State constrained variants of DDP provide the ability to plan trajectories while avoiding obstacles, but these methods require a large increase in computational time per iteration which hinders the overall speed of the algorithm. ORCA utilizes simplified dynamics to recognize potential collisions along a trajectory and provides an optimal velocity for the avoidance of multiple vehicles and obstacles. These velocity commands, however, may not result in a dynamically feasible trajectory for DDP to plan around. As such, a Bernstein polynomial curve that considers the general dynamic constraints of the vehicle is generated to approximate a trajectory based on the velocity commands. COBRA-DDP optimizes this suggested trajectory via unconstrained DDP to provide a dynamically feasible trajectory that provides collision avoidance. This new trajectory can be applied to the vehicle or used to warm-start the state constrained DDP algorithms to decrease computation time. The benefits and effectiveness of the algorithm are demonstrated on a UAM vertical takeoff and landing (VTOL) vehicle simulation with highly nonlinear dynamics.