A computationally efficient algorithm for state-to-state quadrocopter trajectory generation and feasibility verification

An algorithm is proposed allowing for the rapid generation and evaluation of quadrocopter state interception trajectories. These trajectories are from arbitrary initial states to final states defined by the vehicle position, velocity and acceleration with a specified end of time. Sufficient criteria are then derived allowing trajectories to be tested for feasibility with respect to thrust and body rates. It is also shown that the range of a linear combination of the vehicle state can be solved for in closed form, useful e.g. for testing that the position remains within a box. The algorithm is applied by revisiting the problem of finding a trajectory to hit a ball towards a target with a racket attached to a quadrocopter. The trajectory generator is used in a model predictive control like strategy, where thousands of trajectories are generated and evaluated at every controller update step, with the first input of the optimal trajectory being sent to the vehicle. It is shown that the method can generate and evaluate on the order of one million trajectories per second on a standard laptop computer.