A Computationally Efficient Motion Primitive for Quadrocopter Trajectory Generation

A method is presented for the rapid generation and feasibility verification of motion primitives for quadrocopters and similar multirotor vehicles. The motion primitives are defined by the quadrocopter´s initial state, the desired motion duration, and any combination of components of the quadrocopter´s position, velocity, and acceleration at the motion´s end. Closed-form solutions for the primitives are given, which minimize a cost function related to input aggressiveness. Computationally efficient tests are presented to allow for rapid feasibility verification. Conditions are given under which the existence of feasible primitives can be guaranteed a priori . The algorithm may be incorporated in a high-level trajectory generator, which can then rapidly search over a large number of motion primitives which would achieve some given high-level goal. It is shown that a million motion primitives may be evaluated and compared per second on a standard laptop computer. The motion primitive generation algorithm is experimentally demonstrated by tasking a quadrocopter with an attached net to catch a thrown ball, evaluating thousands of different possible motions to catch the ball.