A multiphase DMOC-based trajectory optimization method

Discrete mechanics and optimal control (DMOC) is a methodology that takes advantage of variational structure to solve certain optimal control problems for mechanical systems. This paper proposes to combine a multiphase strategy with the original DMOC method, resulting in a new multiphase DMOC (MDMOC) method and making optimal trajectory generation more efficient. The advantages of the proposed method are demonstrated mathematically, and in addition, a quadrotor, unmanned aerial vehicle, simulation example is presented to show its superiority over the DMOC method. Furthermore, to show its potential application, an arbitrarily chosen controller was used to track the desired trajectory generated by MDMOC. This new MDMOC methodology can also be applied to other mechanical systems such as mobile robots and underwater gliders.