Abstract
Optimal control techniques have become increasingly important for the autonomous operation of unmanned aerial vehicles, particularly quadrotors, due to their nonlinear dynamics and underactuated structure. In this paper, a direct multiple shooting method is investigated for solving optimal control problems and applied to the energy-efficient control of a quadrotor. The multiple shooting method divides the optimisation horizon into several smaller intervals and transforms the original optimal control problem into a nonlinear programming (NLP) problem by introducing additional state variables and continuity constraints. The resulting NLP is solved by computing the zeros of the Lagrangian Jacobian using Newton’s method. First, the theoretical foundations of the direct multiple shooting approach are presented. Then, a numerical example is used to demonstrate the effectiveness of the method. Finally, the proposed approach is applied to a quadrotor control problem focused on minimising energy consumption while ensuring accurate trajectory tracking. Simulation results indicate that the direct multiple shooting method provides stable convergence, improved numerical robustness, and efficient control performance for quadrotor systems.
Keywords: optimal control, multiple shooting method, nonlinear programming, Newton’s method, quadrotor, energy minimisation.