Time-optimal control of a hovering quad-rotor helicopter

The time-optimal control problem of a hovering quad-rotor helicopter is addressed in this paper. Instead of utilizing the Pontryagin's Minimum Principle (PMP), in which one needs to solve a set of highly nonlinear differential equations, a nonlinear programming (NLP) method is proposed. In this novel method, the count of control steps is fixed initially and the sampling period is treated as a variable in the optimization process. The optimization object is to minimize the sampling period such that it will be below a specific minimum value, which is set in advance considering the accuracy of discretization. To generate initial feasible solutions of the formulated NLP problem, genetic algorithms (GAs) are adopted. With the proposed method, one can find a time-optimal movement of the helicopter between two configurations. To show the feasibility of the proposed method, simulation results are included for illustration.