Optimal Control Based on Minimum-Energy Trajectory Planning of a Quadrotor

Quadrotors have high energy consumption due to their inherent structure, hence minimization of their energy consumption play a crucial role in terms of enhancing their operational range and flight time. In this paper, optimal control based on a minimum-energy trajectory planning algorithm of a quadrotor has introduced between two certain points to maximize operation time. To do this, first, dynamic equations of quadrotor and Brushless motor are derived. Energy consumption of quadrotor is introduced as a cost function and the minimum energy path is determined using optimal control theory. To satisfy constraints, all of them are combined with a Hamiltonian equation using Lagrange multiplier. Finally, simulation results are compared with results of conventional trapezoidal velocity profile which shows energy saving up to 4% compared with conventional trapezoidal velocity profile. Also, results reveal that the influence of operation time is far more than path length on energy consumption. In order to verify the validity of the simulation results, they are compared with the results of an experimental model which is consisting Brushless motor, sensor and, control board. As well as using simulation results in different situations, a mathematical equation was extracted among path length, operation time and energy consumption which can be useful to estimate the maximum flight range or operation time considering the amount of energy of the battery.