Optimal Trajectory Planning of a Quadrotor Based on Minimum Effort

The optimal design of path planning for unmanned aerial vehicles with many potential applications ranging from mapping to supporting rescue operations will improve their performance. Hence, the aim of this paper is to determine the optimal trajectory of quadrotor robot based on minimizing engine torque in point-to-point motion. First, the dynamic equations of quadrotor motion are derived in state space form by using Newton’s method. In this investigation, the computational method to solve the trajectory planning problem is based on the indirect solution of open-loop optimal control problem. The Pontryagin’s minimum principle (PMP) is used to obtain the optimality conditions, which is lead to a standard form of a two-point boundary value problem. Finally, to evaluate the efficacy of the proposed method, numerical simulation is performed for a quadrotor and the optimal trajectory is designed based on minimize torque. The results illustrate the power and efficiency of the method to overcome the high nonlinearity nature of the problem such as path optimization of multi-rotor helicopters (tri, quad, hexa, octa, etc.).