Trajectory Planning of Quadrotor UAV with Maximum Payload and Minimum Oscillation of Suspended Load Using Optimal Control

This paper focuses on the problem of transporting a cable-suspended load by a quadrotor UAV for safer flight and more efficiency. The dynamic model of a quadrotor coupled to the suspended load is derived using the Euler-Lagrange formulation. The optimal trajectory for carrying the maximum payload and minimum oscillation of swinging load will be obtained. The optimal cable length to increase the maximum payload capacity and reduce the maximum oscillation angle of swinging load is obtained. Also, the effect of load mass on the maximum oscillation angle of swinging load is studied. In this paper, the optimization procedure is based on the solution of the optimal control problem from the class of open loop with an indirect method. The application Pontryagin's Minimum Principle lead to deriving the optimality conditions and subsequently a two-point boundary value problem (TPBVP) which is solved by a numerical method. An appropriate algorithm is presented for calculating the maximum payload to move between two specified points. The main superiority of this method is that it can solve a wide range of optimal maneuvers for arbitrary initial and final configurations relevant to every considered cost function. Generating various optimal paths with different maximum payloads and oscillation angles by modifying the values of the penalty matrices. In order to verify the efficiency of the proposed method and the presented algorithm, a simulation study is performed for a quadrotor with a suspended load in maneuver between two specified points and various object function.