UAV path planning via Legendre pseudospectral method improved by differential flatness

A Legendre pseudo spectral combination algorithm introduced by the theory of differential flatness is proposed, which transforms the unmanned aerial vehicles path planning problem into an optimal control problem. The vehicles kinematics state equations are built, and the optimal control problem which uses the equations as constraints and the shortest flight time as the cost is also built. By the differential flatness, the equations of motion state can be converted, that is the control variables and constraints of the optimal control problem can be simplified by the use of flatness output. Then optimal control problem after simplified can be solved through Legendre pseudo spectral method. The proposed combination algorithm has been compared with Legendre pseudo spectral method, and the simulation by Matlab is used to verify that the algorithm can reduce approximately 60% computation time with ensuring accuracy. The result has proved the high engineering value of the proposed algorithm.