The minimum jerk trajectory generation of a quadrotor based on the differential flatness

This paper described a nonlinear trajectory generation (NLTG) algorithm to generate smooth optimal trajectories based on the differential flatness of a quadrotor. In the algorithm, all states and inputs of a quadrotor were expressed by a set of outputs and their derivatives, smooth and effective trajectories were designed in flat out space while considering the dynamic constraints and environmental constraints. Then the trajectory generation was considered an optimal control problem. B-spline was used to parameterize the selected flat outputs, the optimal solution was then solved by transforming the optimal control problem into a nonlinear programming problem. At last the optimal trajectories were generated. Simulation results show that, this algorithm can smooth out movements and minimize the accumulative jerk and the second derivative of the torque which can decrease trajectory tracking errors effectively.