Minimum Jerk Trajectory Generation of a Quadrotor Based on the Differential Flatness

In order to improve smoothness of task trajectories, this paper describe algorithms to generate smooth-optimal trajectories based on the differential flatness of quadrotor. B-spline is used to parameterize the selected flat outputs, and the dynamic constraints or kinematical constraints on quadrotor are transferred to the control point constraints of B-spline. The trajectory generation is then considered an optimal control problem by adopting the integral of squared jerk. And then the optimal solution is solved by transforming the optimal control problem into a nonlinear programming problem. At last the smoothness-optimal trajectories are generated. Simulation results show that, this method can smooth out movements and minimize the accumulative jerk which can decrease trajectory tracking errors effectively.