Convergence-Guaranteed Trajectory Optimization for Quadrotors Subject to Aerodynamic Drag

Considering aerodynamic drag in the trajectory optimization of quadrotors is critical for improving the trajectory tracking performance, though it brings more nonlinearity to the dynamics. This article addresses how to reliably and efficiently solve the problem with free final time by convex optimization. Change of variables is first applied to move certain nonlinearity in the dynamics into path constraints, which are then convexified based on linearization. Next, we propose to introduce a nonlinear equality constraint to continue removing the nonlinearity related to the drag in the dynamics. The introduced constraint is then convexified based on a technique of replacing an unknown optimization variable with a known parameter, which is updated iteratively to approach the real value of the variable. This convexification technique plays a significant role in enabling us to theoretically establish the convergence of our designed iterative algorithm. Numerical examples will be provided to show the effectiveness and efficiency of the algorithm and the improvement of the trajectory tracking performance.