Quadrotor trajectory generation in dynamic environments using semi-definite relaxation on nonconvex QCQP

In this paper, we present an optimization-based framework for generating quadrotor trajectories which are free of collision in dynamic environments with both static and moving obstacles. Using the finite-horizon motion prediction of moving obstacles, our method is able to generate safe and smooth trajectories with minimum control efforts. Our method optimizes trajectories globally for all observed moving and static obstacles, such that the avoidance behavior is most unnoticeable. This method first utilizes semi-definite relaxation on a quadratically constrained quadratic programming (QCQP) problem to eliminate the nonconvex constraints in the moving obstacle avoidance problem. A feasible and reasonably good solution to the original nonconvex problem is obtained using a randomization method and convex linear restriction. We detail the trajectory generation formulation and the solving procedure of the nonconvex quadratic program. Our approach is validated by both simulation and experimental results.