Trajectory Generation Using Semidefinite Programming For Multi-Rotors

Trajectory generation is one of the most popular techniques for multi-rotors to achieve autonomous navigation capabilities. In this paper, we present an optimization-based approach for generating smooth, feasible and collision-free trajectories. Our method does not require a prior proper time allocation but attempts to optimize time allocation automatically. This method first optimizes trajectories subjected to dynamic constraints and 3D corridor constraints using a quadratic program. Then time allocation is optimized as a semidefinite program by leveraging semidefinite relaxation. A feasible solution is obtained using the rank-one approximation and used to update previous time allocation. This method run iteratively until a feasible trajectory is obtained. Our approach is validated with simulation results. Kinematic simulation results show the proposed method ensures to generate feasible trajectory from collision-free path in clutter environments.