This thesis presents an efficient and reliable trajectory generation framework that enables the computation of feasible, safe and collision-free trajectories for teams of autonomous vehicles while satisfying timing constraints imposed by
real-time applications. The proposed framework aims to address a few key issues related to multi-vehicle trajectory generation:
(i) Satisfying collision-avoidance constraints at all time instances during a mission; Majority of the existing trajectory generation methods rely on discretization in time or space and, thus, ensuring that constraints are satisfied in between discretization nodes is only possible by employing a fine discretization grid. To avoid the complications associated with time gridding, we parameterize trajectories with Bézier curves and propose the Bernstein relaxation and refinement method to guarantee that constraints are satisfied at any time instant.
(ii) Considering the rotational motion of a drone to avoid infeasibility problems with flights in tight spaces; To incorporate the rotational motion of a drone into the problem we approximate the drone body as an ellipsoid whose principal axes are aligned with the body frame axes. The ellipsoid model allows an explicit consideration of the drone’s shape and orientation which is necessary for trajectory generation in environments with narrow gaps.
(iii) Decoupling inter-vehicle collision-avoidance constraints for a distributed scheme with low communication demands; To alleviate the computational complexity of solving the problem centrally for a large group of vehicles, we present a scheme that enables local distributed trajectory generation by solving a small-scale optimization problem that only involves a vehicle’s individual variables. To ensure that local decisions satisfy the coupling collision avoidance constraints we adopt the Voronoi partitioning of space and enforce each vehicle to generate its trajectory inside its Voronoi cell.
The thesis concludes with extensive simulation results, with up to 100 drone, to illustrate the efficacy of the proposed trajectory generation framework.