Abstract
In this paper a trajectory planner for n autonomous vehicles following a common leader is presented, with the planning being accomplished in real time and in a three dimensional setting. The trajectory planner is designed such that n follower vehicles behave as n distinct points of a unique two dimensional trailer attached to a single leader vehicle. We prove that for a wide range of initial conditions the trailer reference frame converges to a unique solution, thus guaranteeing that each follower can plan its trajectory independently from its peers, thereby reducing the need for communications among vehicles. Additionally, convergence to a fixed formation of n+1 vehicles with respect to the trailer reference frame is also guaranteed. Finally, we present bounds on the planned velocity and acceleration, which provide conditions for the feasibility of the planned trajectory. An experimental validation of the planner's behavior is presented with quadrotor vehicles, demonstrating the richness of the planned trajectories.
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