Concurrent Goal Assignment and Collision-Free Trajectory Generation for Multiple Aerial Robots

Centralized Collision-free Polynomial Trajectories and Goal Assignment for Aerial Swarms

“…This work begins by establishing mathematical and notational preliminaries; where applicable, the notation of [18] is followed. Unlike the authors' previous work [36] which restricted agents to 2-dimensional planes and assumed instantaneous switching between these planes, now a fully 3dimensional Euclidean space is considered and accompanying trajectory generation algorithms developed which support implementation on a physical robotic system. To be clear, in this work all objects and geometry with physical extent reside within a common 3-dimensional Euclidean space.…”

“…Like the previous work in [36], the proposed method aims to minimize the total, or equivalently average, time-in-flight of all agents. This is a useful cost metric for many applications e.g.…”

“…It was found that the difference between the degree 7 and 9 polynomials was extremely slight and in practice the reference tracking error was dominated by other noise sources. For comparison, degree 1 polynomials represent constant speed trajectories; this was effectively the approach taken in the authors' previous work [36]. The procedure for calculating the base polynomial is as follows:…”

“…It is demonstrated that the proposed method significantly reduces total time-in-motion relative to [18] with only modest ad-ditional computational expense which becomes negligible for large numbers of agents. The authors' prior work [36] presented a similar approach, but required a simple kinematic model which assumed an unrealistic ability to instantaneously change positions vertically and instantaneously change velocities horizontally; these assumptions are removed in the present work. Further, more extensive simulations and an experimental implementation on a multi-robot testbed are provided.…”

“…The remainder of the paper is organized as follows. First a variation of the trajectory planning problems given in [18,36] is defined, then a strategy in which goal assignment is performed based on initial trajectory plans is proposed, followed by a refinement step to resolve potential collisions using either time delays or altitude assignment. Throughout, constraints on the magnitude of time derivatives of position (speed, acceleration, jerk, etc.)…”