Reachable Set of Unmanned Aerial Vehicles in Cyclic Pursuit with Heterogeneous Controller and Damping Gains

Abstract

Cyclic pursuit problems for multi-agent systems like unmanned vehicles modelled as point-masses with singleor double-integrator dynamics, have received a lot of attention in the literature. However, there are very limited works which discuss the reachable set with respect to a given initial configuration for these agents engaged in the pursuit. This work discusses the reachable set for a group of double-integrator agents which rendezvous at a point while engaged in cyclic pursuit. Heterogeneity in both the position consensus gains and velocity damping gains aid in expanding the reachable set beyond the convex hull formed by the initial position of the agents. We accommodate heterogeneity in damping gains which together with the initial velocities of each vehicle correspond to modification in the effective initial position of the vehicles. We find that the overall reachable set is analogous to the union of reachable sets for single-integrator cases, where the initial configuration is defined by the effective configuration mentioned above. This work finds usefulness for nonzero initial velocities as this impels additional flexibility in the design method.