Design of Planar Collision-free Trochoidal Paths for a Multi-robot Swarm

The distributed consensus protocol (CP) presented in [1] enables a connected swarm of agents, modelled as single integrators, to trace repeated geometric paths in both 2-dimensional (2-D) and 3-D spaces. The parameters of the protocol, the connection topology of the swarm, and the initial positions of the agents define the characteristics of the generated paths. The applications of agents, or robots, tracing such paths have been well identified in the literature, for example, persistent coverage and surveillance of a region, guarding an asset, and target detection; the cited references provide an exhaustive list. In such applications, the issues of collisions between robots, communication range, feasibility of path tracking, and time taken to trace the path, have to be considered explicitly. Further, in applications involving guarding a specific region or an asset, the path should be defined by making the asset the centre of rotation (CoR). In this paper, the protocol is designed for a connected swarm of 3 unicycle-robots of finite size moving in a 2-D Cartesian space; the use of 3 robots leads to the generation of trochoidal paths, where each robot traces a unique trochoid. For a given communication topology, design of the trochoidal paths involves the selection of 3 scalars for the CP, a positive integer,k, with magnitudek 2, and the initial coordinates of the 3 robots inX Y space, thus leading to a total of 10 design variables.