On convergence results for nonlinear cyclic pursuit strategies

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The paper focuses on the generation of a circular formation centred at a target point using a homogeneous group of autonomous agents in a cyclic pursuit framework. The agents are assumed to have a severely under-actuated form of the unicycle kinematics, with the linear speeds being constant and the angular speeds being their only control inputs. The target is assumed to be stationary and can represent a landmark, beacon, etc. In order to achieve the desired formation, the controller design is carried out in two stages. In the first stage, a bearing based attractive control law is proposed for every agent. Under the proposed law, the analysis of the relative motions reveals interesting behaviours like gathering and scattering of the agents. Building upon the attractive control law, in the second stage, the appropriate values of the controller parameters are determined which lead to a target centric circular formation. These parameters can also be suitably adjusted to achieve a pre-specified value of the radius of the circle and a desired distribution of the agents along the circle. The highlight of the work is that the convergence to the desired formation is guaranteed from almost all initial conditions of the agents by controlling only their angular speeds. Simulation results are also presented to illustrate the proposed theoretical results.