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Tunable formation realization for nonholonomic mobile robots using the stress matrix

In this paper, we investigate the formation control problem for a team of nonholonomic mobile robots, in which the overall formation shape needs to be adapted to the change in its surroundings. To cope with the limited accessibility to the desired formation pattern, as well as the inherent nonholonomic constraints, we propose a distributed controller by invoking the stress-matrix-based technique, which gives extra freedom in controlling formations. Theoretical analysis is provided in the context of Lyapunov stability to show that tunable formations can be achieved using our proposed control strategy. Besides, it is also proved that collision avoidance can be ensured in the process of formation deformation. Simulations are carried out to validate the theoretical results.