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This paper addresses the formation control problem without collisions for multiagent systems. A general solution is proposed for the case of any number of agents moving on a plane subject to communication graph composed of cyclic paths. The control law is designed attending separately the convergence to the desired formation and the noncollision problems. First, a normalized version of the directed cyclic pursuit algorithm is proposed. After this, the algorithm is generalized to a more general class of topologies, including all the balanced formation graphs. Once the finite-time convergence problem is solved we focus on the noncollision complementary requirement adding a repulsive vector field to the previous control law. The repulsive vector fields display an unstable focus structure suitably scaled and centered at the position of the rest of agents in a certain radius. The proposed control law ensures that the agents reach the desired geometric pattern in finite time and that they stay at a distance greater than or equal to some prescribed lower bound for all times. Moreover, the closed-loop system does not exhibit undesired equilibria. Numerical simulations and real-time experiments illustrate the good performance of the proposed solution.

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This paper presents the extension of leader-follower behaviours, for the case of a combined set of kinematic models of omnidirectional and differential-drive wheeled mobile robots. The control strategies are based on the decentralized measurements of distance and heading angles. Combining the kinematic models, the control strategies produce the standard and new mechanical behaviours related to rigid body or n-trailer approaches. The analysis is given in pairs of robots and extended to the case of multiple robots with a directed tree-shaped communication topology. Combining these behaviours, it is possible to make platoons of robots, as obtained from cluster space or virtual structure approaches, but now defined by local measurements and communication of robots. Numerical simulations and real-time experiments show the performance of the approach and the possibilities to be applied in multirobot tasks.

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