This paper addresses the problem of multi-agent coordination and control under multiple objectives, and presents a set-theoretic formulation amenable to Lyapunov-based analysis and control design. A novel class of Lyapunov-like barrier functions is introduced and used to encode multiple, non-trivial control objectives, such as collision avoidance, proximity maintenance and convergence to desired destinations. The construction is based on recentered barrier functions and on maximum approximation functions. Thus, a single Lyapunov-like function is used to encode the constrained set of each agent, yielding simple, gradient-based control solutions. The derived control strategies are distributed, i.e., based on information locally available to each agent, which is dictated by sensing and communication limitations. Furthermore, the proposed coordination protocol dictates semi-cooperative conflict resolution among agents, which can be also thought as prioritization, as well as conflict resolution with respect to an agent (the leader) which is not actively participating in collision avoidance, except when necessary. The considered scenario is pertinent to surveillance tasks and involves nonholonomic vehicles. The efficacy of the approach is demonstrated through simulation results. 0018-9286 (c)

Vision-based formation control of multiple agents, such as mobile robots or fully autonomous cars, has recently received great interest due to its application in robotic networks and automated highways. This paper addresses the cooperative motion coordination of leader-follower formations of nonholonomic mobile robots, under visibility and communication constraints in known polygonal obstacle environments. We initially consider the case of N = 2 agents moving in L-F fashion and propose a feedback control strategy under which L ensures obstacle avoidance for both robots, while F ensures visibility maintenance with L and intervehicle collision avoidance. The derived algorithms are based on set-theoretic methods to guarantee visibility maintenance, dipolar vector fields to maintain the formation shape, and the consideration of the formation as a tractor-trailer system to ensure obstacle avoidance. We furthermore show how the coordination and control design extends to the case of N > 2 agents, and provide simulation results, which demonstrate the efficacy of the control solutions. The proposed algorithms do not require information exchange among robots, but are instead based on information locally available to each agent. In this way, the desired tasks are executed and achieved in a decentralized manner, with each robot taking care of converging to a desired configuration, while maintaining visibility with its target.Index Terms-Leader-follower formations, nonholonomic motion planning, path planning for multiple mobile robot systems, visibility maintenance.

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This paper presents a novel feedback method on the motion planning for unicycle robots in environments with static obstacles, along with an extension to the distributed planning and coordination in multi-robot systems. The method employs a family of 2-dimensional analytic vector fields, whose integral curves exhibit various patterns depending on the value of a parameter λ. More specifically, for an a priori known value of λ, the vector field has a unique singular point of dipole type and can be used to steer the unicycle to a goal configuration. Furthermore, for the unique value of λ that the vector field has a continuum of singular points, the integral curves are used to define flows around obstacles.An almost global feedback motion plan can then be constructed by suitably blending attractive and repulsive vector fields in a static obstacle environment. The method does not suffer from the appearance of sinks (stable nodes) away from goal point. Compared to other similar methods which are free of local minima, the proposed approach does not require any parameter tuning to render the desired convergence properties. The paper also addresses the extension of the method to the distributed coordination and control of multiple robots, where each robot needs to navigate to a goal configuration while avoiding collisions with the remaining robots, and while using local information only. More specifically, based on the results which apply to the single-robot case, a motion coordination protocol is presented which guarantees the safety of the multi-robot system and the almost global convergence of the robots to their goal configurations. The efficacy of the proposed methodology is demonstrated via simulation results in static and dynamic environments.

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