Novel potential-function based control schemes for nonholonomic multi-agent systems to prevent the local minimum problem



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Research on multi-agent systems performing cooperative tasks has received considerable attention in recent years. Because multiple agents perform cooperative tasks in close proximity, the coordination control of multiple agents to avoid collisions holds one of the critical keys to mission success. The potential function approach has been extensively employed for collision avoidance, but it has one inherent limitation of local minimum. This dissertation proposes a new avoidance strategy for the issue of local minimum. The primary objective of this research is to construct novel potential-function-based control schemes that drive agents from their initial to the goal configurations while avoiding collision with other agents and obstacles. The control schemes enable agents to avoid being trapped at a local minimum by forcing them to exit from the regions that may contain a local minimum. This dissertation consists of three studies, each of which has different technical assumptions. In the first study, all-to-all communication ability among agents is assumed. In addition, each agent is assumed to a priori know the location of all obstacles. In the second study, all-to-all communication ability is again assumed, but each agent is assumed to determine the location of obstacles using a sensor with a limited sensing range. In the third study, limited communication ability is assumed (i.e., each agent exchanges information only with agents within its limited communication range), and each agent is assumed to determine the location of the obstacles using its sensor with a limited sensing range. Relative to existing solutions, the new control schemes presented here have three distinct advantages. First, our avoidance strategy can provide cost-efficient solutions in applications because agents will never be trapped at a local minimum. Second, our control signals are continuous, which allows agents to change their speed in a realistic manner that is consistent with their natural motion traits. Finally, our control scheme allows for setting the upper bound of the velocity of each agent, which guarantees that the speed of agents will never exceed a maximum speed limit.