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A constructive method is presented to design bounded and continuous cooperative controllers that force a group of N mobile agents with limited sensing ranges to stabilize at a desired location, and guarantee no collisions between the agents. The control development is based on new general potential functions, which attain the minimum value when the desired formation is achieved, are equal to infinity when a collision occurs, and are continuous at switches. The multiple Lyapunov function (MLF) approach is used to analyze stability of the closed loop switched system. | 1 Relative formation control of mobile agents K. D. Do Abstract A constructive method is presented to design bounded and continuous cooperative controllers that force a group of N mobile agents with limited sensing ranges to stabilize at a desired location, and guarantee no collisions between the agents. The control development is based on new general potential functions, which attain the minimum value when the desired formation is achieved, are equal to infinity when a collision occurs, and are continuous at switches. The multiple Lyapunov function (MLF) approach is used to analyze stability of the closed loop switched system. Index Terms Formation stabilization, bounded control, multiple Lyapunov function, switched system. I. I NTRODUCTION Technological advances in communication systems and the growing ease in making small, low power and inexpensive mobile agents make it possible to deploy a group of networked mobile vehicles to offer potential advantages in performance, redundancy, fault tolerance, and robustness. Formation control of multiple agents has received a lot of attention from both robotics and control communities. Basically, formation control involves the control of positions of a group of the agents such that they stabilize/track desired locations relative to reference point(s), which can be another agent(s) within the team, and can either be stationary or moving. Three popular approaches to formation control are leader-following (e.g. [1], [2]), behavioral (e.g. [3], [4]), and use of virtual structures (e.g. [5], [6]). Most research works investigating formation control utilize one or more of these approaches in either a centralized or decentralized manner. Centralized control schemes, see e.g. [2] and [7], use a single controller that generates collision free trajectories in the workspace. Although these guarantee a complete solution, centralized schemes require high computational power and are not robust due to the heavy dependence on a single
