Triangular formation control using range measurements: An application to marine robotic vehicles

This paper addresses the problem of maintaining an autonomous robotic vehicle in a moving triangular formation by regulating its position with respect to two leader vehicles. The robotic vehicle has no a priori knowledge of the path described by the leaders and its goal is to follow them by constantly regulating the inter-vehicle distances to a desired fixed value, using range-only measurements. To solve this station keeping problem, we propose a control strategy that estimates the formation speed and heading from the ranges obtained to the two leading vehicles, and uses simple feedback laws for speed and heading commands to drive suitably defined common and differential errors to zero. For straight-line motion, we provide guaranteed conditions under which the proposed control strategy achieves local convergence of the distance errors to zero. We also indicate how our design procedure can be extended to full dynamic models of marine robotic vehicles equipped with inner loops for yaw and speed control. Simulation results using realistic models are described and discussed.