Formation control of underactuated ships with elliptical shape approximation and limited communication ranges

Based on the recent theoretical development for formation control of multiple fully actuated agents with an elliptical shape in Do (2011), this paper develops distributed controllers that force a group of N underactuated ships with limited communication ranges to perform a desired formation, and guarantee no collisions between any ships in the group. The ships are first fitted to elliptical disks for solving collision avoidance. A coordinate transformation is then proposed to introduce an additional control input, which overcomes difficulties caused by underactuation and off-diagonal terms in the system matrices. The control design relies on potential functions with the separation condition between elliptical disks and the smooth or p-times differentiable step functions embedded in.