2003 Volume 39 Issue 12 Pages 1108-1116
This paper presents a distributed control scheme for multiple nonholonomic wheeled mobile robots of the Hilare-type to make group formations. The Hilare-type mobile robot is kinematically equivalent to a unicycle-type mobile robot. Each robot in this control scheme has its own coordinate system, and it senses and controls its relative position to other robots, which means that each robot has relative position feedback. Via this feedback, this robotic system consisting of the multiple mobile robots becomes a large-scale visually articulated multi-body system. Each robot especially has a two-dimensional control input referred to as a “formation vector” and the formation is controllable by the vectors. The mobile robots have nonholonomic constraints and they cannot move in an omni-direction instantaneously, so that such nonholonomic mobile robots cannot be asymptotically stabilized by smooth static feedback control laws. We introduce a distributed smooth time-varying feedback control law whose asymptotic stability is guaranteed in a mathematical framework, averaging theory. To prove its asymptotic stability, we apply Eckhaus'/Sanchez-Paleucia's theorem. We specifically deal with a matrix whose components are averaged over time by integration and whose eigenvalue distribution describes stability of this control law. Since the eigenvalue distribution is analytically shown by Hölder's inequality in functional analysis, stability analysis of this control law is given in averaging theory and it is technically related with functional analysis. The validity of this control law is supported by computer simulations.
