State parametrization in optimal control problems and low level controller design for multiple autonomous mobile robot systems

Previous studies have established the concept of polynomial controllability in linear time-invariant systems. This paper considers further this concept with regard to optimal control problems in linear and nonlinear systems. The first part of the paper establishes a simple procedure for computing a control function that accomplishes a given task while minimizing a quadratic index of performance. Next we study the application of the approach to single and multi-mobile-robot systems. Indeed, in the so-called intelligent spaces it could be more effective to use multiple simpler and cheaper mobile robots instead of one complex and expensive robot. In this regard the present study develops suboptimal control strategies for single and group of mobile robots in point-to-point and trajectory tracking control tasks. In particular we consider here a group of unicycle-like mobile robots which are subjected to nonholonomic constraints and drive in a convoy-like formation.