Dynamic Trajectory-Tracking Control of an Omnidirectional Mobile Robot Based on a Passive Approach

The traditional control problems of trajectory-tracking and regulation have been extensively studied in the field of mobile robotics. In particular, the differential and the omnidirectional mobile robots, also known, respectively, as the (2,0) and the (3,0) robots (see (Bétourné & Campion, 1996), (Campion et al., 1996), have attracted the interest of many control researchers. It is a common practice in mobile robotics to address control problems taking into account only a kinematic representation. In (Canudas et al., 1996) and (Campion et al., 1996) the kinematic models for diverse types of mobile robots are presented. From a kinematic perspective, the trajectory-tracking control problem of (2,0)-type robot has been addressed and solved for example in (D’Andrea-Novel et al., 1992) following a dynamic feedback linearization approach. In (Oriolo et al., 2002) a real time implementation of a dynamic feedback linearization tracking-controller is presented. For the same class of robot, a discrete time approach is considered in (Niño-Suárez et al., 2006) where a pathtracking controller based on a sliding mode control technique is presented. The regulation and trajectory-tracking problems for the omnidirectional mobile robot (3,0), have also received sustained attention. Considering, only its kinematic model, several control strategies have been proposed. In (Liu et al., 2003), it is designed a nonlinear controller based on a Trajectory Linearization strategy and in (Velasco-Villa et al., 2007), the remote control of the (3,0) mobile robot is developed based on a discrete-time strategy assuming a time-lag model of the robot. In (Velasco-Villa et al., 2007b) the trajectorytracking problem is solved by means of an estimation strategy that predicts the future values of the system based on the exact nonlinear discrete-time model of the robot. A more reduced number of contributions have been focused on the dynamic representation of the omnidirectional mobile robot. For example, in (Carter et al., 2001), it is described the mechanical design of a (3,0) robot and based on its dynamic model it is proposed a PID control for each robot wheel. Authors in (Bétourné & Campion, 1996) consider an Euler15