INVARIANT AND CONTRACTIVE SETS IN MOTION STABILITY ANALYSIS OF A MOBILE ROBOT

Robot systems represent an important class of applications where the theory of invariant sets can provide important supplementary information for complementing the classical stability analysis. Within this context, we develop a scenario for exploring the invariant and contractive sets of nonlinear systems, which is further used as a powerful instrument for investigating the motion of an autonomous mobile robot. Our approach relies on the concept of “flow-invariant exponential stability”, introduced as a particular type of exponential stability that concomitantly ensures the existence of contractive sets invariant with respect to the state-space trajectories. The new mathematical results are applied in order to identify contractive sets inside the stability domain found by other researchers for the motion of a mobile robot controlled by visual servoing.