A new way of understanding position error in wheeled mobile robots control problem

The problem of path-tracking of wheeled mobile robot (WMR) has been well studied and many algorithms have been presented to solve the problem. However, most of the existed methods are based on Lyapunov function while few works have been done on error analysis of the control law caused by imperfect conditions, especially by inaccurate controlling. In this paper, a discrete-time system model is established to obtain both theoretical and simulative results of a ground robot's position error caused by inaccurate control actions. We provide a general framework to analyze the problem, which enables other position error calculations adopting similar method. As indicated by the experimental results on Pioneer-3DX robots, the theoretical work is valid.