Motion control for a differential vehicle with variable point of interest. Application: Smart cane control

Abstract

This article addresses an unified solution to the trajectory tracking and path following problems for differential drive mobile robots (DDMR) considering a point of interest (PoI) with variable location relative to the vehicle. The mobile robot is modeled with an extended kinematic model avoiding typical singularities of this kind of vehicles, and allowing a straightforward definition of the corresponding inverse kinematics controller (IKC). This classical IKC fulfills the control objective with exponential error convergence but with the shortcoming of generating backward navigation when the PoI is located behind the DDMR, which is undesirable in some practical applications where the forward navigation must be preserved. This situation is theoretically analyzed, concluding that even though both forward and backward navigations correspond to equilibrium points of the closed loop, the stability of the forward navigation requires a PoI located in front of the DDMR, and the stability of the backward navigation requires a PoI located behind the DDMR. Finally, the article presents novel alternative controllers in order to always fulfill the motion objectives with stable forward navigation. Simulation results are presented to show the performance of the proposed controllers, and a real application of a robotic cane guiding its user is experimentally developed.