Variable Structure Feedback Construction Algorithm for controlling measurement-imploded leader-follower ground robots

This paper presents a systematic approach for decreasing the error growth of a formation system consisted of a leader and a number of followers which are open-loop in position measurements (position, linear velocity and relative distance to the leader). Using conventional algorithms to control such a system may lead to an unstable network with increasing consensus error. A 3-phase algorithm is proposed to address open-loop systems of the mentioned form. The algorithm is specifically beneficial to the case where linear velocity and position sensors get damaged. The main idea of the proposed algorithm is to use fundamental relations between feedbacks and construct some of them using the others which in case of car-like ground vehicles, angular sensors' feedbacks are used to estimate linear feedbacks. The error and input mathematical relations are formulated using kinematic of car-like robots. The stability of the proposed method is proved using a quadratic CLF, and the numerical simulation results are presented to assess the effectiveness of the algorithm compared to a conventional open-loop form. The algorithm is also applied on a pair of ground car-like robots. The experimental results verify the conclusions based on simulation. Various simulation results show that the proposed algorithm has improved the divergence rate of follower's path from leader's, from 0.3 msec for the unit of velocity's uncertainty to about zero.