Leader-follower formation control without leader's velocity information

In this paper, we consider the mobile robots formation control problem without direct measurement of the leader robot's linear velocity. Two decentralized nonlinear algorithms are proposed, respectively, based on adaptive dynamic feedback and immersion Rz invariance estimation based second order sliding mode control methodologies. The main idea is to solve formation problem by estimating the leader robots's linear velocity, while maintaining the given predefined separation distance and bearing angle between the leader robot and the follower robot. The stability of the closed-loop system is proven by means of the Lyapunov method. The proposed controllers are smooth, continuous and robust against unknown bounded uncertainties such as sensor inaccuracy between the outputs of sensors and the true values in collision free environments. Simulation examples and physical vehicles experiments are presented to verify the effectiveness of the proposed design approaches, and the proposed designed methodologies are carefully compared to illustrate the pros and cons of the approaches.