Practical Hybrid Graph-Based Formation Control Architecture for Leader-Follower Trajectory Tracking Problem

This paper extends the traditional single vehicle trajectory tracking problem to develop a control approach for a group of N-vehicles which are capable of converging to a desired formation while moving on a predefined trajectory. A novel hybrid control algorithm is introduced to handle the two aforementioned problems separately. The proposed controller integrates three different techniques; graph theory, Lyapunov stability and leader-follower approach. The controller structure consists of two main subsystems. In the first subsystem, a leader virtual robot is responsible for the trajectory tracking problem, actuated via a Lyapunov-based controller. Simultaneously, a graph-based controller is used to guarantee the convergence of the follower mobile robots to the desired formation using local positioning information; thus, ensuring the stability of the formation of the follower robots with respect to the moving leader. This new hybrid approach handles the problem of impractical velocities providing control inputs within acceptable ranges that can be practically implemented. Furthermore, it eliminates the oscillations in the motor inputs. Several scenarios are implemented to verify the proposed hybrid control algorithm. The simulations show significant and promising results which prove the effectiveness of this hybrid approach.