|M.Sc Student||Rozenheck Oshri|
|Subject||Distance-Constrained Formation Tracking Control|
|Department||Department of Autonomous Systems and Robotics||Supervisor||Professor Daniel Zelazo|
This work considers a multi-agent formation control problem where a designated leader is subjected to an additional velocity reference command. The entire formation should follow the leader while maintaining the inter-agent distance constraints. The formation error is defined from the zero-input dynamics of agents modeled as single integrators.
A local stability proof is provided by using the dynamics of the formation error and employing Lyapunov's indirect method. Finding an upper bound on the steady state error of the linearized dynamics also reveals significant relations between the error properties to those of the graph topology. By augmenting a standard gradient formation controller with a proportional-integral control on the formation error, we are able to prove the stability of the formation error dynamics with velocity input while ensuring zero steady-state formation error.
To agents with double integrator dynamics we add a consensus-based control loop on the velocities to achieve the formation maintenance problem. The formation error is augmented with a velocity error, that defines the differences between the velocity of each agent to that of the reference. Lyapunov's second method is used to prove that the system is asymptotically stable.
For a system with an external reference velocity a decentralized control is proposed to manipulate the agents' velocities and a velocity feedback mechanism is implemented on the leader to assure the formation tracks the reference signal. Numerical simulations are shown to illustrate the theoretical results.