Trajectory Tracking by Multiple Agents in Formation With Collision Avoidance and Connectivity Assurance

This paper is concerned with the trajectory tracking by multiple agents in formation. Each agent is modeled as a double-integrator system. The proposed algorithm works on a connected graph instead of a fully connected graph that requires lesser communication and computation. The three aspects of the control scheme-connectivity assurance, collision avoidance, and formation have been ensured by the design of the novel control law consisting of four terms. A novel bounded potential function has been introduced that ensures interagent collision avoidance through the innovative design of critical parameters associated with this potential function. Another novel bounded potential function has been designed to ensure the connectivity in the group. The concept of consensus has been used to acquire and maintain the desired formation pattern with velocity agreement among agents. The proposed control scheme is further extended to the problem of trajectory tracking while achieving other control objectives. Both the schemes have been shown to be convergent using Barbalat's Lemma. Detailed theoretical analysis of the algorithms has been carried out including boundedness of the control actions. The performance of proposed algorithms has been demonstrated through extensive simulations in 2-D and 3-D environments using 6 and 60 agents, respectively.