Collision-Free Formation Control and Tracking for Multi-Agent Systems under Motion Constraints

The cohesive motion of a group of vehicles remains stable when all agents achieve velocity consensus and maintain a constant desired speed. However, when the reference velocity changes over time, the formation tracking controllers may struggle to ensure collision-free motion during transitional phases. In this paper, the simultaneous formation control and tracking task is formulated as a constrained optimization problem where the control input actions are restricted within a defined search space. The control objective is to ensure a desired formation geometry while tracking a time-varying reference trajectory by satisfying inter-agent separation conditions for collision avoidance and adhering to input saturation limits that define the allowable control space. Due to the sensor limitations of the deployed agents, the inter-agent distances are estimated using only relative bearing and velocity measurements. The stability and tracking convergence of the proposed distributed control and observer designs are analyzed and validated through simulations in a multivehicle deployment scenario. The results show that the control inputs stay within the feasible limits and effectively prevent inter-agent collisions while achieving the control objectives.