Adaptive Performance Control for Bipolar-Coordinate Based Multi- Robot Formations under Input Saturation

This thesis investigates the application of Prescribed Performance Control (PPC) to multi-agent formation systems with realistic robotic constraints. Building on the bipolar coordinate framework, the work develops a saturation aware extension of PPC that enables decentralized formation control for differential drive mobile robots. The methodology combines finite-time funnels, adaptive bound modulation, and reference relaxation to guarantee transient and steady-state performance under actuator limits. Additional ingredients such as initialization-free shaping, topology switching during agent crossings, and an heuristic collision handling are integrated to enhance robustness in practice. The proposed framework is validated through real experiments on TurtleBot3 robots, using a Qualisys motion capture system and a ROS2-based architecture. Results demonstrate that the controller is able to achieve formation tracking while preserving shape, scale, and orientation in the presence of input saturation, sensing noise, and communication imperfections. The findings confirm that PPC can be effectively adapted to non-holonomic agents in realistic environments, offering a scalable and flexible approach to formation control.