Connectivity and Obstacle Avoidance Method for Formation Tracking with Uncertain Multiple Nonholonomic Mobile Robots with Unknown Faults

This paper delves into the challenge of ensuring connectivity and steering clear of obstacles for multiple uncertain nonholonomic mobile robots that face limitations in communication and sensing distances under the influence of unknown actuator defects. It operates under the assumption that the nonlinear dynamics of these robots are completely unknown. The necessary relative angles to sustain connectivity and simultaneously avoid obstacles are derived. Furthermore, an innovative strategy for obstacle avoidance that also maintains connectivity is introduced. Then, making use of these designated relative angles and performance functions that maintain connectivity and avoid collisions, a leader-follower formation tracker is designed to achieve network upkeep, crash prevention, and robotic obstacle navigation. Simultaneously, to compensate for the effects of intermittent unknown actuator faults and enable the robots to continue interacting with their leader and uninterruptedly track the leader's time-varying reference trajectory during actuator failures, an adaptive law with unknown parameters is further proposed for time-varying formations, ensuring that all signals are semi-globally uniformly ultimately bounded. Finally, the stability analysis is performed using the Lyapunov equation.