Pre-Assigned Time Safe Formation Tracking Control for Nonholonomic Mobile Robots With Spatiotemporal Constraints

In this paper, a pre-assigned-time safe formation control problem with limited perceptual ability (LPA) and collision avoidance (CA) is investigated for multi-nonholonomic mobile robots (MNMRs). Firstly, considering the limited scope and perspective, as well as the challenge of collision avoidance, a pre-assigned time performance function is introduced to impose spatiotemporal constraints on the robot to ensure connectivity and avoid collisions, while maintaining transient and steady-state performance. Subsequently, a new pre-assigned time extended state observer (PTESO) based on time scale function is developed to estimate unknown dynamics, laying the foundation for control design. Through this design, the controller and system parameters are decoupled, giving greater flexibility to the formation time and adapting to different operating environments and task requirements. Finally, the Lyapunov function is used to prove that all signals in the closed-loop system are bounded, and the effectiveness of the method is verified through a series of simulations.