Safe prescribed time controller for wheeled mobile robots by using control barrier functions as a safety filter

Area of Science:

• Robotics and Control Systems
• Applied Mathematics

Background:

• Achieving precise trajectory control within a specified timeframe is a significant challenge in robotics and autonomous systems.
• Ensuring system safety and preventing collisions during trajectory execution is paramount for real-world applications.

Purpose of the Study:

• To design and validate a control methodology that guarantees trajectory convergence to a desired equilibrium point within a user-defined time.
• To implement a safety mechanism using control barrier functions (CBFs) to prevent collisions with predefined unsafe regions.
• To ensure the system maintains stability and error convergence at the equilibrium point beyond the prescribed time.

Main Methods:

• Design of a prescribed time controller for trajectory tracking.
• Integration of a proportional controller for post-convergence error maintenance.
• Application of a control barrier function (CBF) for safety enforcement and collision avoidance.
• Extensive simulations across diverse scenarios to validate the control scheme.

Main Results:

• The proposed controller successfully achieved trajectory convergence to the equilibrium point within the user-defined prescribed time.
• The system demonstrated robustness, reaching the equilibrium point irrespective of initial conditions and the chosen prescribed time.
• The control barrier function effectively prevented the system from entering predefined unsafe zones, ensuring safe operation.
• The proportional controller maintained system errors at the equilibrium point beyond the prescribed time.

Conclusions:

• The developed control strategy effectively combines prescribed time trajectory tracking with guaranteed safety through CBFs.
• The methodology offers a reliable solution for applications requiring precise and safe trajectory control within a finite time.
• Simulation results confirm the efficacy and robustness of the proposed control system across various operational scenarios.