Fixed-Time VFO Control Design for Nonholonomic Mobile Robots With Constrained Control Inputs.

Area of Science:

• Robotics
• Control Systems
• Nonholonomic Systems

Background:

• Unicycle-like nonholonomic mobile robots present unique control challenges due to their kinematic constraints.
• Achieving set-point control under constraints requires advanced control strategies for stability and efficiency.
• Existing methods may struggle with predictable transient state evolution and guaranteed convergence times.

Purpose of the Study:

• To develop a fixed-time vector-field-orientation (VFO) control law for unicycle-like nonholonomic mobile robots.
• To address challenges posed by control input and task-execution time constraints.
• To provide a control solution with non-oscillatory and predictable transient state behavior.

Main Methods:

• Implementation of the vector-field-orientation (VFO) control methodology.
• Formal stability analysis of the closed-loop dynamics using Lyapunov theory.
• Development of a method for a priori estimation of convergence time upper bounds under input constraints.

Main Results:

• A novel fixed-time VFO control law was designed for unicycle robots.
• The control law ensures non-oscillatory and predictable transient state evolution.
• Stability was formally proven, and convergence time bounds were estimated, validated by simulations and experiments.

Conclusions:

• The proposed fixed-time VFO control law effectively addresses set-point control for unicycle robots under constraints.
• The method guarantees stability and provides predictable performance, crucial for real-world applications.
• The approach offers a robust solution for mobile robot navigation with time and input limitations.