[Paper Review] Fuzzy-based Navigation and Control of a Non-Holonomic Mobile Robot

Razif Rashid, Irraivan Elamvazuthi+2 more|arXiv (Cornell University)|Mar 22, 2010

Control and Dynamics of Mobile Robots10 references20 citations

TL;DR

This paper proposes a fuzzy logic-based controller for navigating non-holonomic mobile robots using kinematic modeling and membership function optimization. It demonstrates that a three-member membership function set outperforms five- and seven-member sets in simulation, achieving superior trajectory tracking and stability with reduced computational load.

ABSTRACT

In recent years, the use of non-analytical methods of computing such as fuzzy logic, evolutionary computation, and neural networks has demonstrated the utility and potential of these paradigms for intelligent control of mobile robot navigation. In this paper, a theoretical model of a fuzzy based controller for an autonomous mobile robot is developed. The paper begins with the mathematical model of the robot that involves the kinematic model. Then, the fuzzy logic controller is developed and discussed in detail. The proposed method is successfully tested in simulations, and it compares the effectiveness of three different set of membership of functions. It is shown that fuzzy logic controller with input membership of three provides better performance compared with five and seven membership functions.

Motivation & Objective

• To develop a fuzzy logic controller for autonomous navigation of non-holonomic mobile robots.
• To analyze the impact of different membership function configurations on controller performance.
• To identify the optimal number of membership functions for effective navigation and control.

Proposed method

• A kinematic model of the non-holonomic mobile robot is established as the foundation for control design.
• A type-1 fuzzy logic controller is designed with inputs derived from robot position and orientation errors.
• Three different membership function sets (three, five, and seven functions) are implemented and compared.
• The controller uses Mamdani inference with singleton fuzzification and center-of-gravity defuzzification.
• Simulation experiments are conducted to evaluate performance across varying path types and initial conditions.
• Performance is quantified using trajectory tracking error, convergence time, and control effort metrics.

Experimental results

Research questions

• RQ1 How does the number of membership functions in a fuzzy logic controller affect navigation performance in non-holonomic mobile robots?
• RQ2 Which membership function configuration (three, five, or seven) yields the best trade-off between accuracy and computational efficiency?
• RQ3 Can a fuzzy logic controller effectively manage the non-holonomic constraints of mobile robot kinematics in dynamic environments?

Key findings

• The fuzzy logic controller with three membership functions achieved the lowest trajectory tracking error compared to five- and seven-function configurations.
• The three-member membership function set demonstrated faster convergence and smoother control inputs in simulation.
• The five- and seven-function sets exhibited higher control effort and oscillatory behavior near goal points.
• The proposed controller successfully navigated the robot along complex paths while maintaining stability.
• The results indicate that increasing membership function count does not improve performance and may degrade it due to increased complexity.