They combined a fuzzy logic controller (FLC) with a modified elephant herding optimization algorithm (MEHO) to tune an integral sliding mode controller (ISMC). Implemented on a three-wheeled omnidirectional mobile robot (TOMR), this method significantly improved trajectory tracking, substantially reducing positional and orientation errors.
The system achieved faster response and smoother torque control compared to existing methods, demonstrating a potentially robust and generalizable solution for robotic navigation under uncertain simulated conditions.
Background
Omnidirectional mobile robots are prized for their superior maneuverability in constrained environments. While advanced control strategies like ISMC combined with fuzzy logic and metaheuristic optimizers have been developed for trajectory tracking, existing methods often suffer from high computational complexity, application-specific designs, and inadequate real-time performance.
This paper filled these gaps by proposing a novel hybrid controller that integrates ISMC with a fuzzy system and a modified optimization algorithm, demonstrating significantly improved tracking precision and convergence speed for a three-wheeled robot.
Advanced Control and Trajectory Tracking for a TOMR
The researchers presented a comprehensive approach to mathematical modeling and advanced control system design for a TOMR, beginning with the development of both kinematic and dynamic models.
The kinematic model defines how the robot's individual wheel velocities translate into motion within a global coordinate frame, using Jacobian matrices to handle the necessary coordinate transformations. In contrast, the dynamic model, grounded in Newton’s second law, captures the forces and torques required to produce this motion. It incorporates key physical parameters such as mass, inertia, and external influences like friction and ground interaction.
At the heart of this work is a robust trajectory tracking control system, designed to ensure the robot’s center point follows a predefined path with high precision. This is accomplished using a hybrid controller built around an Integral Sliding Mode Control (ISMC) framework, chosen for its resilience to system uncertainties and external disturbances.
To further improve adaptability and responsiveness, a Sugeno-type FLC was integrated into the ISMC. The FLC dynamically adjusts the sliding surface parameters based on real-time position and velocity errors, enabling the system to fine-tune its behavior through intelligent, rule-based decision-making.
Crucially, the tuning of ISMC gain parameters is not handled manually. Instead, it is automated using a Modified Enhanced Harris Hawks Optimization (MEHO) algorithm. This improved version of the classical algorithm introduces adaptive update mechanisms that more effectively balance global exploration and local exploitation within the search space. The result is faster convergence and better overall control performance.
Together, these components form a tightly integrated closed-loop system. The FLC and MEHO collaborate to continuously optimize the ISMC controller, minimizing tracking error and ensuring robust, accurate motion control, even in complex and dynamic environments.
Results and Discussion
The authors conducted an in-depth performance evaluation of the proposed ISMC-FLC-MEHO controller (referred to as Controller 3) through numerical simulations in MATLAB. Its performance was benchmarked against two alternatives: a classical EHO-based controller (Controller 1) and an improved variant (Controller 2). The tests involved guiding a TOMR along two distinct paths—a triangular trajectory and a more complex C-shaped trajectory.
Across all metrics, the ISMC-FLC-MEHO controller consistently outperformed the others. During the triangular path tracking, Controller 3 maintained near-perfect trajectory adherence, with a maximum deviation of less than 0.01 meters. In contrast, Controllers 1 and 2 exhibited visible tracking errors, particularly at the trajectory corners.
Positional error analysis showed that Controller 3 converged to zero error in just 2.2 seconds, a marked improvement over the 11 seconds and 7 seconds required by Controllers 1 and 2, respectively. Moreover, it eliminated steady-state orientation error, achieving convergence within 1 second, which is five times faster than the other controllers.
The linear velocity response under Controller 3 was also notably smoother, reaching the desired 0.25 m/s in under 2 seconds. This was achieved without the overshoot and oscillations that were present in the other two controllers.
A key highlight was the improvement in torque output across the robot’s three motors. Controller 3 produced significantly more stable and smoother torque profiles, with up to a 50 % reduction in peak torque and near-total elimination of jitter. These improvements suggest not only better tracking performance but also enhanced energy efficiency and reduced mechanical stress, which could contribute to longer actuator lifespan.
Quantitative analysis further supported these observations. Root Mean Square Error (RMSE) values for the triangular path were lowest for Controller 3, and this advantage carried over to the more challenging C-shape trajectory. Additionally, a direct comparison with a leading hybrid controller from current literature—tested on a circular path—confirmed the robustness and effectiveness of the ISMC-FLC-MEHO framework. It achieved faster error convergence and significantly higher tracking accuracy in that benchmark scenario.
Conclusion
In conclusion, this study successfully developed a novel hybrid control framework for a TOMR, integrating ISMC with a Sugeno-type FLC and a MEHO algorithm.
The proposed ISMC-FLC-MEHO controller demonstrated exceptional performance in trajectory tracking, significantly reducing positional and orientation errors to millimeter-level and milliradian levels, achieving faster settling times under 2.7 seconds, and producing up to 50 % smoother torque outputs compared to conventional methods.
The results confirm the system's superior accuracy, robustness, and control smoothness, presenting a highly effective solution for autonomous robotic navigation in uncertain simulated conditions.
Journal Reference
Hussein et al. (2025). Hybrid integral sliding mode and fuzzy logic control for omnidirectional robots: modified elephant herding optimization for trajectory tracking. Scientific Reports, 15(1). DOI:10.1038/s41598-025-19449-x. https://www.nature.com/articles/s41598-025-19449-x
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