5 May 2026

Hierarchical Rule-Base Reduction-Based ANFIS with Online Optimization Through DDPG

Abstract: This article presents a comprehensive approach to designing and optimizing a hierarchical rule-base reduction-based adaptive-network-based fuzzy inference system (ANFIS) for symmetric linguistic variables. Specifically, the linguistic connected membership functions that underlie the ANFIS are defined, focusing on symmetrical inputs/outputs and jointly optimized trapezoid membership functions to reduce the number of training parameters. Further optimizations for the ANFIS were derived based on design assumptions, including training the membership functions on closed or single-sided domains. The optimal output membership weights based on mean square error optimization were also symbolically obtained. The online training of the ANFIS’s input/output membership functions was performed using the deep deterministic policy gradient (DDPG) algorithm. A simulated skid-steered vehicle was used to validate the approach and performed waypoint-to-waypoint path following. Experimental results using the Clearpath Jackal demonstrated that the ANFIS model converged quickly, typically within 6 to 10 episodes of training, from an initial mean absolute error (MAE) and root mean squared error (RMSE) of 0.88 and 1.02 m, respectively, to a final MAE and RMSE of 0.087 and 0.10 m. The results highlight the effectiveness of the ANFIS approach for vehicular robotics applications and suggest promising avenues for future research and development.

23 Apr 2026

Hierarchical Rule-Base Reduction Fuzzy Control for Path Tracking Variable Linear Speed Differential Steer Vehicles

Abstract: A novel waypoint navigation controller for a skid-steer vehicle is presented, where the controller is a multiple input-multiple output nonlinear angular velocity and linear speed controller. Hierarchical rule-base reduction was used in defining the controller. This entailed selecting inputs/outputs, determining the most globally influential inputs, generating a hierarchy relating inputs, selecting only the rules corresponding to the hierarchy, and, in effect, designing a symmetric rule-base. This dramatically reduced the rule-base size, by 97.7%, while maintaining global operating environment coverage. The stability analysis proved the asymptotic stability of the closed-loop controller-vehicle system. In addition, test courses were used to examine the effects of steering disturbance, phase lag, and overshoot as expressed in root mean square error (RMSE) and max error (ME). Outdoor experimental results for the controller’s performance were contrasted with a benchmark waypoint navigation controller, pure pursuit, and a simpler implementation that only output linear speed. The controller was found to outperform the pure pursuit and simpler implementation experimentally by 72% and 50% in RMSE, 71% and 40% in ME, validating the controllers viability.