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.