This paper presents a comprehensive approach to designing and optimizing a Hierarchical Rule-Base Reduction (HRBR) based Adaptive-Network-Based Fuzzy Inference System (ANFIS) for symmetric linguistic variables. Specifically, the linguistic joint 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 DDPG (Deep Deterministic Policy Gradient) 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 MAE and RMSE of 0.88 and 1.02 meters, respectively, to a final MAE and RMSE of 0.087 and 0.10 meters. The results highlight the effectiveness of the ANFIS approach for vehicular robotics applications and suggest promising avenues for future research and development.

We present a Multiple Input Multiple Output fuzzy path tracking controller that reduced its rule-base using Hierarchical Rule Base Reduction. A stability proof and outdoor results are also presented.

A new form of waypoint navigation controller for a skid-steer vehicle is presented, which consisted of a multiple input-single output nonlinear fuzzy angular velocity controller. The mem- bership functions of the fuzzy controller employed a trape- zoidal structure with a completely symmetric rule-base. No- tably, Hierarchical Rule-Base Reduction (HRBR) was incorpo- rated into the controller to select only the rules most influen- tial on state errors. This was done by selecting inputs/outputs and generating a hierarchy of inputs using a Fuzzy Relations Control Strategy (FRCS). Similar to some traditional fuzzy con- trollers, the system provided coverage for the global operat- ing environment. However, a rule for every possible combi- nation of variables and states was no longer necessary. Con- sequently, HRBR fuzzy controllers effectively increase both the number of inputs and their associated fidelity without the rule-base dramatically increasing. To contextualize the performance of the controller, a background on vehicle dy- namic modeling methodologies and an in-depth explanation of the related simulation model are provided. An examina- tion of the proposed controller is then completed employing test courses. The test courses examine the effects of steer- ing disturbance, phase lag, and overshoot as expressed in Root Mean Square Error (RMSE), Max Error (ME), and Course Completion Time (CCT). Finally, simulation and experimental results for the controller’s performance were compared with a state-of-the-art waypoint navigation vehicle controller, ge- ometric pure pursuit. The fuzzy was found to outperform the pure pursuit experimentally by 52.1 percent in RMSE, 26.8 percent in ME, and 1.07 percent in CCT, on average, validat- ing the viability of the controller.