Integrating artificial intelligence (AI) and stochastic technologies into the mobile robot navigation and control (MRNC) framework while adhering to rigorous safety standards presents significant challenges. To address these challenges, this paper proposes a comprehensively integrated MRNC framework for skid-steer wheeled mobile robots (SSWMRs), in which all components are actively engaged in real-time execution. The framework comprises: 1) a LiDAR-inertial simultaneous localization and mapping (SLAM) algorithm for estimating the current pose of the robot within the built map; 2) an effective path-following control system for generating desired linear and angular velocity commands based on the current pose and the desired pose; 3) inverse kinematics for transferring linear and angular velocity commands into left and right side velocity commands; and 4) a robust AI-driven (RAID) control system incorporating a radial basis function network (RBFN) with a new adaptive algorithm to enforce in-wheel actuation systems to track each side motion commands. To further meet safety requirements, the proposed RAID control within the MRNC framework of the SSWMR constrains AI-generated tracking performance within predefined overshoot and steady-state error limits, while ensuring robustness and system stability by compensating for modeling errors, unknown RBF weights, and external forces. Experimental results verify the proposed MRNC framework performance for a 4,836 kg SSWMR operating on soft terrain.