Trajectory tracking is a crucial task for autonomous mobile robots, requiring smooth and safe execution in dynamic environments. This study uses a nonlinear model predictive controller (MPC) to ensure accurate trajectory tracking of a four-wheel drive, four-wheel steer (4WD-4WS) mobile robot. However, the MPC's performance depends on the optimal tuning of its key parameters, a challenge addressed using the Multivariate Gaussian Mixture Model Continuous Ant Colony Optimization (MGMM-ACOR) algorithm. This method improves on the classic ACOR algorithm by overcoming two major limitations: the lack of consideration for interdependencies between optimized variables, and an inadequate balance between global exploration and local exploitation. The proposed approach is validated by a two-phase evaluation. Firstly, benchmark function evaluations demonstrate its superiority over established optimization algorithms, including ACO, ACOR, and PSO and its variants, in terms of convergence speed and solution accuracy. Secondly, MGMM-ACOR is integrated into the MPC framework and tested in various scenarios, including trajectory tracking with circular and eight trajectories and dynamic obstacle avoidance during trajectory tracking. The results, evaluated based on trajectory error, control effort, and computational latency, confirm the robustness of the proposed method. In particular, the explicit modeling of correlations between variables in MGMM-ACOR guarantees stable, collision-free trajectory tracking, outperforming conventional ACOR-based approaches that optimize variables independently.