This research addresses the challenges of using the Rapidly Exploring Random Tree (RRT) algorithm as a mobile robot path planner. While RRT is known for its flexibility and wide applicability, it has limitations, including careful tuning, susceptibility to local minima, and generating jagged paths. The main objective is to improve the smoothness of RRT-generated trajectories and reduce significant path curvature. A novel approach is proposed to achieve these, integrating the RRT path planner with a modified version of the Whale Optimization Algorithm (RRT-WOA). The modified WOA algorithm incorporates parameter variation () specifically designed to optimize trajectory smoothness. Additionally, Piecewise Cubic Hermite Interpolating Polynomial (PCHIP) instead of conventional splines for point interpolation further smoothes the generated paths. The modified WOA algorithm is thoroughly evaluated through a comprehensive comparative analysis, outperforming other popular population-based optimization algorithms such as Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and Firefly Algorithm (FA) in terms of optimization time, trajectory smoothness, and improvement from the initial guess. This research contributes a refined trajectory planning approach and highlights the competitive advantage of the modified WOA algorithm in achieving smoother and more efficient trajectories compared to existing methods.