To address the time-energy-smoothness path optimization and trajectory motion control challenges in mobile robot navigation under uncertain conditions, this study constructs map environments and available paths using Delaunay triangulation. A free-space judgment criterion is proposed, and a collision-free model is established. The paper presents optimization methods that include acute vertex deletion, path replacement, and redundant point removal, as well as a cubic NURBS path fitting approach. Furthermore, non-probabilistic reliability is introduced to evaluate path states, with optimal reliability paths and their weighting concepts defined and explained. A cost function integrating path task time risk and energy risk metrics is designed. Meanwhile, constraints such as peak curvature limits, restrictions on curvature change rates, and safety distances are integrated into the model. The optimal path smoothing planning and a five-stage S-type acceleration-deceleration motion control with a jerk that satisfies the ′Bang-Bang-Singular′ strategy are carried out. Experimental results demonstrate that our method achieves a 1.907% reduction in time risk and a 40.57% decrease in energy risk compared to approaches employing quadratic B-spline path planning with acceleration control that satisfies the ′Bang-Bang-Singular′ strategy, and the movement is smoother, safer, and more efficient. In contrast to trajectory planning using the VGSP algorithm, the time risk index shows a slight increase, while the energy risk index decreases by 86.46%, with improved safety guarantees for robot operation. Field tests further validate the effectiveness of our method in solving optimal trajectory planning for mobile robots under stringent constraints, ensuring both smooth trajectory curves and the system′s dynamic and flexible performance during motion. This approach achieves unified geometric-motion planning and optimal non-probabilistic reliability regarding task-time and energy.