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Robotics is among the much-touted treatment and therapy solutions in modern dentistry. A unique Particle Swarm Optimization PSO is utilized to manage the needle tip location and direction as a function of the knots along the path between the end-effector segments in a dentistry robotics navigation system recently suggested. The innovative "Numeric Alphabet Flow" (NAF) method may control any point-to-point surgical motions for a three-link robotic guiding system. The new NAF approach creates a brand-new form known as the NAF-PSO methodology by using flowing values and alphanumeric characters in the fuzzy rules and employing particle swarm optimization techniques. Within that paper, we use the novel NAF-PSO to improve robotic tracking performance. This study introduces a unique route planner that specifies the suggested NAF-PSO function as minimizing space and traveling time while not reaching a maximal preset force and avoiding obstacles. [ABSTRACT FROM AUTHOR]