Abstract: Within the domain of robotic manipulations, an advanced analytical solution tailored for seven-joint robotic arms has been meticulously designed, thereby introducing a pioneering trajectory control algorithm specifically developed for such robotic arms. The basis of this innovative algorithm draws inspiration from the well-established bi-interpolation method. The pivotal component of this approach focuses on exploiting the precise position vector at the heart of the wrist joint of the robotic arm. By skillfully deriving the sophisticated interpolation computational equation based on this vector within the Trajectory Planner (TP), the algorithm ensures seamless and smooth planning of the movement trajectory of the robotic arm. Moreover, the algorithm demonstrates its adaptability by calculating the rotation angle of the pivotal seventh joint by interpreting data derived from the position vector of the wrist center point. During each meticulous interpolation cycle, the algorithm combines the calculated rotational value with the seventh joint angle value, obtained through a rigorous analytical inverse solution with high precision. This incorporation enables the system to achieve notable high-precision control over the joint trajectory of the robotic arm, thereby establishing new benchmarks in the field. Simultaneously, the globally recognized gradient projection method is used to compute an array of joint angle values. These values, functioning as robust alternative solutions to the analytical solution, play a pivotal role in effectively mitigating the challenging effects posed by singular points often encountered in robotic computations. To ensure its reliability and dominance, this method has undergone rigorous testing and validation phases in public platforms, namely, the LinuxCNC real-time control and Matlab simulation platforms. During these assessments, the end-point precision of the robotic arm was selected as the primary evaluation metric, ensuring that the results are firmly based on practical applications. The comprehensive research findings resulting from these rigorous tests unmistakably indicate that when compared to conventional methods, such as the gradient projection method, this innovative algorithm is superior, particularly in the field of robotic arm joint trajectory control. Its proficiency in enhancing end-point precision and reducing errors is particularly notable. Therefore, this groundbreaking research work offers an invaluable contribution to industrial automation by presenting a trajectory control methodology for seven-joint robotic arms, thereby assuring enhanced reliability and increased efficiency. By addressing current technological gaps, this work paves the way for further technological advancements in industrial robotic arm applications, promising a future with optimized precision and efficiency across diverse production processes.