Three-Dimensional Trajectory Planning for Robotic Manipulators Using Model Predictive Control and Point Cloud Optimization

Robotic manipulators increasingly operate in complex three-dimensional workspaces where accuracy and strict limits on position, velocity, and acceleration must be satisfied. Conventional geometric planners emphasize path smoothness but often ignore dynamic feasibility, motivating control-aware trajectory generation. This study presents a novel model predictive control (MPC) framework for three-dimensional trajectory planning of robotic manipulators that integrates second-order dynamic modeling and multi-objective parameter optimization. Unlike conventional interpolation techniques such as cubic splines, B-splines, and linear interpolation, which neglect physical constraints and system dynamics, the proposed method generates dynamically feasible trajectories by directly optimizing over acceleration inputs while minimizing both tracking error and control effort. A key innovation lies in the use of Pareto front analysis for tuning prediction horizon and sampling time, enabling a systematic balance between accuracy and motion smoothness. Comparative evaluation using simulated experiments demonstrates that the proposed MPC approach achieves a minimum mean absolute error (MAE) of 0.170 and reduces maximum acceleration to 0.0217, compared to 0.0385 in classical linear methods. The maximum deviation error was also reduced by approximately 27.4% relative to MPC configurations without tuned parameters. All experiments were conducted in a simulation environment, with computational times per control cycle consistently remaining below 20 milliseconds, indicating practical feasibility for real-time applications. This work advances the state-of-the-art in MPC-based trajectory planning by offering a scalable and interpretable control architecture that meets physical constraints while optimizing motion efficiency, thus making it suitable for deployment in safety-critical robotic applications.