The research examines the potential for adaptive planning in the trajectory construction of a collaborative manipulator in the presence of humans, such as public health service or crowded workplaces . Mathematical models are proposed that integrate the gradient field of potential functions, adaptive weighting of social repulsion, and the change of the motion vector through fuzzy logic. The models provide safe and effective trajectories considering the operator's proximity, obstructions, and the target. The proposed models are examined through their software implementation in the Python environment. These techniques facilitated the simulation of effector motion, the construction of a gradient field, and the assessment of system behavior under varying environmental configurations. The results indicate successful evasion of physical objects and the human comfort zone while achieving the intended objectives. The developed models possess the capability for incorporation into collaborative robotics systems in alignment with the specifications of Industry 5.0. Subsequent study may focus on incorporating reinforcement learning, extending to three-dimensional space, and conducting real hardware testing.
