This article presents a comparative analysis of methods for predicting object movement trajectories in a collaborative robots-manipulator working area. The following approaches are evaluated: linear method, Kalman filter, extended Kalman filter (EKF), behavioral models and LSTM models. A mathematical description of each method is accompanied by an analysis of their advantages and disadvantages, including prediction accuracy, implementation complexity, and resource requirements. The results show that the choice of the method depends on the specifics of the task and the robot's operating conditions, which allows for an optimal combination of efficiency and computational costs.