Abstract: When the manipulator's movement has process noise, or its external closed-loop feedback sensors have specific observation noise, the single actual movement trajectory of the manipulator can deviate from the predefined trajectory randomly. However, the movement error of the manipulator has a probability distribution when it repeats the same action for many times. The non-deterministic movement state is described by the Gaussian distribution which is widespread in nature. The probability theory combing with the manipulator's linear control and Kalman filter estimation is used to plan the trajectory and evaluate the apriori probability distribution of movement error of the manipulator. Firstly, Linear control method is used in combination with Kalman filter to establish error model of Gaussian motion system. Then, a predefined trajectory is assessed iteratively with the Gaussian motion model to calculates the error distributions of the entire trajectory. Through Gaussian movement prior probability estimates, the security can be estimated qualitatively and the successful probability of arriving at the object region can be calculated quantificationally. At last, the effectiveness and practicability of the algorithm proposed can be verified by the comparison between simulation and experiment data.

Key words: manipulator, optimal decision, probability, trajectory planning