Uncertainty analysis and allocation of joint tolerances in robot manipulators based on interval analysis

Many uncertain factors influence the accuracy and repeatability of robots. These factors include manufacturing and assembly tolerances and deviations in actuators and controllers. The effects of these uncertain factors must be carefully analyzed to obtain a clear insight into the manipulator performance. In order to ensure the position and orientation accuracy of a robot end effector as well as to reduce the manufacturing cost of the robot, it is necessary to quantify the influence of the uncertain factors and optimally allocate the tolerances. This involves a study of the direct and inverse kinematics of robot end effectors in the presence of uncertain factors. This paper focuses on the optimal allocation of joint tolerances with consideration of the positional and directional errors of the robot end effector and the manufacturing cost. The interval analysis is used for predicting errors in the performance of robot manipulators. The Stanford manipulator is considered for illustration. The unknown joint variables are modeled as interval parameters due to the inherent uncertainty. The cost-tolerance model is assumed to be of an exponential form during optimization. The effects of the upper bounds on the minimum cost and relative deviations of the directional and positional errors of the end effector are also studied.