Probabilistic error model of robot end-effector's dynamic state

摘要

In most error analysis of robot motion, only kinematics and no forces are considered and it is assumed that the errors of joint variables are independent of each other. Such approach ignores the dynamic coupling effects and assumes zero correlation coefficients among the robot links. In this dissertation, a probabilistic method is presented to study the error of robot dynamic state by incorporating the coupling forces among the robot links. The robot's perturbed state vector is first obtained by employing the well developed dynamic equations. Next, by assuming that the probabilistic characteristics of process noise are known, the probabilistic characteristics of robot end-effector's position vector are determined. The error covariance matrix of the robot's perturbed state is found to be infinite due to the fact that robot is an unstable system and therefore a feedback controller for stabilizing the perturbed system is needed. With the assumptions that only joint variables are measurable and that the probabilistic characteristics of measurement noise are known, a Kalman filter is employed to estimate the perturbed state, and a feedback controller designed according to the separation theorem is proposed. The error covariance matrices of estimated perturbed state and residual perturbed state are obtained by application of Kalman filter theory, and then added to find the true perturbed state error covariance. Finally, the error covariance matrix of end-effector's position vector is determined by transforming that of the true perturbed state. The size and shape of an envelope within which the probability value of the perturbed position of the end-effector is confined is quantified. The theoretical developments in this error model are first developed for a Two-Link robot and then generalized to an n-link robot. The Two-Link robot is also used as a sample case to illustrate the numerical calculations involved. The cross correlation coefficients of the Two-Link robot's true perturbed state, estimated perturbed state, and the error between them are all verified using a Monte-Carlo simulation.