Tolerance Volume Due to Joint Variable Errors in Robots

The locational uncertainty of a manipulator is largely due to the errors of the joint variables. But these errors cannot be easily compensated for because they are dependent on the operation (i.e., robot-configuration). Motivated by the need to conduct precision engineering and the intellectual curiosity of geometric uncertainty, the probabilistic tolerance volume due to joint errors is investigated. By defining the locational uncertainty in Cartesian space as a tolerance volume, the investigation focuses on the automatic generation of the tolerance volume from a given confidence level. For this purpose, the linear mapping form Δq space to Δd space through Jacobian matrix is analyzed probabilistically. Probabilistic approach is advantageous since the tolerance volume by the deterministic approach is found to be unnecessarily large. With the assumption of normality of joint variables, this paper begins with the computation of the confidence level for a given tolerance volume. A fast analytic procedure, which gives a considerable time-reduction compared to the commonly used Monte-Carlo simulation, is presented. Based on the monotonic relation between confidence level and tolerance volume, the procedure is used to generate the tolerance volume covering the desired confidence level. The scheme is tested with the six degrees-of-freedom Stanford manipulator and shows a significant (more than 5 times) reduction in the size of the tolerance volume with a 0.3 percent probability of error.