On the repeatability of planar 2R manipulators with rotary encoders

The performance of position control systems for manipulators directly depends on the accuracy of its measurement system. Robots with revolute joints typically use rotary encoders for measuring the joint angles. The quantization in the joint angle measurements leads to a discretization of the configuration space and thereby limits accuracy and repeatability. Configuration space coordinates transform to workspace coordinates via nonlinear direct kinematic maps. The equidistant discretization of the configuration space therefore results in a non-equidistant discretization of the workspace. One effect of this non-equidistant workspace discretization is that repeatability is not constant over the workspace but depends on the configuration of the robot. In this work, we present a measure for repeatability that is able to deal with this configuration-dependence. Based on this measure, we are able to provide regions of maximal repeatability, which are regions where the positioning error due to discretization is minimal. The methodology is demonstrated for planar 2R manipulators.