A Method to Estimate the Encoder Dependent Repeatability of General Serial Manipulators

A crucial parameter for the operational capability of a serial robot is its accuracy. For recurring tasks the high repeatability of the manipulator is utilized by programming the robot online. Therefore, the end effector is moved manually to all desired or necessary poses of a given task and the joint angles of the manipulator are stored at these poses. The end effector can return to these stored poses very accurately due to the high repeatability of industrial robots. But even this repeatability is subject to limits. A major influencing factor is the finite resolution of the encoders integrated within the manipulators joints. Based on the discrete encoder readings, the end effector pose can only be estimated. Despite the typically high resolution of encoders in modern industrial robots, it is worth considering this issue in detail, as one can identify interesting structural properties that are invariant with respect to the encoder resolution. In this work, we will show how to compute the upper limit of the estimation error depending on a desired pose and posture of the manipulator. Both positioning and orientation error due to this discretization effects are considered. Simulation results are illustrated by means of a general 6R serial manipulator and a path, which the end effector can follow with 16 different postures.