The physical upper bound on pose repeatability of general serial manipulators based on joint resolution

The accuracy of a serial robot to perform a recurring manipulation task is an important parameter to characterise its operational capability. In online programming, for example, one moves the end effector manually to all desired or necessary poses for a given task and stores the associated joint angles of the manipulator. The robot can then automatically perform this task by executing the sequence of joint angles and thus returning to the poses very accurately. This high repeatability of a typical industrial robot is due to the high resolution of the encoders that are used to measure the robot's joint angles. This finite resolution of the angular encoders imposes a natural limit on a robot's repeatability as the robot's control system operates on these discrete estimates of the angular positions. Even for typical modern industrial robots, that utilise high-resolution encoders, it is worthwhile to consider this issue in detail as one can obtain interesting information regarding the structural properties for a robot that are invariant regarding the resolution of its encoders. For this purpose, we provide a systematic method for computing the upper limit of the estimation error for position and orientation for a desired pose and posture of the robot. The knowledge about the end effector repeatability can be used for optimisation such as manipulator placement. Simulation studies that utilise a general 6R serial robot are used to illustrate this methodology and to analyse the diverse accuracy characteristics of its up to 16 different postures for a given task.