Quasi-Static Compliance Calibration of Serial Articulated Industrial Manipulators

Abstract

This article presents a procedure for the quasi-static compliance calibration of serial articulated industrial manipulators. Quasi-static compliance refers to the apparent stiffness displayed by manipulators at low-velocity movements, i.e., from 50 to 250 mm/s. The novelty of the quasi-static compliance calibration procedure lies in the measurement phase, in which the quasi-static deflections of the manipulator’s end effector are measured under movement along a circular trajectory. The quasi-static stiffness might be a more applicable model parameter, i.e., representing the actual manipulator more accurately, for manipulators at low-velocity movements. This indicates that the quasi-static robot model may yield more accurate estimates for the trajectory optimization compared with static stiffness in the implementation phase. This study compares the static and apparent quasi-static compliance. The static deflections were measured at discretized static configurations along circular trajectories, whereas the quasi-static deflections were measured under circular motion along the same trajectories. Loads of different magnitudes were induced using the Loaded Double Ball Bar. The static and quasi-static displacements were measured using a linear variable differential transformer embedded in the Loaded Double Ball Bar and a Leica AT901 laser tracker. These measurement procedures are implemented in a case study on a large serial articulated industrial manipulator in five different positions of its workspace. This study shows that the measured quasi-static deflections are bigger than the measured static deflections. This, in turn, indicates a significant difference between the static and apparent quasi-static compliance. Finally, the implementation of the model parameters to improve the accuracy of robots and the challenges in realizing cost-efficient compliance calibration are discussed.

Influence of the velocity on quasi-static deflections of industrial articulated robots

“…The trajectories under investigation were circular due to the design constraints of the utilised measurement instrument, the loaded double ball bar (LDBB) [27]. A more detailed description of the measurement procedure can be found in [21] and [28].…”

“…There were mainly two different kinds of transient phases in the measurement stages associated with loaded circular testing, which corresponded to acceleration and deceleration as well as trigger movements. For instance, for the measurement of quasi-static stiffness, the industrial manipulator is moving along a trajectory at a constant velocity [21]. At the beginning of the test, the manipulator had to accelerate until it reached constant velocity and, at its end, decelerate back to zero velocity.…”

“…However, when the actual contact application is performed, geometric and non-geometric (motion dependent) errors contribute to the robot's positioning accuracy [20]. Therefore, Theissen et al [21] proposed a measurement scheme in which the industrial manipulator moved at velocities from 50 to 250 mm s −1 . In preceding research work, the authors reported an apparent difference between static and quasistatic (QS) deflections of industrial manipulators.…”

Accuracy Assessment of Articulated Industrial Robots using the Extended- and the Loaded-Double-Ball-Bar

“…Figure 7 shows the specific error-sensitive measurement path on the Comau NJ-130 test carrier. The procedure measures quasi-static deflections, i.e., deflections of the manipulator's end-effector under movement along a circular trajectory [29]. The conceptual measurement setup is delineated in Fig.…”