This research outlines the methodology and application of quasi-static loaded circular testing on serial articulated industrial robots using the Loaded Double Ball Bar (LDBB). The article focuses on measuring the quasi-static path accuracy and repeatability of industrial manipulators to evaluate their performance in industrial contact applications such as trimming, grinding, or deburring. The manipulator is measured under quasi-static loads of 100, 350, 500, and 600N using circular testing following the guidelines of ISO 230-4. The data can be used to discuss core aspects of process planning with industrial manipulators such as workpiece placement, optimal robot pose selection for dexterity as well as stiffness optimization. The article contains a case study of quasi-static loaded circular testing of a mid-size articulated industrial robot from ABB using the LDBB and a Leica AT960 laser tracker for validation. At a load of 600N the path accuracy for both Clock-Wise (CW) and Counter Clock-Wise (CCW) were 2:4 mm, measured with the LDBB, compared to 2.9 mm, measured with the AT960. Finally, the paper ends with a discussion about the opportunities and challenges for the implementation of loaded circular testing for elasto-geometrical calibration of industrial manipulators. 

Industrial manipulators are desired to be commonly used for material removal applications due to their high flexibility, low cost, and large working space. However, their lower stiffness (compared to a machine tool) leads to a reduction in path accuracy. This reduction directly affects the dimensional accuracy of the machined part. Additionally, the low stiffness in the presence of dynamic process forces creates vibrations influencing the surface quality, tool life, and service life of the manipulator. Static stiffness models, optimization, and compensation techniques exist to minimize force-induced deflections. Multi-body dynamics analytical models still lack the required accuracy in predicting the position-dependent dynamics of the manipulator. Dynamics data-driven models are rising to tackle the uncertainties in modeling the robot properties. This study presents the position-dependent variation of the dynamic characteristics, namely frequency and damping, of a mid-size articulated industrial manipulator, which were determined through experimental modal analysis. The position-dependent dynamics is investigated and quantified in a low-frequency range and is discretely measured and presented in two perpendicular planes (horizontal and vertical) of the robot working space. The study concludes with a discussion on the potential to apply the dynamic information obtained experimentally for the process planning and working space optimization in contact applications. 

This article presents a procedure for the quasi-staticcompliance calibration of serial articulated industrialmanipulators. Quasi-static compliance refers to theapparent stiffness displayed by manipulators at lowvelocitymovements, i.e., from 50 to 250 mm/s. Thenovelty of the quasi-static compliance calibration procedurelies in the measurement phase, in which thequasi-static deflections of the manipulator’s end effectorare measured under movement along a circulartrajectory. The quasi-static stiffness might be amore applicable model parameter, i.e., representingthe actual manipulator more accurately, for manipulatorsat low-velocity movements. This indicates thatthe quasi-static robot model may yield more accurateestimates for the trajectory optimization comparedwith static stiffness in the implementation phase. Thisstudy compares the static and apparent quasi-staticcompliance. The static deflections were measured atdiscretized static configurations along circular trajectories,whereas the quasi-static deflections were measuredunder circular motion along the same trajectories.Loads of different magnitudes were inducedusing the Loaded Double Ball Bar. The static andquasi-static displacements were measured using a linearvariable differential transformer embedded in theLoaded Double Ball Bar and a Leica AT901 lasertracker. These measurement procedures are implementedin a case study on a large serial articulatedindustrial manipulator in five different positions of itsworkspace. This study shows that the measured quasistaticdeflections are bigger than the measured staticdeflections. This, in turn, indicates a significant differencebetween the static and apparent quasi-staticcompliance. Finally, the implementation of the modelparameters to improve the accuracy of robots and thechallenges in realizing cost-efficient compliance calibrationare discussed.

Industrial manipulators are rarely used in high-force processes even though they provide flexibility, adaptability, relatively low cost, and a large workspace. This limited utilization is mainly due to their inherent low stiffness, which results in significant deformation. Hence, it is necessary to improve their accuracy in order to achieve high-precision requirements while performing tasks under load. This paper focuses on the development and implementation of an online compliance error compensation system for industrial manipulators. The proposed algorithm computes the compensation based on an elasto-geometric robot model and process forces measured with a force sensor mounted between the robot mechanical interface and the end effector. The performance of the compensation system is evaluated experimentally in two high payload robots from different manufacturers in which the compensation was carried out to reduce the mean deformation of circular trajectories under load.

Industrial articulated robots appeal to high force processes such as material removal applications mainly due to their high flexibility and large working space. However, due to the articulated robot's lower stiffness, significant deformations arise in the presence of process forces which reduces the robot's positioning accuracy. To improve the positioning accuracy in tasks performed under load, offline or online compliance compensation methods are implemented. This study presents an experimental comparison of the implementation and performance of offline and online compliance compensation strategies in a high-force application, i.e., loaded circular trajectory, characterized by the presence of quasi-static forces. The performance of the two compensation strategies was evaluated by calculating the mean deformation (comparison between unloaded and loaded trajectories). The results indicate that the performance of the online compensation strategy exceeded the offline compensation strategy performance for the case study analyzed. The limitations and potentialities of the different compensation strategies are discussed in terms of implementation and applicability for contact applications.

This article presents the measurement and analysis of the influence of velocity on the quasi-static deflections of industrial manipulators of three different manufacturers. Quasi-static deflection refers to the deflection of the end effector position of articulated robots during movement at low velocity along a predefined trajectory. Based on earlier reported observations by the authors, there exists a difference in the static and quasi-static deflections considering the same points along a trajectory. This work investigates this difference to assess the applicability of robotic compliance calibration at low velocities. For this assessment, the deflections of three industrial articulated robots were measured at different speeds and loads. Considering the similarity among the robot models used in this investigation, this work also elaborates on the potential influence of the measurement procedure on the measured deflections and its implications for the compliance calibration of articulated robots. For all industrial articulated robots in this investigation, the quasi-static deflections are significantly larger than the static ones but similar in trend. Additionally, the magnitude of the quasi-static deflections presents a proportional relationship to the Cartesian velocity.

While robot calibration is crucial for performing high-precision tasks, traditional calibration methods are time-consuming and resource-intensive. Within the constraints of industrial settings, extensive calibration requirements call for alternative methods that minimize the implementation costs while maintaining acceptable accuracy levels. This paper investigates the feasibility of transferring compliance error compensation parameters among articulated robots of the same model in contact-based applications. Experimental results demonstrate the feasibility of the transferability, achieving significant error reduction with a modest performance decrease compared to individual robot calibration. This approach offers a promising avenue for balancing calibration effort with the specific application requirements.