Validation of a Redundant Robotic Manipulator for Shoulder in Vitro Biomechanical Testing.

Cadaveric joint simulators are commonly used to explore native and pathological joint function as well as to test medical devices. Recently, robotic manipulators have been proposed as a new gold standard for in vitro biomechanical testing as they offer higher possibilities than Universal Testing Machines in terms of degrees of freedom (DOF). However, current protocols remain conducted in extra-corporal conditions by xing one segment of a diarthrodial joint while mobilising the other segment. Moreover, induced motions are commonly not specimen-specic and do not respect related joint kinematic constraints and physiologic boundaries. In this study, using a 7 DOF redundant robotic manipulator, an intra-corporal condition protocol was dened. This protocol allows 1) the analysis of the shoulder girdle full kinematic chain, 2) the replication of specimen-specic humerus motions initially induced by an operator. On the 10 shoulders tested, the robotic manipulator was able to perform requested end-effector motions with a reliability of 0.28 ± 0.57 mm and 0.15 ± 0.25°, and a delity of 0.27 ± 0.56 mm and 0.22 ± 0.28°. This protocol will be used in the future to explore joint function as well as to test medical devices, on the shoulder girdle and potentially other joints.


Introduction
Cadaveric joint simulators are commonly used to explore the native and pathological joint function 1 as well as to test medical devices 2 . While Universal Testing Machines (UTM) have been recognised these last decades as a standard for joint biomechanical testing 3 , the use of robotic manipulators is proposed as a new gold standard for in vitro biomechanical testing 4 . This is mainly motivated by the fact that they offer higher possibilities than UTM in terms of degrees of freedom (DOF). This is essential for the assessment of complex joints such as the shoulder 5 . Several clinical applications have thus been proposed to assess acromioclavicular joint stability 6 , to evaluate the in uence of a reverse shoulder prosthesis design on scapula notching 7 , or to characterise percutaneous osseointegrated implant systems 5 .
However, most of the current protocols are conducted in extra-corporal conditions by rigidly xing one segment (e.g. the scapula) of a diarthrodial joint (e.g. the acromioclavicular joint) while inducing a motion on the other segment (e.g. the clavicle) 6,7 . Hence, only few studies have explored the use of robotic manipulators on kinematic chains 8, 9 and, to the best of our knowledge, such an approach has never been applied on the shoulder girdle. Indeed, exploring this whole kinematic chain is challenging as it is composed of three bones (i.e. humerus, scapula, clavicle) and four joints (i.e. glenohumeral, sternoclavicular, acromioclavicular and scapulothoracic), but also regarding the large available range of motion 10 .
Using a robotic manipulator, induced motions are commonly de ned around anatomical axes 6,11 . These axes are sometimes de ned through well recognised recommendations (e.g. International Society of Biomechanics (ISB) recommendations for segment coordinate axes de nition 12 ) to allow for interspecimen and intersession comparisons 13 . In some other studies, datasets obtained from healthy participants are used to replicate motion patterns observed during various dynamic tasks 5,8 . Such an approach is interesting to reproduce complex in vivo human motions, but may be subject to measurement errors due to soft tissue artefacts acting on motion capture sensors (e.g. re ective cutaneous markers) 14 . Furthermore, unlike manually-induced motions that may respect specimen-speci c kinematic constraints (e.g. bony or soft tissue constraints that may limit further joint motion) 1 , in vivo human motions applied by the operator on the specimen have to be adapted to the specimen joint characteristics. This can be done by a scaling data procedure 15 or by the use of a 6-axis universal force-moment sensor to limit forces and moments applied by the manipulator on the joint 7 . However, to the best of our knowledge, manually-induced motions recorded on the investigated specimen have never been directly replicated by the use of a robotic manipulator. Whereas such an application can allow for replication of speci c motions (e.g. intraoperative joint assessment performed by the surgeon 16 ) in a higher repeatable manner than during manually-induced motions 17 .
The rst objective of this study was to develop an advanced joint testing protocol using a 7 DOF redundant robotic manipulator to explore the shoulder girdle kinematics during specimen-speci c humerus motions in native intra-corporal conditions. The second objective was to assess the protocol reliability, validity and delity to replicate a set of consecutive quasi-static humerus motions. These motions were initially manuallyinduced on the specimen by an experienced operator. Errors below 1 mm and 1° were expected regarding the reliability and delity of the manipulator end-effector position and orientation, respectively.

Robotic manipulator
A KUKA LBR IIWA 14 R820 (KUKA Robotics Corp, Germany) redundant robotic manipulator was used in this study (Fig. 1). This 7 DOF manipulator has a manufacturer reported maximal payload of 14 kg and a endeffector position reliability of 0.1 mm.
None of the shoulders had a degenerative joint disease or previous ligamentous injury con rmed by direct inspection and radiographs before experiments. All specimens were acquired at the Anatomy Teaching Unit of the Geneva Faculty of Medicine. These specimens were all selected from the body donation program of the University of Geneva. The Cantonal Commission for Research Ethics approved this study (2020 − 00598). All procedures were performed in accordance with the ethical standards of the institutional research committee and with the 1964 Helsinki Declaration and later amendments. Table 1 Details about the specimens and applied solutions in terms of position (in the MCS) and orientation (around the Z MCS , 0° corresponds to X MCS and Z TCS aligned) of the specimen and humerus cut length, for each shoulder of each specimen (MCS: manipulator coordinate system, TCS: thorax coordinate system). Specimens were stored at -20° and thawed at room temperature during approximately 72 h prior to testing.
They were positioned in a sitting position on a custom-made vertical support with wedges at cervical and lumbar levels to avoid any con ict between scapula and support ( Fig. 1). Straps were tied at cervical and lumbar levels to stabilise specimens.
Manipulator workspace and humerus reachable workspace tting The thoracic coordinate system (TCS, Fig. 3) was used to describe the specimen position and orientation. It was de ned following ISB recommendations 12 using the re ective cutaneous marker 3D trajectories de ned thereafter. Specimen position and orientation, with respect to the manipulator coordinate system (MCS, Fig.  3), were crucial parameters to ensure that the humerus reachable workspace (HRW) was contained in the robotic manipulator workspace (RMW) for humerus motion replication.
RMW was de ned as the volume between an inferior sphere and a superior sphere centered at the manipulator workspace centre, with a radius equal to the distance between joint axes 2 and 4, and to the distance between joint axes 2 and 6, respectively (Fig. 2). The between axes distances were based on the manufacturer documentation 18 . Security margins, set at 20 mm, were added to the spheres radius.
Due to a limited RMW, it was necessary to reduce the humerus length to t the HRW into the manipulator workspace. For that, a submaximal HRW was computed for each virtual point (HCi) equally distributed every 1 cm along the humerus longitudinal axis between GJC and EJC. These virtual points aimed at representing potential humerus transection locations. Each resulting HRW was de ned as the 3 previously de ned  (Table 1) was selected so as to keep the longest humerus length while using a median TCS position and orientation across all solutions related to the selected humerus cut length.
Each humerus was then transected, potted in a custom 3D-printed cylinder (ABS thermoplastic polymer) by use of bone cement (Palacos LV, Heraeus, Germany), and rigidly mounted via a custom xture to the manipulator end-effector ( Fig. 1). All soft tissues (e.g. muscles, ligaments, joint capsules) were left intact along the whole shoulder girdle. The specimen position and orientation was adjusted and rigidly secured to the table using clamps.

Manipulator motion planning
During surgery, shoulder range of motion (ROM) is commonly assessed using manual testing by passively mobilising the humerus until bony or soft tissue constraints prevent further motion. In order to reproduce this intraoperative assessment, manually-induced humerus motions were replicated by the manipulator. For that, a new set of re ective markers was used to record manually-induced motions of the transected humerus. To obtain true kinematics, free from soft tissue artefacts, these markers were put on the 3D-printed cylinder (rigidly secured to the bone) to de ne its related coordinate system. The cylinder design ensured that the axes of its coordinate system were coaxial with those of the manipulator end-effector coordinate system (ECS, Fig. 3). The rigid transformation between these coordinate systems was thus de ned based on geometry features.
Once again, the operator manipulated the humerus using the same motions as previously de ned. Threedimensional marker trajectories were gap-gilled and ltered (2nd order Butterworth lter, 6 Hz cut-off) and used to compute the matrix corresponding to the trajectory of the end-effector centre and the quaternion of its 3D orientation, both discretised into 100 waypoints for each manually-induced motion. These data were then sent to ROS (Robot Operating System, version 16.04.6 "Kinetic") 21

Statistical analysis
In order to assess the manipulator ability to replicate manually-induced humerus motions, the following analyses were conducted.
The reliability and validity of the manipulator joint angles were assessed by comparing, for each humerus motion, these angles with their average value across all cycles, and with the planned trajectory, respectively. The reliability and delity of the end-effector position and orientation (and thus the humerus position and orientation) were assessed by comparing, for each humerus motion, these parameters with their average value across all cycles, and with the position and orientation measured during manually-induced physiological humerus motion, respectively.
As the motion velocity was not constrained, it may have varied between cycles and between manipulatorinduced and manually-induced motions. Thus, a dynamic time warping (DTW) approach 23 was used to map the compared time-series. The root mean square difference (RMSD) was then computed between the resulting mapped data for each humerus motion cycle. The RMSD related to reliability, validity and delity were nally reported, for each humerus motion, by their mean and standard deviation values across cycles and specimens.

Manually-induced humerus motions
The average thoracohumeral joint (i.e. humerus relative to the thorax) angles measured during each manually-induced humerus motion are reported in Fig. 4.

Reliability and validity of the manipulator joint angles
The average RMSD related to reliability and validity were respectively 0.35 ± 0.45° and 0.32 ± 0.43° across all specimens, joints, motions and cycles ( Table 2). No joint angle reached an average RMSD higher than 1° concerning reliability and validity.
Reliability and delity of the manipulator end-effector position The average RMSD related to reliability and delity were respectively 0.28 ± 0.57 mm and 0.27 ± 0.56 mm across all specimens, joints, motions and cycles (Table 3). Only one joint angle reached an average RMSD higher than 1 mm concerning its reliability (position along the Z MCS axis during exion-extension). Concerning delity to the manually-induced motions, an average RMSD higher than 1 mm was observed along the X MCS axis (during horizontal exion-extension) and Z MCS axis (during exion-extension and adduction-abduction), and higher than 2 mm along the Y MCS axis (during horizontal exion-extension).

Reliability and delity of the manipulator end-effector orientation
The average RMSD related to reliability and delity were respectively 0.15 ± 0.25° and 0.22 ± 0.28° across all specimens, joints, motions and cycles (Table 3). No joint angle reached a RMSD higher than 1° concerning its reliability and delity.

Discussion
The key outcome of this study was the validation of a 7 DOF robotic manipulator for the in vitro replication of manually-induced humerus motions on a native whole shoulder girdle. The present results demonstrated that the opportunities offered by robotic manipulators can be extended to complex kinematic chains in intra- According to the manufacturer speci cations, the KUKA LBR IIWA 14 R820 has an instrumental error of 0.1 mm. Regarding the present results, another source of error may have decreased our protocol accuracy. As pointed out by several authors 5,26 , the relationship between the manipulator end-effector coordinate system and the attached segment coordinate system (humerus coordinate system in our case) may be subject to errors. The rigid transformation between these two coordinate systems has been estimated in the literature by the use of custom xtures 26 or by an identi cation procedure using an optical tracking system 5 . In this study, a custom 3D-printed cylinder was rigidly secured on the transected humerus and mounted via a custom xture to the manipulator end-effector. The motions observed on the cylinder were expressed in the endeffector coordinate system under the assumption of fully known rigid transformations (based on the geometry of the different parts) and ush mount joints. While they were not assessed in this study, some errors may have been introduced on these assumptions and should thus be estimated in the future.
Except in several studies investigating foot/ankle dynamics 8,9 , most of the previously published joint cadaveric simulators based on a robotic manipulator focused on a single diarthrodial joint. By proposing an intra-corporal condition protocol, our study made the full kinematic chain of the shoulder girdle available for do not limit the explored kinematic chain length. Still, the manipulator has a limited workspace that restrains the potential positions of the exploring bones and joints in the manipulator coordinate system. In robotics, it may be more common to adapt the position of the robot (e.g. mobile manipulator, humanoid robot) than to move the targeted object 27 . In the present study, this issue was managed by optimising the spatial organisation of the specimen with respect to the manipulator to allow requested motions. This procedure, repeated for each shoulder, allowed for the personalisation of specimen position and orientation depending on humerus length and humerus range of motion.
Another feature of this study was that our protocol allowed to reproduce specimen-speci c humerus motions induced by an operator. This procedure simulates intra-operative shoulder passive mobilisation performed by the surgeon to assess joint reconstruction or joint arthroplasty e ciency 16 . As observed by Goldsmith et al. 17 using a similar protocol to explore the hip joint, the use of a robotic manipulator allows for reliability in induced motions. However, while these authors used prede ned rotation axes to approximately replicate manually-induced motions, our protocol directly uses the recorded manually-induced motions (i.e. the intraoperative shoulder passive mobilisation performed by the surgeon) for the robotic motion planning. To the best of our knowledge, this is the rst time that specimen-speci c motions, recorded during manual passive mobilisation, are used for robotic motion planning. Instead, several studies used various motions obtained from open-source datasets compiling records made on healthy participants 5,15,28−31 . The use of specimenspeci c motions better allows to respect related joint kinematic constraints (e.g. bony or soft tissue constraints that may limit further joint motion) and thus to better respect physiologic boundaries. Still, the application of specimen-speci c motions recorded during the native condition of a joint may not be applicable in injured or repaired joint conditions, where related joint kinematic constraints may have been modi ed 17 . Thus, the replication of native humerus motions may not be applied under injured or repaired joint conditions without the monitoring of the resulting passive moment 17 to avoid tissue degradation or joint dislocation. The replication of native humerus motions, though, allows assessing whether the injured or repaired joint still permits the requested motion.
This study remains subject to some limitations. First, all specimens used were over 60 years old. While the shoulders were inspected prior to inclusion in terms of degenerative joint disease or previous ligamentous injury, resulting range of motion may be lower than in younger subjects. Still, the humerus elevation amplitudes reported in this study are similar to the ones reported during in vivo studies 32 or cadaveric studies 1 . Second, humerus motions did not include muscle contraction. Consequently, bones kinematics, and in particular scapula kinematics, might not be comparable to the in vivo kinematics observed in healthy subjects. However, acromioclavicular joint kinematics observed on cadaveric specimens during passive humerus motions is known to be similar to the joint kinematics measured on healthy participants during active humerus motions 1,33 . Furthermore, the present protocol can be compared to intraoperative joint assessment performed by the surgeon, during full muscle relaxation, as suggested by Goldsmith et al. 17 .
Third, as specimen-speci c motions were de ned and applied for each shoulder, induced motions may not be perfectly similar between shoulders. Furthermore, without a rigorous humerus mobilisation protocol, the resulting motions may not have been perfectly performed around anatomical axes. This issue can be corrected by de ning precisely anatomical axes, for example by applying the recommendations of the ISB 4,12 . However, in our case, the goal was more to reproduce intraoperative humerus mobilisations (i.e. not necessarily fully aligned with anatomical axes) than to produce pure rotations around a single axis. Last, the present protocol does not allow for specimen repositioning. The optimised position and orientation applied on the specimen in the manipulator coordinate system remained strictly the same between the manually-induced humerus motions and the following motion replications using the robotic manipulator. Consequently, if the specimen has to be removed and then replaced (e.g. to perform a surgery), the validity of the resulting humerus motion replications can not be ensured. The literature has already proposed some procedures to cover this issue. However, to the best of our knowledge, they were applied on a unique bony segment, during single diarthrodial joint analysis 26 . Still, these procedures could be applied on the thorax of the specimens to ensure the correct repositioning of the end of the kinematic chain of the shoulder girdle.

Conclusion
To conclude, an advanced joint testing protocol using a 7 DOF redundant robotic manipulator was used to explore the shoulder girdle during specimen-speci c humerus motions in native intra-corporal conditions.
Using this protocol on 10 shoulders, the manually-induced humerus motions were replicated by the robotic manipulator with high reliability and delity. This protocol will be used in the future to explore the native and pathological joint function as well as to test medical devices, of the shoulder girdle and potentially other joints. Table 3. Reliability and delity of the manipulator end-effector position and orientation expressed in the manipulator coordinate system (metrics are reported by their mean value and standard deviation across cycles and specimens. FE: exion-extension, AA: abduction-adduction, IER: internal-external rotation, HFE:

Declarations
horizontal exion-extension, VT: vertical traction, HC: horizontal compression, RXY: orientation of X or Y axis, RZ: orientation of Z axis). Figure 1 Robotic test bench assembly.

Figure 2
Illustration of the manipulator workspace (on the left) and humerus reachable workspace (on the right). The manipulator workspace is a volume de ned by a 340° revolution of the grey surface around the A1 joint axis  Segment coordinate systems used in the analysis (MCS: manipulator coordinate system, TCS: thorax coordinate system, ECS: end-effector coordinate system). ECS is shared between the manipulator end-effector and the 3d-printed humeral cylinder.