Compact series elastic actuator integration

Abstract

An elastic actuator device includes a motor that includes a motor housing and a motor shaft; a bearing assembly that includes a first ring attached to the motor housing and further includes a second ring arranged concentrically with the first ring such that the first and second rings are rotatable with respect to each other with bearings therebetween; and a gearbox that includes a gearbox housing mechanically coupled to the second ring of the bearing assembly. A transmission assembly for an elastic actuator device includes a bearing assembly that includes a first ring configured to be attachable to a motor housing of a motor and further includes a second ring arranged concentrically with the first ring such that the first and second rings are rotatable with respect to each other with bearings therebetween; and a gearbox that includes a gearbox housing mechanically coupled to the second ring of the bearing assembly.

Description

Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 COMPACT SERIES ELASTIC ACTUATOR INTEGRATION CROSS REFERENCE TO RELATED APPLICATIONS

[0001] The present patent application claims priority benefit to US Provisional Patent Application No. 63 / 656,851, filed on June 6, 2024, the entire content of which is incorporated herein by reference. FEDERALLY SPONSORED RESEARCH

[0002] This invention was made with government support under Grant Number MH127104 awarded by the National Institutes of Health. The government has certain rights in the invention. BACKGROUND 1. Technical field

[0003] The currently claimed embodiments of the present invention relate to series elastic actuators (SEAs) and components, and more particularly to compact and / or MRI compatible SEAs and components. 2. Discussion of related art

[0004] While robots have proven effective in enhancing the precision and time efficiency of MRI-guided interventions across various medical applications [1], safety remains a formidable challenge for robots operating within MRI environments due to several factors. As the robots assume full control of medical procedures, the reliability of their operation becomes paramount. Precise control over robot forces is particularly crucial to ensure safe interaction within the MRI environment. Furthermore, the confined space in the MRI bore complicates the safe operation of human-robot interaction, presenting challenges to maneuverability.

[0005] However, there exists a notable scarcity of force-controlled robot actuators specifically tailored for MRI applications. Conventional MRI-compatible robot actuators mainlyAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 operate on velocity control or lack back-drivability, rendering them sub-optimal for effective force control and heightening safety risks during human-robot interactions within MRI environments. SUMMARY

[0006] An elastic actuator device according to an embodiment of the current invention includes a motor that includes a motor housing and a motor shaft; a bearing assembly that includes a first ring attached to the motor housing and further includes a second ring arranged concentrically with the first ring such that the first and second rings are rotatable with respect to each other with bearings therebetween; and a gearbox that includes a gearbox housing mechanically coupled to the second ring of the bearing assembly. The gearbox further includes a gear assembly that includes an input shaft and output shaft. The gearbox housing is elastically coupled to the motor housing, the input shaft is configured to mechanically couple with the motor shaft so as to drive the input shaft, and the bearing assembly further includes a third ring arranged concentrically with the first ring and the second ring and includes bearings between the second and third rings such that the first, second and third rings are all rotatable with respect to each other. The third ring is mechanically coupled to the output shaft.

[0007] A transmission assembly for an elastic actuator device according to an embodiment of the current invention includes a bearing assembly that includes a first ring configured to be attachable to a motor housing of a motor and further includes a second ring arranged concentrically with the first ring such that the first and second rings are rotatable with respect to each other with bearings therebetween; and a gearbox that includes a gearbox housing mechanically coupled to the second ring of the bearing assembly. The gearbox further includes a gear assembly comprising an input shaft and output shaft, the gearbox housing is configured to be elastically coupled to the motor housing, the input shaft is configured to mechanically couple with a motor shaft of the motor so as to drive the input shaft, and the bearing assembly further includes a third ring arranged concentrically with the first ring and the second ring and includes bearings between the second and third rings such that the first, second and third rings are all rotatable with respect to each other, the third ring being mechanically coupled to the output shaft.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 BRIEF DESCRIPTION OF THE DRAWINGS

[0008] Embodiments of the present invention, as well as the methods of operation and functions of the related elements of structure and the combination of parts and economies of manufacture, will become more apparent upon consideration of the following description and the appended claims with reference to the accompanying drawings, all of which form a part of this specification, wherein like reference numerals designate corresponding parts in the various figures. It is to be expressly understood, however, that the drawings are for the purpose of illustration and description only and are not intended as a definition of the limits of the invention.

[0009] FIG.1 provides a schematic illustrations of: (a), a conventional direct force sensing SEA positions its spring element between the output gear and the load. Contrarily, in (b), a transmission force sensing SEA according to an embodiment of the current invention situates its spring element between the gearbox housing and the ground. The transmission force sensing SEA architecture enables the construction of a more compact SEA suitable for MRI scanners. fsdenotes the spring force. N୧୭, N୧୦, and N୭୦denote the gear ratios between the input and the output, between the input and the gearboxand between the output and the gearbox housing.

[0010] FIG. 2 is a schematic illustration to explain some concepts according to an embodiment of the current invention.

[0011] FIG. 3 shows the architecture of our compact SEA module according to an embodiment of the current invention with the following components: a spring element (a), a gearbox (b), an USM (c), and an optical spring encoder (d). Integration is facilitated by a triple ring bearing (e), allowing the entire framework to fit seamlessly into a cylindrical space, as depicted in (f), with a diameter of 80 mm and a total length of 66 mm according to an embodiment of the current invention.

[0012] FIG.4 is a perspective cutaway view corresponding to (f) in FIG.3.

[0013] FIG.5 is a cutaway view of some components shown in (f) of FIG.3.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2

[0014] FIG.6 is an exploded view corresponding to (f) in FIG.3.

[0015] FIG.7 is another view of some of the compnents shown in FIG.6.

[0016] FIGS. 8A-8B are schematic illustrations showing an SEA robot maneuvers a transcranial magnetic stimulator (TMS) towards a patient’s head in an example. The SEA force controller needs to address the challenges posed by both (a) the minimal external impedance of the medical device before it makes contact with the patient and (b) the substantial impedance encountered upon contact with the human body.

[0017] FIGS. 9A-9D are schematic illustrations of a model to explain some concepts of an embodiment of the current invention. In (a), the velocity-sourced SEA encounters uncertain and finite external impedance, posing challenges to force control. Conversely, our DOB’s reference model in (b) has an infinitely large external impedance attached to its output. Unlike the direct force controller depicted in (c), our control framework in (d) incorporates the DOB to compel the actual velocity-sourced SEA system to emulate the behavior of the reference model. This framework ensures that a proportional controller can achieve effective force reference tracking despite the uncertain external impedance. The bond graphs in (c) and (d) represent the SEA model in (a). In the bond graphs, I, R, C, Sf, and Se denote the nodes representing inertia, damper, spring, velocity source, and force source, respectively, in a mechanical system.

[0018] FIGS.10A-10D show an expermental setup according to an embodiment of the current invention. In this experimental setup, the SEA is controlled by a NUCLEO- F446RE MCU in (a), which gathers position measurements from encoders and sends motor velocity commands to the USM driver. The perturbation testbed in (b) consists of our SEA module on the left and an additional USM on the right, serving as the perturbation source. The outputs of these two actuators are connected through a shaft coupler. In our MRI test setup depicted in (c), a SEA pendulum testbed in (d) is positioned at the center of the bore of a 3T MRI scanner. The motor driver and MCU are located outside the MRI room, transmitting power and control signals through 10-meter-long cables, as illustrated in (c).Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2

[0019] FIG. 11 shows experimental results according to an embodiment of the current invention. Experimental results from T-A-M, T-A-1, T-A-2, T-B-1, and T-B-2 are presented in distinct rows. The first column corresponds to the SEA output displacement θ^, the second column represents the SEA output torque τ^, and the third column displays the torque tracking error τ^െ τௗ^. In a.3, b.3, and c.3, small windows are zoomed into the highlighted impulse response detailsof τ^ െ τௗ^. These small windows share the same scale as d.3 and e.3.DETAILED DESCRIPTION

[0020] Some embodiments of the current invention are discussed in detail below. In describing embodiments, specific terminology is employed for the sake of clarity. However, the invention is not intended to be limited to the specific terminology so selected. A person skilled in the relevant art will recognize that other equivalent components can be employed, and other methods developed without departing from the broad concepts of the present invention. All references cited anywhere in this specification are incorporated by reference as if each had been individually incorporated.

[0021] Some embodiments of the current invention are directed to a compact force- controlled actuator module for robot integration within MRI scanners, prioritizing compactness and force control efficacy to address critical safety considerations inherent to MRI guided interventions. Unlike non-MRI environments, the strong magnetic field within MRI scanners renders conventional electromagnetic robot actuators unsafe for medical applications in MRI. While fluidic actuators offer MRI compatibility [2], [3], the lack of back-drivability in hydraulic actuators poses significant risks in medical scenarios involving human interaction. Pneumatic actuators [4], known for their compliance, enhance safety in human-robot interactions, yet their restricted force output and controllability confine their applicability to specific medical procedures, such as needle-based interventions [5]. Ultrasonic motors (USMs) [6], [7], utilizing non-magnetic piezoelectric materials for actuation, offer both precision and compatibility with MRI environments. However, akin to hydraulic actuators, they encounter inherent challenges such as high impedance and lack of back-drivability. Typically, these motors are utilized as velocityAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 sources, restricting their applications to controlling human-robot interaction forces within MRI settings.

[0022] In [8], the series elastic actuator (SEA) concept is introduced, presenting a unique architecture for robot actuators that enhances safety during human-robot interaction. By placing a spring element in series with a rigid actuator, compliance is added to the system. While traditional SEAs typically utilize force-sourced motors, this innovative approach also offers advantages for velocity-sourced actuators [9]. Through the application of Hooke’s law, the spring element functions as a force sensor, enabling the control of actuator force to be translated into the regulation of spring deflection, thus facilitating precise control over velocity and position.

[0023] In

[0010] , the development of MRI-compatible SEAs is initially presented for the implementation of an MRI-guided rehabilitation robot. This system achieves force-controlled actuation by integrating an USM, a pair of extension springs serving as the spring element, and a linear bearing. While the SEA in

[0010] is tailored for linear actuation, the evolution of this technology continued with a rotary SEA in

[0011] . However, this particular actuator relies on an electromagnetic motor located outside the MRI room, connected via a lengthy cable-driven transmission, thus limiting its applicability for in-bore MRI robotic tasks. Notably, while compact SEA designs based on electromagnetic motors have been extensively investigated in non-MRI robot applications

[0012] ,

[0013] ,

[0014] ,

[0015] , the development of integrated compact SEAs utilizing MRI-compatible motors remains an area yet to be fully explored.

[0024] Accordingly, some embodiments of the current invention address the above- mentioned challenges associated with MRI-compatible force-controlled actuators for robotic applications within MRI scanners. In the following, we introduce a novel MRI-compatible SEA module that seamlessly integrates an USM, a rotary gearbox, and a spring element into a transmission force sensing SEA structure, as depicted in FIG.1 (i.e., (b)). Notably, this SEA is the first rotary SEA to operate entirely within an MRI scanner.

[0025] In some embodiments, the SEA is specifically designed to accommodate disk- shaped ultrasonic motors, yielding a cylindrical shape with a length shorter than its diameter. These actuators can enable both actuation and precise force control for robots, for example. SomeAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 embodiments of the current invention are particularly valuable for force-controlled robots operating within confined spaces, where traditional series elastic actuator configurations may be impractical.

[0026] While a conventional SEA positions its spring element between the output of a geared motor and the load (Pratt, Gill A., and Matthew M. Williamson. "Elastic actuator for precise force control." U.S. Patent No.5,650,704.22 Jul.1997), our design follows the same approach as the SEA configuration presented in (Sehoon, O. H., and Chan Lee. "Elastically actuating device." U.S. Patent No. 10,533,904. 14 Jan. 2020). In this configuration, the spring element is situated between the gearbox housing and the grounded motor housing. Herein, we distinguish the conventional SEA as a direct force sensing series elastic actuator (FSEA) and the variant introduced in (USPN 10,533,904) as a transmission force sensing series elastic actuator (TFSEA).

[0027] In FIG. 1, the structural difference between an FSEA and a TFSEA is illustrated. As indicated in (Lee, Chan, and Sehoon Oh. "Configuration and performance analysis of a compact planetary geared elastic actuator." IECON 2016-42nd Annual Conference of the IEEE Industrial Electronics Society. IEEE, 2016. However, the TFSEA presents several advantages for implementation in a confined space. Notably, the spring element of the TFSEA is affixed to the grounded motor housing, rather than moving with the actuator output. This design facilitates a more compact integration of the motor, gearbox, and spring element within the confined space. Moreover, siting the electronic components of the spring deflection encoder on the motor housing side of the spring element eliminates the necessity for movement in the encoder cable. Although gearbox friction and backlash in the TFSEA slightly compromise output force sensing accuracy, these drawbacks are overshadowed by its advantages.

[0028] In (b) of FIG. 1, the gearbox housing of a TFSEA moves relative to the motor housing, necessitating extra bearings to reduce friction and compromising compactness. Our TFSEA design according to some embodiments depicted in FIGS.2-7 minimizes bearing count by utilizing a triple-ring ball bearing, as opposed to previous designs. This bearing secures the inner ring to the output gear, the middle ring to the gearbox housing, and the outer ring to the motor housing. Additionally, a regular double-ring ball bearing within the spring element secures the inner ring to the output gear and the outer ring to the motor housing. This configuration ensuresAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 coaxial constraints among the output gear, gearbox housing, and motor housing, enabling a more compact integration.

[0029] FIG.2 provides a schematic illustration of an elastic actuator device 100 according to an embodiment of the current invention. The elastic actuator device 100 includes a motor 102 that includes a motor housing 104 and a motor shaft 106. The elastic actuator device 100 also includes a bearing assembly 108 that includes a first ring 110 attached to the motor housing 104 and a second ring 112 arranged concentrically with the first ring 110 such that the first and second rings (110, 112) are rotatable with respect to each other with bearings therebetween 114. The elastic actuator device 100 further includes a gearbox 116 that includes a gearbox housing 118 mechanically coupled to the second ring 112 of the bearing assembly 108. The gearbox 116 further includes a gear assembly 120 that has an input shaft 122 and output shaft 124. The gearbox housing 118 is elastically coupled 126 to the motor housing 104.

[0030] The term “bearings” is intended to have a broad meaning which can include, but is not limited to, ball bearings, roller bearings and / or magnetic bearings, for example. It can further refer to a material such as a lubricant or other material to provide low friction.

[0031] The input shaft 122 is configured to mechanically couple with the motor shaft 106 so as to drive the input shaft 122. The bearing assembly 108 further includes a third ring 128 arranged concentrically with the first ring 110 and the second ring 112 and includes bearings 130 between the second and third rings (112, 128) such that the first, second and third rings (110, 112, 128) are all rotatable with respect to each other. The third ring 128 is mechanically coupled to the output shaft 124.

[0032] In some embodiments, the bearing assembly 108 is a three-ring bearing assembly. However, other embodiments could include four or more rings without departing from the general concepts of the current invention. The three-ring embodiment as illustrated in FIG.2 can provide a compact elastic actuator device 100, for example.

[0033] FIGS. 3, 4 and 6 show CAD drawings of an embodiment of an elastic actuator device 200 as a specific example of the elastic actuator device 100. FIGS. 5 and 7 show aAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 subassembly of the elastic actuator device 200 which we refer to as a transmission assembly 300. FIGS.3-7 show embodiments of components that correspond to the components described in FIG. 2, but further showing an encoder 232, for example, attached on the motor housing side of the spring element.

[0034] The examples of FIGS. 3-7 illustrated the gearbox (116, 216) as a planetary gearbox. However, the general concepts of the current invention are not limited to only planetary gearboxes and are not limited to the particular example that has one set of four planetary gears. There could be less than four or more than four planetary gears in other embodiments, and there could be a plurality of sets of planetary gears, for example. In some embodiments the gearbox 116 can be one of a planetary gearbox, a cycloidal gearbox, or a harmonic gearbox, for example. The general concepts of the current invention are not limited to only these examples.

[0035] In some embodiments the motor 102 can be, but is not limited to, a disk-shaped motor as is illustrated in FIGS.3, 4 and 6. In some embodiments, the disk-shaped motor can be a disk-shaped ultrasonic motor.

[0036] In some embodiments, the elastic actuator device 100, 200, 300 can be cylindrical with an axial length less than half of a transverse width. In some embodiments, all structural elements of the elastic actuator device 100, 200, 300 are compatible with magnetic resonance imaging (MRI) systems.

[0037] In some embodiments, by incorporating the integrated mechanism (transmission assembly) that includes the spring element, gearbox, and bearings into a cylindrical form with a length also less than half of its diameter, we achieve an overall cylindrical shape with dimensions where the length is smaller than the diameter.

[0038] In some embodiments, the triple-ring bearing assembly can be extended to conventional FSEAs or reaction force sensing SEAs (RFSEAs), for example. In the case of FSEA, the triple-ring bearing secures the inner ring to the load, the middle ring to the output gear, and the outer ring to the motor housing. Different from both FSEA and TFSEA, RFSEA (Paine, Nicholas, Jonas Fox, and Bradley Resh. "Compact, high performance series elastic actuator." U.S. PatentAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 No.11,035,743.15 Jun.2021) involves fixing the gearbox housing to the ground and positioning the spring element between the grounded gearbox housing and a floating motor housing. For RFSEA, the triple-ring bearing secures the inner ring to the output gear, the middle ring to the floating motor housing, and the outer ring to the grounded gearbox housing.

[0039] REFERENCES [1] H. Su, K.-W. Kwok, K. Cleary, I. Iordachita, M. C. Cavusoglu, J. P. Desai, and G. S. Fischer, “State of the art and future opportunities in MRI-guided robot-assisted surgery and interventions,” Proceedings of the IEEE, vol.110, no.7, pp.968–992, 2022. [2] Z. Guo, Z. Dong, K.-H. Lee, C. L. Cheung, H.-C. Fu, J. D. Ho, H. He, W.-S. Poon, D. T.-M. Chan, and K.-W. Kwok, “Compact design of a hydraulic driving robot for intraoperative MRI-guided bilateral stereotactic neurosurgery,” IEEE Robotics and Automation Letters, vol.3, no.3, pp.2515–2522, 2018. [3] Z. Dong, Z. Guo, K.-H. Lee, G. Fang, W. L. Tang, H.-C. Chang, D. T. M. Chan, and K.-W. Kwok, “High-performance continuous hydraulic motor for MR safe robotic teleoperation,” IEEE Robotics and Automation Letters, vol.4, no.2, pp.1964–1971, 2019. [4] N. Yu, C. Hollnagel, A. Blickenstorfer, S. S. Kollias, and R. Riener, “Comparison of MRI-compatible mechatronic systems with hydrodynamic and pneumatic actuation,” IEEE / ASME transactions on Mechatronics, vol.13, no.3, pp.268–277, 2008. [5] R. Monfaredi, K. Cleary, and K. Sharma, “MRI robots for needlebased interventions: systems and technology,” Annals of biomedical engineering, vol.46, pp.1479–1497, 2018. [6] G. S. Fischer, A. Krieger, I. Iordachita, C. Csoma, L. L. Whitcomb, and G. Fichtinger, “MRI compatibility of robot actuation techniques–a comparative study,” in MedicalAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 Image Computing and Computer-Assisted Intervention–MICCAI 2008: 11th International Conference, New York, NY, USA, September 6-10, 2008, Proceedings, Part II 11. Springer, 2008, pp.509–517. [7] A. Krieger, S.-E. Song, N. B. Cho, I. I. Iordachita, P. Guion, G. Fichtinger, and L. L. Whitcomb, “Development and evaluation of an actuated MRI-compatible robotic system for MRI-guided prostate intervention,” IEEE / ASME Transactions on Mechatronics, vol. 18, no.1, pp.273–284, 2011. [8] G. A. Pratt and M. M. Williamson, “Series elastic actuators,” in Proceedings 1995 IEEE / RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots, vol.1. IEEE, 1995, pp.399–406. [9] G. Wyeth, “Demonstrating the safety and performance of a velocity sourced series elastic actuator,” in 2008 IEEE International Conference on Robotics and Automation. IEEE, 2008, pp.3642–3647.

[0010] F. Sergi, A. C. Erwin, and M. K. O’Malley, “Interaction control capabilities of an MR-compatible compliant actuator for wrist sensorimotor protocols during fMRI,” IEEE / ASME Transactions on Mechatronics, vol.20, no.6, pp.2678–2690, 2015.

[0011] Y. M. Senturk and V. Patoglu, “MRI-VisAct: a Bowden-cable-driven MRI- compatible series viscoelastic actuator,” Transactions of the Institute of Measurement and Control, vol.40, no.8, pp.2440–2453, 2018.

[0012] K. Kong, J. Bae, and M. Tomizuka, “A compact rotary series elastic actuator for human assistive systems,” IEEE / ASME transactions on Mechatronics, vol.17, no.2, pp. 288–297, 2011.

[0013] N. Paine, S. Oh, and L. Sentis, “Design and control considerations for high- performance series elastic actuators,” IEEE / ASME Transactions on Mechatronics, vol.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 19, no.3, pp.1080–1091, 2013.

[0014] C. Lee and S. Oh, “Configuration and performance analysis of a compact planetary geared elastic actuator,” in IECON 2016-42ndAnnual Conference of the IEEE Industrial Electronics Society. IEEE, 2016, pp.6391–6396.

[0015] T. Kim, K. Shi, and K. Kong, “A compact transmitted-force-sensing series elastic actuator with optimized planar torsional spring for exoskeletons,” in 2021 IEEE / ASME International Conference on Advanced Intelligent Mechatronics (AIM). IEEE, 2021, pp. 572–577. EXAMPLES

[0040] The general concepts of the current invention are not limited to the embodiments described in the following examples. In this section, we aim to address the above-mentioned challenges associated with MRI-compatible force-controlled actuators for robotic applications within MRI scanners with reference to an example embodiment. This can be summarized as follows: ^ In Sec.1 below, we introduce a novel MRI-compatible SEA module that seamlessly integrates an ultrasonic motor (USM), a rotary gearbox, and a spring element into a transmission force sensing SEA structure, as depicted in FIG.1, part (b). Notably, this SEA is the first rotary SEA to operate entirely within an MRI scanner. Compared to the linear MRI-compatible SEA in (Sergi, Erwin, and O’Malley 2015), our SEA module has six times power-to-volume density, offering the potential for a wider range of MRI robotic applications. ^ In Sec.2 below, we present a DOB-based (disturbance observer based) controller for actuator torque control in our compact SEA module. This controller distinguishes itself from previous DOB-based SEA control strategies (Kong, Bae, and Tomizuka 2011; Paine, Oh, and Sentis 2013; Nakamura et al. 2021), which were primarily designed for force- sourced or position-controlled motors. Notably, our DOB-based controller is specificallyAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 crafted for SEA systems featuring velocity-sourced motors, such as the MRI-compatible velocity-controlled USM integrated into our SEA module. ^ In Sec.3 below, we validate the functionality of our compact SEA module within a 3 Tesla MRI scanner, demonstrating consistent performance across both MRI and non-MRI environments. In comparison to direct force control strategies employed in velocity- sourced SEAs (Wyeth 2008; Sergi, Erwin, and O’Malley 2015; Senturk and Patoglu 2018), our DOB-based controller exhibits enhanced robustness against varying external impedance, positioning our SEA module as a more suitable choice for the MRI robotic applications. 1. Mechanical Design

[0041] In this section, we present a compact SEA design according to an embodiment of the current invention that seamlessly integrates an USM, a rotary gearbox, and a spring element into a unified module. Towards the conclusion, we offer a comparative analysis with previous MRI-compatible SEAs and assess the MRI-compatibility of our SEA module. Transmission Force Sensing SEA

[0042] While a conventional SEA positions its spring element between the output of a geared motor and the load (Pratt and Williamson 1995), our design follows the approach as the SEA configuration presented in (Lee and Oh 2016). In this configuration, the spring element is situated between the gearbox housing and the ground. In this section, we distinguish the conventional SEA as a direct force sensing series elastic actuator (FSEA) and the variant introduced in (Lee and Oh 2016) as a transmission force sensing series elastic actuator (TFSEA).

[0043] In FIG. 1, the structural difference between an FSEA and a TFSEA is illustrated. As indicated in (Lee and Oh 2016), both types of SEA share the same mathematical model and kinematic constraints. However, the TFSEA presents several advantages for implementation in MRI scanners. Notably, the spring element of the TFSEA is affixed to the ground and motor housing, rather than moving with the actuator output. This design facilitates a more compact integration of the motor, gearbox, and spring element within the confined space of an MRI scanner.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 Moreover, siting the electronic components of the spring deflection encoder on the ground side of the spring element eliminates the necessity for movement in the encoder cable. Although gearbox friction and backlash in the TFSEA slightly compromise output force sensing accuracy, these drawbacks are overshadowed by its advantages.

[0044] In FIG.3, component (b), our SEA incorporates a planetary gearbox design. This configuration, akin to the gearbox illustrated in FIG.1, section (b), features a sun gear as the input gear, an assembly of four planet gears serving as the output gear, and an inner ring gear encompassing the planet gears to form the gearbox housing. The gear ratios are established with ^^^^^^ ൌ 3: 10 between the input and the output and ^^ ^^^^ ൌ 3: 7 between the input and the housing.Spring Element

[0045] In the realm of rotary SEAs, the adoption of helical torsion springs as elastic elements is well-explored, as demonstrated in (Kong, Bae, and Tomizuka 2011; Lee and Oh 2016). Specifically, the spring selection in (Lee and Oh 2016) plays a pivotal role in achieving a compact integration of the SEA by encompassing a brushless direct current (BLDC) motor with a helical torsion spring. However, while implementing a helical torsion spring simplifies rotary SEA design, it does not enhance compactness when paired with a disk-shaped USM, which typically has a larger outer diameter and shorter length compared to the BLDC motor used in (Lee and Oh 2016). To address this, a TFSEA design introduced in (Kim, Shi, and Kong 2021) employs a customized planar torsion spring element to enhance overall compactness. Nonetheless, this planar torsion spring requires more metals than a helical spring, potentially leading to more interference in MR imaging processes.

[0046] FIG.3, component (a), presents the spring element design, drawing inspiration from the SEA in (Wyeth 2008). To address the previously highlighted concerns, the torsion spring element features four off-the-shelf brass helical compression springs arranged in parallel. The loading of these four parallel springs is achieved through two sliders affixed to the housing of the planetary gearbox. Each helical compression spring, with an outer diameter of 9.5 mm and aspring constant of 1.28 N ⋅ mmି^, places its centerline 25 mm from the rotation axis under noadditional load.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2

[0047] When torque is applied, the torsion spring element allows for a rotational range ofേ12^, shifting the centerline of each helical compression spring within a range of 24.14 ∼25.48 mm from the rotation axis of the torsion spring element. Despite this, the total torsion springrate remains relatively constant, ranging from 3.15 ∼ 3.20 N ⋅ m ⋅ radି^. This consistency is dueto the opposing shifts of the centerlines of the two springs on either side of the slider, effectively balancing each other out. At full compression of 12^, the torsion spring element generatesmaximum torques of 0.67 N ⋅ m at the gearbox housing and 0.96 N ⋅ m at the gearbox output.Compact Integration

[0048] FIG.3, component (f), depicts a half-section view of our compact SEA integration, incorporating the spring element, the planetary gearbox, and a Tekceleo WLG-75-R USMaccording to an embodiment of the current invention. At the peak SEA output torque of 0.96 N ⋅m, this USM provides to a maximum velocity of 5.2 rad ⋅ sି^ at the SEA output and yielding apeak output power of 5.0 W.

[0049] To assemble the integrated SEA and mitigate off-axis movement of each component with respect to the ground, we have designed a triple-ring ball bearing. As illustrated in FIG.3, component (e), this triple-ring bearing secures its inner ring to the output gear, the middle ring to the gearbox housing, and the outer ring to the ground. Within the spring element, an additional ball bearing enforces the constraint between the ground and the output gear. To measure the spring deflection, we employ an US Digital EM2-2-10000-I rotary optical encoder module, with the encoder attached to the grounded housing in the spring element and the codewheel affixed to the gearbox housing. While the majority of the SEA components were fabricated through computer numerical control (CNC) with a tolerance of േ0.1 mm, the gearbox was customized using multi jet fusion (MJF) 3D printing for this prototype. This 3D-printed gearbox introduced backlash, resulting in slight vibrations during operation. We addressed this issue by adding small foam padding between each spring slider and the ground layer, effectively mitigating gearbox vibrations with minimal additional in-axis friction.

[0050] As a whole, the spring element, planetary gearbox, and bearing seamlessly fit within a cylindrical space with an outer diameter of 80 mm and a total length of 39.5 mm. ThisAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 comprises a 12 mm length for the spring element, 18 mm for the planetary gearbox, and 9.5 mm for the bearing. When combined with a 22.5 mm thick USM and a 4 mm thick aluminum cooling plate for the motor, the integrated SEA has a total length of 66 mm.

[0051] In Table I, we offer a dimensional comparison between the integrated SEA module in this section and other integrated SEAs employing USMs and electromagnetic motors. Notably, our SEA module has six times the power-to-volume density compared to the linear MRI- compatible SEA depicted in (Sergi, Erwin, and O’Malley 2015). When juxtaposed with non-MRI- compatible SEAs of similar volume but utilizing electromagnetic motors (Paine, Oh, and Sentis 2013; Lee and Oh 2016), the power-to-volume density of our SEA module remains relatively low. This is partly due to the inherently lower power density of commercial USMs compared to electromagnetic motors. Moreover, as outlined in Table II, our efforts to enhance MRI- compatibility by reducing metal usage have necessitated a larger drivetrain to maintain structural integrity.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2

[0052] The exact dimensions for the SEAs in (Sergi, Erwin, and O’Malley 2015; Paine, Oh, and Sentis 2013; Lee and Oh 2016) are not provided. The listed dimensions are approximations based on (Sergi, Erwin, and O’Malley 2015Fig.2), (Paine, Oh, and Sentis 2013Fig.3), (Lee and Oh 2016Fig.7) with reference to their motor dimensions.

[0053] The enclosed volume of an SEA is defined as the total volume of the listed rectangular regions for its drivetrain and motor.

[0054] The peak output power for the SEAs in (Sergi, Erwin, and O’Malley 2015; Paine, Oh, and Sentis 2013) are calculated based on their applications in (Erwin et al.2015; Kwak et al. 2021). MRI Compatibility

[0055] As discussed in (Sergi, Erwin, and O’Malley 2015), the MRI compatibility of an SEA includes the safety and actuator functionality in MRI environment and non-interference in the imaging processes. The safety in MRI environment is ensured by incorporating MRI-safe motor, encoder, and materials into the SEA module. In Sec.3, we will show the validation of the full functionality of our SEA in an MRI scanner.

[0056] The extent of interference in MR imaging processes is largely contingent on the magnetic susceptibility and conductivity of materials (Elhawary et al.2008). Similar to the SEA in (Sergi, Erwin, and O’Malley 2015), the spring element, gearbox, and bearings of our SEA module are fabricated from non-magnetic and non-conductive polymers, with only a small volume of metals utilized in the helical compression springs and fasteners, as outlined in Table II. However, the primary source of imaging interference remains the commercial USM. As proposedin (Fischer et al. 2008; Krieger et al. 2011), USMs should be positioned 20 ∼ 30 cm away fromthe region of interest for MR imaging. Nonetheless, this distance requirement can be addressed in an integrated design of the robot. The compact nature of our SEA contributes to fulfilling this requirement.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 2. Modeling and Control

[0057] In this section, we develop a torque controller tailored for velocity-sourced SEAs, ensuring force regulation quality in the MRI robotic applications with varying external impedance scenarios as illustrated in FIGS.8A-8B. To enhance clarity, all variables introduced in our control design are referenced in the output frame of our SEA. First, we define θ^as the SEA’s output displacement. Accordingly, θ^, θ^, and ^^^denote the reflected USM’s displacement, spring deflection, and spring stiffness respectively, transitioning from their original reference frames to the output frame. The output torque τ^exerted by the spring in our SEA is computed from thespring encoder measurements of θ^ using Hooke’s law: τ^ ൌ ^^^ ⋅ θ^. The output displacement θ^,is computed as the difference between the USM’s encoder measurements of θ^and the spring encoder measurements of θ^. In addition, we define ω^, ω^, and ω^as the time derivative of θ^, θ^, and θ^. Modeling

[0058] In FIG.9A, (a), we model the external system dynamics that attach to the output of our SEA as a mass ^^^, a damper ^^^, and an external force source τ^. The impedance models ^^^^^^^ and ^^^^^^^ for the actuator spring and the external system are defined as ^^ ^^^^ ≜τ^ ൌ ^ ି^^ ^^^^ , ^1^^Combining (1) and(2), we eliminate ω^in the expression and derive an expression for τ^in terms of the motor velocity input ω^and the external force input τ^: τ^ ൌ ^^^^^^^^ ⋅ ω^ ^ ^^^^^^^^ ⋅ τ^, ^3^Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 with the transfer functions ^^^^^^^^ and ^^^^^^^^ define as ^^ ^^^ ^^^^^^^^^ ≜ ^ ^ ^^^ ^^^^^ ^ ^^^^^ ^ ^^ൌ ^^ ^^ଶ ^ ^^ ^^ ^ ^^, ^4^ ^^ ^ ^ ^By including a velocity-controlled USM transfer function ^^^^^^^ ≜ன^ೌwith a 50 Hz bandwidth, we obtainτ^ ൌ ^^ௗ^^ ^^^^ ⋅ ωௗ^ ^ ^^^^^^^^ ⋅ τ^, ^6^where ωௗ is the desired motor ௗ ௗ^ velocity and ^^^^ ^^^^ ≜ ^^^^^^^^^^^^^^^. As indicated in Sec. 1, ω^ isset within േ5.2 rad ⋅ sି^ due to theDOB-Based Torque Control

[0059] As ^^^ → ∞ in (4) and(5), we have ^^^^ → ^^^ and ^^^^ → 0 and obtain the idealactuator model FIG. 9B. The ideal model ^^^^^^^^ ൌ ^^^^^^^, an integrator multiplied by actuatorspring constant ^^ , enables stabilization with a single ௗ ௗ^ proportional controller ω^ ൌ ^^ ⋅ ^τ^ െ τ^^for effective force reference tracking.

[0060] In FIG.9D, we show a disturbance observer (DOB) for realizing this ideal model without actually having infinitely large impedance for ^^^. Under this DOB, we estimate the velocity ω^of the external system as ω^^ ൌ ^^^^^^ ⋅ ^ωௗ^ െ ^^ି^^ ⋅ τ^^ ^7^where ^^^^^^ is a low-pass filter of sufficient order to ensure the observer is causal. By implementingAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 ωௗ^ ൌ ωௗ^ ^ ω^^, ^8^we have the desired velocity ωௗ^ for as new control input of the actuator system. Substituting (7) and (8) into(3), we obtain τ^ ൌ ^^ௗ^^ ^^^^ ⋅ ωௗ^ ^ ^^^^^^^^^ ⋅ τ^. ^9^where ^^^^^^^^ ^^ௗ ^ ^ ^^^ ^^ ≜^^^^^^^^ ^ ^1 െ ^^^^^^, ^10^ ^^ ^^^^

[0061] Similarly, as ^^ → 1 in (10) and (11), we have ^^ௗ^^ → ^^^ and ^^^^^ → 0, therebyimposing the ideal actuator model in FIG.9A. Comparison to Direct P and PI Control

[0062] If we incorporate a first-order filter ^^^^^^ ൌ ^^ା^ into the proposed spring force controller in Sec.2, equations (10) and (11) can befollows: ௗ^ ^^^^^^^^^^ ^^ ^ α^^^^ ^^ ൌ^ ^ ⋅ ⋅⋅ , ^12^ ^^ ^

[0063] By having a small value for the pole α, we can neglect the term ^^ ି^^^^^ ⋅ α ⋅ ^^ inthe denominators of (12) and(13). Consequently, we obtain the approximations: ௗ^^ ^ α^^^^ ^^^^ ^ ^^ௗ^^ ^^^^ ⋅ , for small α, ^14^for small α. ^15^Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2

[0064] Notice that the term^ା^^ in (14), combined with the proportional gain ^^ outside ofthe disturbance observer (DOB) loop, constitutes a PI compensator ^^ ⋅ ^ା^^ , which is similar to the force controller in (Senturk and Patoglu 2018). However, in contrast to the direct P and PI control methods in (Wyeth 2008; Sergi, Erwin, and O’Malley 2015; Senturk and Patoglu 2018), our control approach based on DOB yields several advantages.

[0065] As the pole value α increases from 0 in (12), the term^ା^^ plays a crucial role in mitigating steady-state errors in the closed loop, presenting anover a direct P controller in (Sergi, Erwin, and O’Malley 2015). Moreover, with a continued increase in α, theinfluence of the term ^^^^^^ ⋅ α ⋅ ^^ି^ in the denominators of (12) and (13) becomes morepronounced. This term, ^^^^^^ ⋅ α ⋅ ^^ି^, drives ^^ௗ^^ → ^^^ and ^^^^^ → 0, enhancing reference trackingperformance and reducing sensitivity to external input τ^in the closed loop. These enhancements go beyond the capabilities of a direct PI controller. Controller Parameter Tuning

[0066] In Sec. 2, we demonstrate that ^^ௗ → ^^ and ^^^ → 0 as α → ∞. Since ^^ ൌ^ೞ^^ ^ ^^ ^^ is the spring stiffness ^^^multiplied by an integrator ^ ^, it is straightforward to tune a proportionalcontroller ωௗ ൌ ^^ ⋅ ௗ^ ^τ^ െ τ^^ for the closed-loop force control of our SEA.

[0067] However, an infinitely high value of α is impractical for several reasons. As α →∞, ^^^^^^ → 1, causing the inverse model ^^ି^^ ൌ^ ^ೞin (7) not realizable in a digital system and increasing sensitivity to sensor noise from the spring deflection encoder. To mitigate sensitivity to sensor noise while using higher values of α, we employ ^^^^^^ as a second-order Butterworth మfilter ^^^^^^ ൌ ^ , where ζ ൌ √ଶଶ ensures that ^^^^^^ has its cutoff frequency at α.

[0068] Moreover, the 50 Hz bandwidth of the motor velocity controller in ^^^^^^^ imposes constraints on the values of both the ^^^^^^ filter cutoff frequency α and the proportional gain ^^.Adhering to this bandwidth limitation, the DOB-based controller is configured with ^^ ൌ ^^^ೞandAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2α ൌ 120 rad ⋅ sି^ (^ 19.1 Hz) throughout our experiments. This controller configuration isdesigned to provide a bandwidth of 60 rad ⋅ sି^ (^ 9.5 Hz) and a time constant of t^ ୡൌ^^ sec for the closed-loop force control of our SEA. 3. Experimental Validation and Benchmarking

[0069] In Table III, we summarize the hardware and controller configurations utilized throughout the experiments presented in this section. We experimentally validate the SEA’s capability to track force references within and outside the MRI environment. Following this assessment, perturbation tests on the SEA are conducted. For each experimental category, we present a performance evaluation comparing our DOB-based force controller with the direct force controller in (Sergi, Erwin, and O’Malley 2015).

[0070] FIGS. 10A-10D show the hardware setup for the experimental validation of the compact SEA. The SEA is governed by a microcontroller unit (MCU), which acquires motor position θ^and spring deflection θ^measurements from encoders. Based on these measurements, the MCU transmits motor velocity command ωௗ^ to the USM driver at a frequency of 1000 Hz.MRI and Non-MRI Pendulum Tests

[0071] In T-A-M, T-A-1, and T-A-2, we connect the output gear of our SEA to a pendulum rod constructed from acrylonitrile butadiene styrene (ABS) via 3D printing. As depicted in FIG. 10D, (d), this pendulum rod supports a 125 g brass load positioned 12 cm from its center ofAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2rotation. This setup results in a moment of inertia of ^^ ିଷ ଶ^ ൌ 1.8 ൈ 10 kg ⋅ m , representing alow external impedance to our SEA.

[0072] In T-A-M, this setup is positioned to the center of the bore in a GE MR750W scanner, a 3T MRI machine as depicted in FIG.10C, (c). In T-A-1 and T-A-2, we move this setup to a non-MRI environment. Moreover, in T-A-2, we incorporate a direct P controller with anidentical proportional gain ^^ ൌ ^^^ೞfor comparison with the proposed DOB-based controller employed in T-A-M and T-A-1.

[0073] The angular position θ^of the pendulum rod follows a 0.5 Hz triangle wave reference signal θௗ^^^^^ through an impedance controller τௗ^ ൌ ^^௩ ⋅ ^θௗ^ െ θ^^ ^ ^^௩ ⋅ ^ωௗ^ െ ω^^^, ^16^where ^^௩is a virtual spring stiffness, ^^௩is a virtual damper coefficient, ωௗ^ is the derivative of θௗ^,and ω^^ is the output velocity estimate introduced in (7). We set ^^௩ ൌ⋅ ^^^ and ^^௩ ൌ 0.02 ⋅ ^^^,allowing the SEA to respond to the external force and dynamics with a stiffness reduced to half of its original value ^^^.

[0074] In FIG.11, we present the experimental results from T-A-M and T-A-1, showing the reference tracking performance of our SEA pendulum system in both MRI and non-MRI environments. These results reveal equivalent responses in the output torque tracking error τ^െ τௗ^ for both T-A-M and T-A-1, including the steady-state responses and transient responses to the commands of τௗ^. Notably, both experiments exhibit a settling time of the transient response around 0.1 sec, which is six times the time constant tୡൌ ^ ^^ sec of the desired closed-loop SEAtransfer function, and maintain a steady-state errorേ0.02 N ⋅ m, which is 2% of themaximum output torque. The consistent outcomes across T-A-M and T-A-1 underscore the full functionality of our SEA in MRI.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2

[0075] In contrast to the satisfactory torque tracking performance exhibited in T-A-M and T-A-1, the implementation of a direct P controller in T-A-2 yields a steady-state torque error ofapproximately 0.33 N ⋅ m, 34% of the maximum output torque, as illustrated in FIG. 11, (c).Perturbation Tests

[0076] In FIG. 10B, (b), the output gear of the SEA is mechanically linked via a shaft coupler to the output shaft of an additional USM, which serves as the source of external perturbation. This supplementary motor introduces perturbation by tracking a small-magnitude triangle wave reference signal from its control side. Notably, due to the significantly higher impedance of the USM compared to the SEA spring element, the perturbation motor effectively acts as a velocity source, contributing to the disturbance variable ω^.

[0077] In T-B-1 and T-B-2, we assess the effectiveness of our DOB-based controller alongside the same direct P controller as T-A-2 using the high-impedance perturbation test setup. Similar to the pendulum tests, we implement an impedance controller defined in (16) with ^^௩ൌ0.5 ⋅ ^^ and ^^ ൌ 0.02 ⋅ ^^ . The ௗ^ ௩ ^ reference θ^ in (16) is set to zero, attempting to keep the SEAstationary in response to external perturbations.

[0078] FIG.11, (d)-(c) depict the experimental results from T-B-1 and T-B-2. The torqueerror τ^ െ τௗ^ in T-B-1 resembles the outcomes observed in T-A-M and T-A-1, except for the peakvalues in transient responses, which are mitigated by a slight compliance from the shaft coupler used in the perturbation testbed. In comparison to the results obtained in T-A-2, the direct P controller in T-B-2 eradicates the steady-state torque bias. Benchmarking Analysis

[0079] Assuming ^^^^^^^ ^ 1 at low frequencies, the closed-loop transfer function for thedirect P control method in (Sergi, Erwin, and O’Malley 2015) is ^^^^ ^⋅ீೞೌ^^^^^^^ ^^^^ ൌ, where ^^^^^^^^is defined in (4). When ^^^^^^^ loop gain significantly belowinadequate steady-state performance under low external impedance scenarios. Although thisAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 performance improves considerably under high external impedance conditions, as demonstrated in T-B-2, transitioning from low to high impedance scenarios, as depicted in FIG. 8A-8B, may necessitate a large actuator force to eliminate the steady-state torque error.

[0080] In (Wyeth 2008; Senturk and Patoglu 2018), velocity-sourced SEAs incorporate a PI compensator to mitigate steady-state tracking errors. In contrast to the 1st-order PI controller employed in (Senturk and Patoglu 2018), the SEA system presented in (Wyeth 2008) utilizes a 2nd-order PI controller by cascading two 1st-order PI controllers. The design of this 2nd-order PI controller strategically positions its two zeros to cancel the resonant poles of ^^^^^^^^ in (4). However, without prior knowledge of ^^^^^^^, both the 1st-order and 2nd-order PI compensators may introduce stability issues to the closed-loop SEA system.

[0081] In our force controller, we employ a DOB to compel the SEA to emulate an ideal spring system represented by^ೞ^ in the presence of varying external impedance. The integrator in this ideal spring model naturally mitigates steady-state errors. In the comparison between T-A-1 and T-B-1, we showcase the robustness of our DOB-based force controller in the face of varying external impedance. 4. Conclusion

[0082] In this section, we have developed a compact, efficient rotary SEA module according to an embodiment of the current invention compatible with MRI environments, driven by velocity-sourced ultrasonic motors. Compared to the previous linear SEA system in MRI (Sergi, Erwin, and O’Malley 2015), our SEA module has six times power-to-volume density, broadening potential MRI applications. Through a DOB-based controller tailored for velocity- sourced SEA, we demonstrate robust torque control for our SEA module against varying external impedance, crucial for medical procedures guided by MRI. Tests conducted in a 3 Tesla MRI scanner confirm the SEA’s effectiveness, with quick response time (0.1 seconds) and minimal error in torque output (within 2% of peak torque). Our control system performs consistently well across various impedance scenarios, offering a significant improvement over traditional controllers, especially in low-impedance situations.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2

[0083] REFERENCES ^ Chen, Wen-Hua, Jun Yang, Lei Guo, and Shihua Li.2015. “Disturbance-Observer-Based Control and Related Methods—an Overview.” IEEE Transactions on Industrial Electronics 63 (2): 1083–95. ^ Dong, Ziyang, Ziyan Guo, Kit-Hang Lee, Ge Fang, Wai Lun Tang, Hing-Chiu Chang, Danny Tat Ming Chan, and Ka-Wai Kwok. 2019. “High-Performance Continuous Hydraulic Motor for MR Safe Robotic Teleoperation.” IEEE Robotics and Automation Letters 4 (2): 1964–71. ^ Elhawary, Haytham, Zion Tsz Ho Tse, Abbi Hamed, Marc Rea, Brian L Davies, and Michael U Lamperth. 2008. “The Case for MR-Compatible Robotics: A Review of the State of the Art.” The International Journal of Medical Robotics and Computer Assisted Surgery 4 (2): 105–13. ^ Erwin, Andrew, Marcia K O’Malley, David Ress, and Fabrizio Sergi.2015. “Development, Control, and MRI-Compatibility of the MR-SoftWrist.” In 2015 IEEE International Conference on Rehabilitation Robotics (ICORR), 187–92. IEEE. ^ Fischer, Gregory S, Axel Krieger, Iulian Iordachita, Csaba Csoma, Louis L Whitcomb, and Gabor Fichtinger. 2008. “MRI Compatibility of Robot Actuation Techniques–a Comparative Study.” In Medical Image Computing and Computer-Assisted Intervention– MICCAI 2008: 11th International Conference, New York, NY, USA, September 6-10, 2008, Proceedings, Part II 11, 509–17. Springer. ^ Guo, Ziyan, Ziyang Dong, Kit-Hang Lee, Chim Lee Cheung, Hing-Choi Fu, Justin DL Ho, Haokun He, Wai-Sang Poon, Danny Tat-Ming Chan, and Ka-Wai Kwok.2018. “Compact Design of a Hydraulic Driving Robot for Intraoperative MRI-Guided Bilateral Stereotactic Neurosurgery.” IEEE Robotics and Automation Letters 3 (3): 2515–22. ^ Kim, Taeyeon, Kyeongsu Shi, and Kyoungchul Kong. 2021. “A Compact Transmitted- Force-Sensing Series Elastic Actuator with Optimized Planar Torsional Spring forAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 Exoskeletons.” In 2021 IEEE / ASME International Conference on Advanced Intelligent Mechatronics (AIM), 572–77. IEEE. ^ Kong, Kyoungchul, Joonbum Bae, and Masayoshi Tomizuka.2011. “A Compact Rotary Series Elastic Actuator for Human Assistive Systems.” IEEE / ASME Transactions on Mechatronics 17 (2): 288–97. ^ Krieger, Axel, Sang-Eun Song, Nathan Bongjoon Cho, Iulian I Iordachita, Peter Guion, Gabor Fichtinger, and Louis L Whitcomb. 2011. “Development and Evaluation of an Actuated MRI-Compatible Robotic System for MRI-Guided Prostate Intervention.” IEEE / ASME Transactions on Mechatronics 18 (1): 273–84. ^ Kwak, Jihoo, Wiha Choi, Chan Lee, and Sehoon Oh. 2021. “Gravity and Impedance Compensation of Body Weight Support System Driven by Two Series Elastic Actuators.” IEEE / ASME Transactions on Mechatronics 27 (1): 190–201. ^ Lee, Chan, and Sehoon Oh.2016. “Configuration and Performance Analysis of a Compact Planetary Geared Elastic Actuator.” In IECON 2016-42nd Annual Conference of the IEEE Industrial Electronics Society, 6391–96. IEEE. ^ Monfaredi, Reza, Kevin Cleary, and Karun Sharma.2018. “MRI Robots for Needle-Based Interventions: Systems and Technology.” Annals of Biomedical Engineering 46: 1479–97. ^ Nakamura, Toshiya, Daisuke Yashiro, Kazuhiro Yubai, and Satoshi Komada. 2021. “Torque Control of a Series Elastic Actuator Using an Ultrasonic Motor with Angular- Velocity Saturation.” Electrical Engineering in Japan 214 (2): e23297. ^ Paine, Nicholas, Sehoon Oh, and Luis Sentis.2013. “Design and Control Considerations for High-Performance Series Elastic Actuators.” IEEE / ASME Transactions on Mechatronics 19 (3): 1080–91. ^ Pratt, Gill A, and Matthew M Williamson.1995. “Series Elastic Actuators.” In Proceedings 1995 IEEE / RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots, 1:399–406. IEEE.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 ^ Senturk, Yusuf Mert, and Volkan Patoglu.2018. “MRI-VisAct: A Bowden-Cable-Driven MRI-Compatible Series Viscoelastic Actuator.” Transactions of the Institute of Measurement and Control 40 (8): 2440–53. ^ Sergi, Fabrizio, Andrew C Erwin, and Marcia K O’Malley. 2015. “Interaction Control Capabilities of an MR-Compatible Compliant Actuator for Wrist Sensorimotor Protocols During fMRI.” IEEE / ASME Transactions on Mechatronics 20 (6): 2678–90. ^ Su, Hao, Ka-Wai Kwok, Kevin Cleary, Iulian Iordachita, M Cenk Cavusoglu, Jaydev P Desai, and Gregory S Fischer.2022. “State of the Art and Future Opportunities in MRI- Guided Robot-Assisted Surgery and Interventions.” Proceedings of the IEEE 110 (7): 968– 92. ^ Wyeth, Gordon.2008. “Demonstrating the Safety and Performance of a Velocity Sourced Series Elastic Actuator.” In 2008 IEEE International Conference on Robotics and Automation, 3642–47. IEEE. ^ Yu, Ningbo, Christoph Hollnagel, Armin Blickenstorfer, Spyros S Kollias, and Robert Riener.2008. “Comparison of MRI-Compatible Mechatronic Systems with Hydrodynamic and Pneumatic Actuation.” IEEE / ASME Transactions on Mechatronics 13 (3): 268–77.

[0084] While various embodiments of the present invention have been described above, it should be understood that they have been presented by way of example only, and not limitation. Thus, the breadth and scope of the present invention should not be limited by any of the above- described illustrative embodiments, or following examples, but should instead be defined only in accordance with the following claims and their equivalents.

[0085] The embodiments illustrated and discussed in this specification are intended only to teach those skilled in the art how to make and use the invention. In describing embodiments of the disclosure, specific terminology is employed for the sake of clarity. However, the disclosure is not intended to be limited to the specific terminology so selected. The above-described embodiments, and following examples, may be modified or varied, without departing from the invention, as appreciated by those skilled in the art in light of the above teachings. It is thereforeAtt’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 to be understood that, within the scope of the claims and their equivalents, the invention may be practiced otherwise than as specifically described. For example, it is to be understood that the present disclosure contemplates that, to the extent possible, one or more features of any embodiment can be combined with one or more features of any other embodiment.

Claims

Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 CLAIMS We Claim:

1. An elastic actuator device, comprising: a motor comprising a motor housing and a motor shaft; a bearing assembly comprising a first ring attached to said motor housing and further comprising a second ring arranged concentrically with said first ring such that said first and second rings are rotatable with respect to each other with bearings therebetween; and a gearbox comprising a gearbox housing mechanically coupled to said second ring of said bearing assembly, said gearbox further comprising a gear assembly comprising an input shaft and output shaft, wherein said gearbox housing is elastically coupled to said motor housing, wherein said input shaft is configured to mechanically couple with said motor shaft so as to drive said input shaft, wherein said bearing assembly further comprises a third ring arranged concentrically with said first ring and said second ring and comprising bearings between said second and third rings such that said first, second and third rings are all rotatable with respect to each other, said third ring being mechanically coupled to said output shaft.

2. The elastic actuator device of claim 1, wherein said bearing assembly is a three-ring bearing assembly.

3. The elastic actuator device of claim 1 or 2, further comprising an encoder attached on the motor housing side of the spring element.

4. The elastic actuator device according to any one of claims 1 to 3, wherein said gearbox is one of a planetary gearbox, a cycloidal gearbox, or a harmonic gearbox.

5. The elastic actuator device according to any one of claims 1 to 4, wherein said motor is a disk-shaped motor.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 6. The elastic actuator device of claim 5, wherein said disk-shaped motor is a disk-shaped ultrasonic motor.

7. The elastic actuator device according to claim 5 or 6, wherein said elastic actuator device is cylindrical having an axial length less than half of a transverse width.

8. The elastic actuator device according to any one of claims 1 to 7, wherein all structural elements thereof are compatible with magnetic resonance imaging (MRI) systems.

9. A transmission assembly for an elastic actuator device, comprising: a bearing assembly comprising a first ring configured to be attachable to a motor housing of a motor and further comprising a second ring arranged concentrically with said first ring such that said first and second rings are rotatable with respect to each other with bearings therebetween; and a gearbox comprising a gearbox housing mechanically coupled to said second ring of said bearing assembly, said gearbox further comprising a gear assembly comprising an input shaft and output shaft, wherein said gearbox housing is configured to be elastically coupled to said motor housing, wherein said input shaft is configured to mechanically couple with a motor shaft of said motor so as to drive said input shaft, wherein said bearing assembly further comprises a third ring arranged concentrically with said first ring and said second ring and comprising bearings between said second and third rings such that said first, second and third rings are all rotatable with respect to each other, said third ring being mechanically coupled to said output shaft.

10. The transmission assembly of claim 9, wherein said bearing assembly is a three-ring bearing assembly.Att’y Ref.: 130996-610516 Applicant Ref.: BK-2024-098-2 11. The transmission assembly of claim 9 or 10, further comprising an encoder attached on the motor housing side of the spring element.

12. The transmission assembly according to any one of claims 9 to 11, wherein said gearbox is one of a planetary gearbox, a cycloidal gearbox, or a harmonic gearbox.

13. The transmission assembly according to any one of claims 9 to 12, wherein said motor is a disk-shaped motor.

14. The transmission assembly of claim 13, wherein said disk-shaped motor is a disk-shaped ultrasonic motor.

15. The transmission assembly according to any one of claims 9 to 14, wherein all structural elements thereof are compatible with magnetic resonance imaging (MRI) systems.

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