Systems and methods for teleoperated control of a multi-arm robotic system

Abstract

An apparatus comprising, a major cannula, a first guiding channel, and a first minor cannula. The major cannula can comprise major cannula joints that enable articulation of the major cannula and major cannula tendons operatively coupled with at least a portion of the major cannula joints to control the articulation of the major cannula. The first guiding channel can extend through a portion of the major cannula and can define a first inlet for receiving a first minor cannula. The first minor cannula can comprise a first end and a second end, and the first end can be removably coupled to the first guiding channel. The first minor cannula can comprise minor cannula joints that enable articulation of the first minor cannula and minor cannula tendons operably coupled with at least a portion of the minor cannula joints to control the articulation of the first minor cannula.

Description

SYSTEMS AND METHODS FOR TELEOPERATED CONTROL OF A MULTI-ARM ROBOTIC SYSTEM CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. Provisional Application Serial No.63 / 674,030, filed on 22 July 2024, which is incorporated herein by reference in its entirety as if fully set forth below. GOVERNMENT LICENSE RIGHTS

[0002] This invention was made with government support under 1R21HD101321-01A1awarded by National Institutes of Health (NIH). The government has certain rights in this invention. FIELD OF THE DISCLOSURE

[0003] The various embodiments of the present disclosure relate generally to teleoperatedcontrol of multi-arm robotic systems. BACKGROUND

[0004] Robot-assisted minimally invasive surgery (RAMIS) has become increasinglycommon. RAMIS enables better visualization and control, causes lesser tissue trauma, and has shown improved patient outcomes. In several cases, during RAMIS, surgical tools are inserted through the working channels of an endoscope. While several small incisions can be created to use multiple tools simultaneously during surgical procedures (multi-port systems), single-port systems have multiple working channels and allow surgeries to be performed with a single incision, potentially resulting in lesser tissue damage with one trajectory rather than many through the surrounding structures.

[0005] Single-port (SP) systems can provide several benefits including reduced invasiveness,better cosmetic results, lower postoperative pain, less patient trauma, and quicker recovery. Nevertheless, the limited access afforded by a single incision underscores the need for advancements in the miniaturization and maneuverability of these robotic systems.

[0006] Several unique challenges and requirements remain for constrained minimally invasiveprocedures, such as during endoscopic cranial procedures (ECPs). The fixed volumes of the skull hinder endoscopes from expanding their workspace. Any gross movement of the endoscope may result in adjacent brain parenchymal injury. Also, the eloquence of thefunctional brain parenchyma requires that instruments or endoscopes entering the brain are to be kept as small as possible to avoid permanent neurologic deficit. The working channel is therefore constrained regarding the tools that can be introduced, leading to the use of tools that are typically rigid, unwieldy, and have limited functionality and range of motion by surgeons’ standards. Consequently, this restricts the complexity of cranial diseases that can be treated using minimally invasive endoscopy. Steering the endoscope can facilitate a larger workspace and minimize the tilting of the endoscope at the site of the incision, which reduces tissue trauma.

[0007] Dual-arm SP endoscopic systems have been designed specifically for neuroendoscopyto overcome some of the aforementioned challenges. However, existing dual-arm SP endoscopic systems remain limited for various reasons. For example, existing systems are limited in their ability to access intracranial structures due to unsteerable tools, rely on large external magnetic actuation systems, and have a diameter of the overall system that is larger than 8 mm.

[0008] Therefore, a need exists for a system that can enter the body through a small singleincision with a larger reachable workspace. Such a system can potentially be utilized in several minimally invasive surgical procedures. BRIEF SUMMARY

[0009] A first aspect of the present disclosure provides an apparatus for a robotic system,comprising a major cannula, a first guiding channel, and a first minor cannula. The major cannula can comprise one or more major cannula joints that enable articulation of the major cannula. The major cannula can further comprise one or more major cannula tendons operatively coupled with at least a portion of the one or more major cannula joints to control the articulation of the major cannula. The first guiding channel can extend through at least a portion of the major cannula and can define a first inlet for receiving a first minor cannula. The first minor cannula can comprise a first end and a second end, and the first end can be removably coupled to the first guiding channel. The first minor cannula can comprise one or more minor cannula joints that enable articulation of the first minor cannula and one or more minor cannula tendons operably coupled with at least a portion of the one or more minor cannula joints to control the articulation of the first minor cannula.

[0010] A second aspect of the present disclosure provides an apparatus for a robotic system,comprising a major cannula, a first minor cannula, and a second minor cannula. The major cannula can comprise a plurality of major cannula joints disposed along a length of the majorcannula and guiding first and second channels disposed along at least a portion of the interior of the major cannula. Actuation of the plurality of major cannula joints can cause articulation of the major cannula. The first minor cannula can be disposed within at least a portion of the first guiding channel. The first minor cannula comprises a first plurality of minor cannula joints disposed along a length of the first minor cannula, such that actuation of the first plurality of minor cannula joints causes articulation of the first minor cannula. The second minor cannula can be disposed within at least a portion of the second channel. The second minor cannula can comprise a second plurality of minor cannula joints disposed along a length of the second minor cannula, such that actuation of the second plurality of minor cannula joints causes articulation of the second minor cannula.

[0011] In any of the embodiments disclosed herein, the apparatus can further comprise anactuator system. The actuator system can comprise a plurality of joint actuators and a plurality of tendons having first ends and second ends. The first ends can be operatively coupled to a respective actuator in the plurality of actuators, and the second ends can be operatively coupled to at least one minor or major joint.

[0012] In any of the embodiments disclosed herein, the second ends can be operatively coupledto a distal end of a respective at least one minor cannula joint or major cannula joint.

[0013] In any of the embodiments disclosed herein, at least a portion of the plurality of tendonscan be disposed within a portion of the plurality of major cannula joints.

[0014] In any of the embodiments disclosed herein, the plurality of joint actuators can comprisefirst, second, and third actuators. The first actuator can be configured to actuate a first tendon in the plurality of tendons to actuate a first major cannula joint in the plurality of major cannula joints to articulate the major cannula. The second actuator can be configured to actuate a second tendon in the plurality of tendons to actuate a first minor cannula joint in the first plurality of minor cannula joints to articulate the first minor cannula. The third actuator can be configured to actuate a third tendon in the plurality of tendons to actuate a first minor cannula joint in the second plurality of minor cannula joints to articulate the second minor cannula.

[0015] In any of the embodiments disclosed herein, the first actuator can be configured to rotatea first spool to which the first tendon is operatively coupled, the second actuator can be configured to rotate a second spool to which the second tendon is operatively coupled, and the third actuator can be configured to rotate a third spool to which the third tendon is operatively coupled.

[0016] In any of the embodiments disclosed herein, the first and second minor cannulas can beretractably disposed within the first and second channels, respectively, such that distal portions of the first and second minor cannulas can be configured to retractably extend, independently of one another, out of a distal end of the major cannula.

[0017] In any of the embodiments disclosed herein, each of the pluralities of major and minorcannula joints can be selected from the group consisting of: an active bending joint; a passive bending joint; a torsion or rotation joint; and a prismatic joint.

[0018] In any of the embodiments disclosed herein, at least a portion of the pluralities of majorand minor joints can comprise a plurality of notches arranged in a pattern. The pattern can be selected from the group consisting of: a unidirectional asymmetric notch (UAN) pattern; a bidirectional symmetric notch (BSN) pattern; and a bidirectional asymmetric notch (BAN) pattern.

[0019] In any of the embodiments disclosed herein, the apparatus can be configured to providefor movement with at least nine degrees of freedom.

[0020] In any of the embodiments disclosed herein, the apparatus can further comprise a firsttool disposed at a distal end of the first minor cannula and a second tool disposed at a distal end of the second minor cannula. The first and second tools can be selected from the group consisting of: a camera, a light source, an ablation probe, a knife, forceps, a brush, an injection needle, an ultrasound probe, sensors, scissors, and graspers.

[0021] These and other aspects of the present disclosure are described in the DetailedDescription below and the accompanying drawings. Other aspects and features of embodiments will become apparent to those of ordinary skill in the art upon reviewing the following description of specific, exemplary embodiments in concert with the drawings. While features of the present disclosure may be discussed relative to certain embodiments and figures, all embodiments of the present disclosure can include one or more of the features discussed herein. Further, while one or more embodiments may be discussed as having certain advantageous features, one or more of such features may also be used with the various embodiments discussed herein. In similar fashion, while exemplary embodiments may be discussed below as device, system, or method embodiments, it is to be understood that such exemplary embodiments can be implemented in various devices, systems, and methods of the present disclosure.BRIEF DESCRIPTION OF THE DRAWINGS

[0022] The following detailed description of specific embodiments of the disclosure will bebetter understood when read in conjunction with the appended drawings. For the purpose of illustrating the disclosure, specific embodiments are shown in the drawings. It should be understood, however, that the disclosure is not limited to the precise arrangements and instrumentalities of the embodiments shown in the drawings.

[0023] FIG.1A-C provides schematic diagrams of a teleoperated multi-arm robotic system, inaccordance with some embodiments of the present disclosure.

[0024] FIGS. 2A-B provides a schematic diagram of a steerable major cannula and minorcannula, in accordance with some embodiments of the present disclosure.

[0025] FIGS. 2C-E provide schematic illustrations of an alternating bidirectional notchpattern, a unidirectional asymmetric notch pattern, and a bidirectional asymmetric notch pattern, respectively, in accordance with some embodiments of the present disclosure.

[0026] FIG. 2F provides an illustration of a NiTi tube section of a steerable minor cannulaattached to a stainless-steel tube section, in accordance with some embodiments of the present disclosure.

[0027] FIG. 3A provides an exploded view of a compact actuation system, in accordance withsome embodiments of the present disclosure.

[0028] FIG. 3B provides top view of a compact actuation system, in accordance with someembodiments of the present disclosure.

[0029] FIG. 3C provides a major cannula bending joint actuator, in accordance with someembodiments of the present disclosure.

[0030] FIG. 3D provides a section and exploded view of a 1st minor cannula actuator, inaccordance with some embodiments of the present disclosure.

[0031] FIG. 4A provides an illustration of an exemplary experimental setup for verification ofa derived joint model, in accordance with some embodiments of the present disclosure.

[0032] FIGS. 4B-E provides plots showing model verification for minor cannula joints, inaccordance with some embodiments of the present disclosure.

[0033] FIG. 4F provides a plot showing the tendon stroke and bending angle relationship fora major cannula, in accordance with some embodiments of the present disclosure.

[0034] FIG. 5A provides an illustration of an unactuated major cannula and actuated minorcannulas, in accordance with some embodiments of the present disclosure.

[0035] FIG. 5B provides an illustration of an actuated major cannula and actuated minorcannulas, in accordance with some embodiments of the present disclosure.

[0036] FIGS.5C-H provide plots showing kinematic trajectories of end tips of actuated minorcannulas when the major cannula is unactuated, in accordance with some embodiments of the present disclosure.

[0037] FIGS. 5I-N provide plots showing kinematic trajectories of end tips of actuated minorcannulas when the major cannula is actuated to 23.4 degrees, in accordance with some embodiments of the present disclosure.

[0038] FIG.6A illustrates a cross-sectional view of a unidirectional asymmetric notch pattern,in accordance with some embodiments of the present disclosure.

[0039] FIG. 6B illustrates a view of a bending member of a bidirectional asymmetric notchjoint, in accordance with some embodiments of the present disclosure.

[0040] FIG. 6C illustrates a cross-sectional view of a bidirectional asymmetric notch pattern,in accordance with some embodiments of the present disclosure.

[0041] FIGS. 7A-B provides a schematic of a steerable major cannula in an unactuated stateand actuated state, respectively, with coordinate frames attached to the joints, in accordance with some embodiments of the present disclosure.

[0042] FIG. 7C provides a schematic of a steerable major cannula with the jth minor cannulaand a cross-sectional view of the major cannula’s end tip showing the two minor cannulas with coordinate frames attached to the joints, in accordance with some embodiments of the present disclosure.

[0043] FIG. 7D provides a schematic of the jth unactuated minor cannula showing thecoordinate frames {F4}—{Fmj}, in accordance with some embodiments of the present disclosure.

[0044] FIG. 7E provides a schematic showing each bending joint modeled as a revolute-prismatic-revolute (RPR) joint (frames {F5}, {F6}, and {F7} correspond to the proximal bending joint and frames {F8}, {F9}, and {F10} correspond to the distal bending joint), in accordance with some embodiments of the present disclosure.

[0045] FIG. 7F provides a graph showing the workspace of a steerable major cannula andsteerable minor cannulas, in accordance with some embodiments of the present disclosure.DETAILED DESCRIPTION

[0046] Although preferred exemplary embodiments of the disclosure are explained in detail, itis to be understood that other exemplary embodiments are contemplated. Accordingly, it is not intended that the disclosure is limited in its scope to the details of construction and arrangement of components set forth in the following description or illustrated in the drawings. The disclosure is capable of other exemplary embodiments and of being practiced or carried out in various ways. Also, in describing the preferred exemplary embodiments, specific terminology will be resorted to for the sake of clarity.

[0047] To facilitate an understanding of the principles and features of the present disclosure,various illustrative embodiments are explained below. The components, steps, and materials described hereinafter as making up various elements of the embodiments disclosed herein are intended to be illustrative and not restrictive. Many suitable components, steps, and materials that would perform the same or similar functions as the components, steps, and materials described herein are intended to be embraced within the scope of the disclosure. Such other components, steps, and materials not described herein can include, but are not limited to, similar components or steps that are developed after development of the embodiments disclosed herein.

[0048] As used in the specification and the appended claims, the singular forms “a,” “an” and“the” include plural referents unless the context clearly dictates otherwise.

[0049] Also, in describing the preferred exemplary embodiments, terminology will be resortedto for the sake of clarity. It is intended that each term contemplates its broadest meaning as understood by those skilled in the art and includes all technical equivalents which operate in a similar manner to accomplish a similar purpose.

[0050] Ranges can be expressed herein as from “about” or “approximately” one particularvalue and / or to “about” or “approximately” another particular value. When such a range is expressed, another exemplary embodiment includes from the one particular value and / or to the other particular value.

[0051] Similarly, as used herein, “substantially free” of something, or “substantially pure”, andlike characterizations, can include both being “at least substantially free” of something, or “at least substantially pure”, and being “completely free” of something, or “completely pure”.

[0052] By “comprising” or “containing” or “including” is meant that at least the namedcompound, member, particle, or method step is present in the composition or article or method,but does not exclude the presence of other compounds, materials, particles, method steps, even if the other such compounds, material, particles, method steps have the same function as what is named.

[0053] Mention of one or more method steps does not preclude the presence of additionalmethod steps or intervening method steps between those steps expressly identified. Similarly, it is also to be understood that the mention of one or more components in a device or system does not preclude the presence of additional components or intervening components between those components expressly identified.

[0054] The materials described as making up the various members of the invention areintended to be illustrative and not restrictive. Many suitable materials that would perform the same or a similar function as the materials described herein are intended to be embraced within the scope of the invention. Such other materials not described herein can include, but are not limited to, for example, materials that are developed after the time of the development of the invention.

[0055] Reference will now be made in detail to exemplary embodiments of the disclosedtechnology, examples of which are illustrated in the accompanying drawings and disclosed herein. Wherever convenient, the same references numbers will be used throughout the drawings to refer to the same or like parts.

[0056] The various embodiments of the present disclosure find many use cases. For example,some embodiments can be useful for minimally invasive cranial endoscopic procedures such as brain tumor surgery, pediatric neurosurgery, treatment of hydrocephalus and intracranial cysts, and other neurosurgical procedures. Some embodiments can be useful for natural orifice transluminal endoscopic surgery procedures. Some embodiments can be useful for minimally invasive surgery procedures requiring endoscopic tools.

[0057] Referring now to FIGS. 1A-B, an implementation of a system 100 for teleoperatedcontrol of a robotic system is shown including a robotic arm 102, a compact actuation system (CAS) 104 coupled with the robotic arm 102, and a multi-arm robotic system 106 coupled with the CAS 104. The multi-arm robotic system 106 can be coupled with a steerable major cannula 108. The steerable major cannula 108 can receive and couple with one or more steerable minor cannulas 110. In some implementations, the steerable major cannula 108 can receive and couple with robotic tools. It should be understood that each element (e.g., robotic arm, CAS, multi-arm robotic system, steerable major and minor cannulas) of the system 100 can beremovably coupled from each other. The system 100 can be made of materials compatible with the imaging modality.

[0058] In some implementations, the multi-arm robotic system 106 can further comprise acamera 112. As used herein, the term “camera” refers to any visualization system that utilizes the capture / detection of electromagnetic waves. In some implementations, the camera 112 is disposed at a distal end of the multi-arm robotic system. In this way, the camera has direct visualization of the surrounding environment proximal to the one or more steerable minor cannulas 110. In some embodiments, the system can comprise one or more cameras 112, sensors, tools, or other devices disposed at the end of the multi-arm robotic system 106 or on the end of one or more of the minor cannulas, in which each device is intended for a specific purpose. For example, a first device can be a conventional visualization camera, and a second device can be a fluorescence measurement sensor / device. In some implementations, the robotic arm 102 is a multi-degree-of-freedom robotic arm.

[0059] In some implementations, the robotic arm 102 is a 7 degrees-of-freedom (DoFs) roboticarm (e.g., PA10-7C, Mitsubishi Heavy Industries, Ltd., Japan). In other implementations, the robotic arm 102 is a 9 DoFs robotic system. In still other implementations, the robotic arm 102 is a 10 DoFs robotic system. In still further implementations, the robotic arm 102 is a 12 DoFs robotic system. In some implementations, the robotic arm 102 can be replaced with another fixed platform that can house the CAS and multi-arm robot to enable direct manual control of the various degrees-of-freedom of the appropriate individual system components.

[0060] In some implementations, the system 100 can further comprise a joystick controller.The system 100 can be controlled using a wireless joystick controller (e.g., Xbox 360 Wireless Controller, Microsoft, WA) to provide intuitive, remote, and agile multi-task minimally invasive surgeries (MIS). FIG. 1C shows a schematic illustration of a wireless joystick controller 210 and the corresponding motion of steerable minor cannulas associated with the controller’s buttons. By integrating the steerable cannulas with a robotic arm to form the overall robotic system along with a joystick for intuitive control, the overall robotic system can provide telerobotic manipulation capabilities and can achieve intuitive, remote, and agile multi-tasking for MIS.

[0061] In some implementations, the system 100 has a force sensing capability (e.g., MEMS-based force sensor) on the steerable catheter body (e.g., the major cannula and / or the minor cannulas). In some implementations, a flexible substrate is wrapped over the steerable catheter body (e.g., major cannula and / or minor cannulas) to sense the contact forces of the steerabletools with the environment. In some implementation, pressure sensitive units can be printed or disposed on a flexible substrate and wrapped over the catheter body. The pressure sensitive units can be arranged in an array configuration.

[0062] In some implementations, the major cannula and minor cannulas can be exchangedand / or replaced using connection mechanisms that enable the cannulas to decouple them from the base actuation unit (e.g., compact actuation system 104).

[0063] Multi-arm robotic system

[0064] Referring now to FIG. 2A, and in brief overview, with added reference to FIG. 2B., animplementation of a multi-arm robotic system is shown including a steerable major cannula 108, a proximal routing block 302, a distal routing block 304, a camera channel 306 for receiving a camera, a major cannula tendon 308, one or more guiding channels 310 having guiding channel inlets 312 for receiving one or more steerable minor cannulas 110. In some implementations, the multi-arm robotic system further comprises a camera (e.g., an endoscopic camera) disposed within the camera channel 306. Though some embodiments shown in the various figures and disclosed herein are disclosed in the context of having two minor cannulas 110, the disclosure is not so limited. Rather, as those skilled in the art would appreciate, embodiments of the present disclosure can have any number of steerable minor cannulas 110 (e.g., 3, 4, 5, or more) with corresponding tendons (or other actuating means), guiding channels 310, and inlets 312.

[0065] Still referring to FIGS. 2A-B, and greater detail, the one or more guiding channels 310can be oriented lengthwise within the body 314 of the steerable major cannula 108. The one or more guiding channels 310 can extend through the longitudinal length of the body 314 of the steerable major cannula 108. In some implementations, the one or more guiding channels 310 has a circular cross-section. In other implementations, the cross-section of the one or more guiding channels 310 can be different shapes such as triangular, rectangular, or irregular. A steerable minor cannula 110 can be inserted through an inlet 312 and can be fixedly or removably coupled to a guiding channel 310, with one minor cannula for each guiding channel.

[0066] In some implementations, the steerable major cannula 108 is a cylindrical tube. Thesteerable major cannula 108 can have many different inner and outer diameters, which can vary based on an intended application, as those skilled in the art would appreciate. In some implementations, the steerable major cannula 108 has an inner diameter of 6.3 mm. In some implementations, the steerable major cannula 108 has an outer diameter of a 6.7 mm.Additionally, the steerable major cannula 108 can be made of many different materials, including, but not limited to, nitinol (NiTi).

[0067] In some implementations, the steerable minor cannula 110 is a cylindrical tube. Thesteerable minor cannula 110 can have many different inner and outer diameters, which can vary based on an intended application, as those skilled in the art would appreciate. In some implementations, the steerable minor cannula 110 has an inner diameter of 1.49 mm. In some implementations, the steerable minor cannula 110 has an outer diameter of 1.93 mm. In some implementations, the steerable minor cannula 110 is made of NiTi tube. In some implementations, the steerable major cannula 108 and the minor cannula 110 are made of different materials from each other. In some implementations, the minor cannulas are replaceable. A quick-connect mechanism can be incorporated in the CAS to replace the minor cannulas. In some implementations, the minor cannulas can be sealed at the end.

[0068] The major cannula 108 and the minor cannulas 110 can comprise one or more ofdifferent joint types (e.g., active bending joint, a passive bending joint, a torsion or rotation joint, and a prismatic joint), and the quantity of each joint type can vary. The active bending joint includes joints such as a proximal bending joint, a distal bending joint, and an intermediate bending joint. Additionally, in some embodiments, the active bending joint can comprise intermediate non-bending portions. Passive bending joints can be useful for compliance and the overall functionality of the system. Passive bending joints can be laser-cut in various patterns to maintain sufficient axial stiffness and bending compliance. It should be understood that various combinations of different joint types, various positional arrangements of the joints with respect to each other, and the quantity of each type of joint can vary and are possible for each of the steerable cannulas. In some implementations, joints can be tendon-driven joints and their stiffness can be selected in different planes to reduce inter-joint coupling. To actuate the joints, a tendon can be attached to the distal end of each joint, except for the passive joint. In some implementations, a tendon can be routed within a joint. In some implementations, a tendon can be routed on the outside of a joint. In some implementations, a joint is a tube or tubing. The disclosure, however, is not limited to the use of tendons to actuate the various joints. Rather, as those skilled in the art would understand, joint actuation can be accomplished many ways known in the art, including, but not limited to, multiple nested tubes, electromagnetic energy (e.g., light, electricity, etc.) manipulated materials, and the like.

[0069] In some implementations, compliant out-of-plane end effector joints with stiff passivejoints can be used to reduce joint coupling. In some implementations, to ensure ease ofprismatic motion of the inner cannula inside and outside of the major cannula, the minor cannula joints can be made passively / actively compliant in the bending plane of the major cannula and can have active compliance in the same or other planes when advanced out.

[0070] In some implementations, inner notched tubes can be utilized for a passive joint tointroduce variable stiffness by torquing the minor cannulas. In some implementations, however, stiffness and motion of a joint can be accomplished by means other than notches.

[0071] In some implementations, a passive joint can be actuated to compensate for the coupledmotion.

[0072] Joints can be micromachined by laser-cutting different notch patterns on the body ofthe steerable cannulas. The compliance of the major cannula and minor cannula can be adjusted through parameters of the notch patterns {d, c, h, n}, where d is the depth of cut, h is the notch width, c is the notch spacing, and n is the number of notches. Table 1 (below) shows exemplary machining parameters {d, c, h, n} for each of the notch patterns. Notch patterns can include, but are not limited to: 1) a unidirectional asymmetric notch (UAN) pattern for the major cannula's bending joint, 2) a bidirectional symmetric notch (BSN) pattern for the minor cannula’s passive joint, 3) a UAN pattern for the minor cannula’s proximal joint, and 4) a bidirectional asymmetric notch (BAN) pattern, among others for the minor cannula’s distal joint. The alternating members of the BSN pattern can be orthogonal to each other to increase the compliance of the passive joint in 3D. Additionally, the passive compliant joint can reduce the overall robot’s stiffness, enabling the steering of the major cannula. The laser-cut pattern can be determined by four parameters: depth of cut (d), notch width (h), notch spacing (c), and the number of notches (n). For individual joints, whether they are steerable or passive, these four parameters can either remain consistent or vary during laser cutting. In some implementations, tubing can be placed over joints to decrease friction and increase joint stiffness. For joints, decreasing notch spacing and increasing notches can make it easier to integrate with low friction tubing.

[0073] In some implementations, the steerable major cannula 108 comprises a bending joint316 at a distal end of the steerable major cannula 108. Bending joints can be micromachined by laser-cutting different notch patterns on the body 314 of the steerable major cannula 108 using a femtosecond laser (e.g., Optec Laser S.A., Frameries, Belgium). In some implementations, the bending joint 316 of the steerable major cannula 108 comprises a unidirectional asymmetric notch (UAN) pattern as depicted in FIG.2A.

[0074] The major cannula tendon 308 can be disposed within the bending joint 316 of thesteerable major cannula 108. In this way, the steerable major cannula can be comprised of “tendon-driven joints” which can be controlled by the compact actuation system. In some implementations, the major cannula tendon is made of nitinol (NiTi) tube. In other implementations, the major cannula tendon is made of tungsten (T). In some implementations, a major cannula tendon 308 can be soldered on the inner wall of the steerable major cannula 108 at the tip of the bending joint 316. In some implementations, the outer diameter of thetendon is 0.2 mm. Application of tension to the major cannula tendon causes the major cannula and the components housed within it to bend.

[0075] In some implementations, the steerable major cannula 108 comprises one or more guidingchannels 310 for receiving one or steerable minor cannulas 110. In some implementations, the one or more guiding channels 310 enable independently controllable minor cannulas. In some implementations, the one or more guiding channels 310 receives other steerable or non-steerable tools. In some implementations, the one or more guiding channels 310 are made of Pebax tubes. In some implementations, the Pebax tubes have an inner diameter of 2.41 mm and an outer diameter of 2.67 mm. In some implementations, the one or more guiding channels 310 comprises one or more routing blocks coupled with tubing to form the guiding channels. In some implementations, the one or more guiding channels are multi-lumen tubes.

[0076] In some implementations, the steerable major cannula 108 comprises one or more workingchannels to house additional steerable or non-steerable tools. The working channel can be disposed within the distal routing block 304.

[0077] Routing blocks 302, 304 can be attached at the base and distal end of the bending joint316 of the major cannula 108. The routing blocks can be 3D-printed (e.g., Projet 5600, 3D Systems, USA).

[0078] Referring to FIG. 2B, the steerable minor cannula 110 can include a body 403 having asteerable section 405. In some implementations, the steerable minor cannula 110 further comprises a routing block 412. In some implementations, the minor cannula 110 has three joints. The minor cannula 110 can comprise two active bending joints at the steerable section 405 of the minor cannula 110 and one passive compliant joint proximate to the base 401of the steerable section 405. In some implementations, the minor cannula 110 comprises a compliant passive joint 402, a proximal bending joint 404, and a distal bending joint 406. The steerable section can comprise proximal and distal bending joints that provide two DoFs in the same plane, allowing for S-shape trajectories for bimanual triangulation capabilities. The minor cannulas can advance out and retract in the major cannula. The passive joint can ensure compliance within the actuated major cannula, for example, while the minor cannulas are advanced out. The passive joint can be laser-cut in various patterns to maintain sufficient axial stiffness and bending compliance. In some implementations, additional passive joints can be added to the system 100.

[0079] The steerable minor cannula 110 can further comprise minor cannula tendons 408,410disposed within the joints of the minor cannula. The minor proximal tendon 408 can bedisposed within the proximal joint 404. The minor distal tendon 410 can be disposed within the distal joint 406. In this way, the steerable minor cannula can be comprised of “tendon- driven joints.” In some implementations, the minor cannula tendons are made of nitinol (NiTi) tube. In other implementations, the minor cannula tendons are made of tungsten (T). In some implementations, the proximal 404 and distal joints 406 have a 0.152 mm outer diameter and 0.076 mm outer diameter tendon soldered at the tip of the joint, respectively.

[0080] The proximal and distal joints can be manufactured by laser micromachining differentnotch patterns on the body 403 of the minor cannula 110. In some implementations, the micromachined notch patterns on the minor cannulas are as follows: 1) an alternating bidirectional symmetric notch (BSN) pattern for the minor cannula passive joint (shown in FIG. 2C) a unidirectional asymmetric notch (UAN) pattern for the minor cannula proximal joint (shown in FIG.2D) a bidirectional asymmetric notch (BAN) pattern for the minor cannula distal joint (shown in FIG.2E). The alternating BSN pattern of the passive joint can ensure that the overall system is compliant in the bending plane of the major cannula even when the minor cannula is torqued. The machining parameters {d, c, h, n} that can be used for each of the rectangular notch patterns are shown in Table 1.

[0081] Each-cross section shown in FIGS. 2C-E can be defined by the angle subtended by theremaining region of the notch segment, De, for UAN, and D], for a BAN and is approximated by:while D_for a BSN is given by: ,where: - - <7J : 7_, 7J)where 7dis the outer radius of the cannula being considered.

[0082] A 3D-printed routing block 412 can ensure the minor distal tendon 410 is approximatelyrouted along the neutral axis of the proximal joint 404 such that the motion of the two joints is primarily decoupled.

[0083] Compact Actuation System (CAS)

[0084] Referring now to FIGS. 3A-D, and in brief overview, an implementation of a CAS isshown including a base 701 coupled to a flange 702, a static frame 703 coupled with the base 701, a modular actuator, and a major cannula actuator 761. The CAS can be connected to a robotic arm or a moving platform via the flange 702 and fasteners 709 (e.g., M6 screws). In some implementations, the base 701 is coupled to the flange 702 with fasteners 707,708 (e.g., M4 screws and nuts). In some implementations, the static frame 703 is coupled to the base 701 with fasteners 731. It should be understood that other fastening mechanisms can be used to couple different elements or components with each other. The major cannula 108 can be mounted on the static frame 703. The CAS can translate, rotate, and bend each of the steerable cannulas. As those skilled in the art would appreciate, the diameter of the base and the length 706 of the CAS can vary in accordance with different embodiments of the present disclosure. In some implementations, the diameter 710 of the base 701 is 103 mm. In some implementations, a length 706 of the CAS is 161.5 mm.

[0085] Still referring to FIGS.3A-D, and in greater detail, the CAS can comprise a plurality ofmodular actuators (e.g., minor cannula actuators 704,705). Each modular actuator can be used for actuating the active bending joints (proximal and distal) of the minor cannulas 110a,b. In some implementations, rotation and the prismatic motion of the minor cannulas are possible via the torsion joints, and prismatic joints. In some implementations, a modular actuator comprises one or more joint actuators (e.g., joint actuators 771, 772, 773, 774). In some implementations, a modular actuator comprises a moving motor bracket 777.

[0086] In some implementations, the CAS has nine joint actuators, though other embodimentscan have many other numbers of actuators. In some implementations, the steerable minor cannulas 110a,110b are each controlled independently by separate minor cannula actuators 704,705. Each minor cannula actuator 704,705 can comprise a plurality of joint actuators 771, 772, 773,774. Joint actuators (both minor cannula and major cannula actuators) can activate the joints of the major and minor cannulas. Joint actuator 771 can activate a rotation joint of a minor cannula 110a,b. Joint actuator 772 can activate a distal joint of a minor cannula 110a,b. Joint actuator 773 can activate a proximal joint of a minor cannula 110a,b. Joint actuator 774 can activate a prismatic joint of a minor cannula 110a,b.

[0087] As shown in FIG. 3C, the major cannula actuator 761 can activate a bending joint of amajor cannula 108. In some implementations, the major cannula actuator 761 is coupled to the base. The major cannula actuator 761 can be coupled to the opposing side of the base relative to the static frame 703. The major cannula 108 can be actuated by pulling a major cannulatendon 308. The first end of the major cannula tendon 308 can be attached to the distal tip of a bending joint of the major cannula 108, while the second end of the tendon can be wrapped around a first spool 762. In some implementations, the second end can be routed through one or more apertures disposed on the static frame 703 and the base 701 and then wrapped around the first spool 762. The first spool 762 can be driven by a first gear motor 763 of a major cannula actuator 761. As those skilled in the art would appreciate, the diameter of the major cannula tendon and first spool can vary in accordance with different embodiments of the present disclosure. In some implementations, the diameter of the major cannula tendon is 0.203 mm. In some implementations, the outer diameter of the first spool is 6.86 mm. In some implementations, the first gear motor 763 is a DC gear motor (e.g., 1.2 W, 16 mm outer diameter, Maxon Precision Motors, MA) with a gearbox of gear ratio 141:1. The first gear motor 763 can be attached to the base 701 using a motor bracket 764 and fasteners 765 (e.g., M3 screws) or other fastening mechanisms.

[0088] In some implementations, as shown in FIG. 3D, a second gear motor of a joint actuator773 can pull a tendon that wraps around a second spool 775 attached to the motor’s shaft through a pulley mechanism 776 (e.g., pulley, pulley with washer), thereby actuating the proximal bending joint of a minor cannula. In some implementations, the second gear motor, is a DC gear motor (e.g., HPCB 6V dual-shaft, gear ratio 986.41:1, Pololu Corp., NV). The second gear motor and pulley 776 can be attached to the moving motor bracket 777 using fasteners 778 (e.g., M2 screws, shoulder screw).

[0089] The distal joint of the minor cannula can be actuated using the same or similar actuationmechanism as the proximal bending joint with a gear motor having the same gear ratio or a different gear ratio. In some implementations, as shown in FIG. 3D, a third gear motor of a joint actuator 772 can pull a tendon that wraps around a third spool 779 attached to the motor's shaft through a pulley mechanism 780, thereby actuating the distal joint of the minor cannula. In some implementations, the third gear motor is a DC gear motor. In some implementations, the gear ratio of the third gear motor has a gear ratio 380:1. The third gear motor and pulley 780 can be attached to the moving motor bracket 777 using fasteners.

[0090] As shown in FIG. 3D, the rotation of a minor cannula110a,b can be achieved using oneor more slots defined by the cannula tube connector 781. In some implementations, the cannula tube connector 781 defines two slots. In some implementations, the minor cannula is retained in the one or more slots using a plurality of washers 782 and one or more sections of heat shrink 783. In some implementations, the washers 782 are stainless steel washers. As those skilled inthe art would understand, the washers 782 can have many different dimensions. In some implementations, the washers 782 have an inner diameter 1.94 mm, an outer diameter of 2.80 mm, and a thickness of 0.25 mm. In some implementations, the washers 782 are micromachined with an Optec Femtosecond laser. In some implementations, the heat shrink 783 is a polyethylene terephthalate (PET) heat shrink (e.g., 0.2 mm wall, Zeus, Orange burg, SC). In some implementations, there are two sections of heat shrink 783 that are 14 mm and 156 mm long, respectively.

[0091] The cannula tube connector 781 can be affixed to a moving motor bracket 777 withfasteners 784 (e.g., M3 screws). A tendon (e.g., polyethylene, ultra-high molecular weight polyethylene (UHMWPE), Kevlar) can wrap around a heat shrink (e.g., the shorter heat shrink section) and a fourth spool 785, facilitating force transmission. Rotation / torsion motion can be achieved when the spool fourth spool 785, connected to a fourth gear motor of the joint actuator 771, rotates. In some implementations, the fourth gear motor is a DC gear motor (Pololu Corp., NV). In some implementations, the fourth gear motor has a gear ratio of 380:1.

[0092] For prismatic motion of the minor cannula, the modular actuator (e.g., minor cannulaactuators 704,705) can slide along parallel rods 786 attached to the base 701 and the static frame 703 using fasteners (e.g., M2 screws). A lead screw nut 787 (e.g., M3 lead screw nut) can be attached to the moving motor bracket 777, and a fifth gear motor of a joint actuator 774. The fifth gear motor can be attached to the base 701 to actuate the lead screw 787, thereby advancing and retracting the minor canula. In some implementations, the lead screw 787 is a M3 screw (e.g., M3×50mm, 0.5 mm pitch). In some implementations, the fifth gear motor is a DC gear motor (e.g., HPCB 6V dual-shaft, gear ratio 100:1, Pololu Corp., NV).

[0093] Each moving motor bracket 777 can define one or more slots 788 for installing a tendonactuator (similar to the proximal or distal joint actuator) to operate an end-effector (e.g., grasper, scissor(s), sensor(s)). It should be understood that other tool attachments such as an electrocautery probe or other diagnostic and / or therapeutic devices at the end of the steerable minor cannulas are also contemplated within the scope of the present disclosure.

[0094] Tendon routing block 789 can be positioned (as shown in FIG. 2F) to route each of thetendons and to join a NiTi tube section with a rigid tube connected to the actuation system. In some implementations, the tendon routing block 789 can be 3D printed. In some implementations, the rigid tube is a stainless-steel tube. In some implementations, the outer diameter of the stainless tube is 1.97 mm and the inner diameter of the tube is 1.4 mm. In someimplementations, tendon routing blocks can be implemented to decrease joint coupling (e.g., end-effector joint tendons routed along neutral axis of proximal and passive joints).

[0095] In some implementations, the system can have 9 DoFs, summarized as follows: oneDoF major cannula (UAN joint), two DoFs (active) of each minor cannula bending joints that include a proximal UAN joint and a distal BAN joint, one DoF of each minor cannula prismatic joint, and one DoF of each minor cannula rotation joint. On actuating the robot arm or platform, higher degrees-of-freedom (DoF) motions can be achieved.

[0096] The CAS offers several advantages. For example, 1) simultaneous actuation of the end-effector, proximal, distal, rotation, and / or prismatic joints, 2) a smaller overall diameter, 3) a single tendon wrapped in one direction around the spool for actuating steerable joints, and 4) low-cost and miniature DC motors.

[0097] The systems and methods described herein can offer several advantages including, butnot limited to, dexterity, modular and compact design, reduced procedure time, bimanual triangulation, and / reduced trauma. For example, the systems and methods can consist of a steerable major cannula which increases the workspace of the overall system, a plurality of minor cannulas composed of joints, and a compact actuation mechanism. The compact actuation system can be modular, low-cost, and extended to multi-arm configuration. The systems and methods can incorporate a plurality of minor cannulas, which enable faster surgical manipulation and decrease the time to replace the tools in comparison to single-channel catheters. The minor cannulas can have an overlapping workspace, which can allow several tools to operate together and in close proximity to each other, which can be useful in various surgical procedures. The systems and methods can enable surgical procedures to be completed with a single incision, resulting in less pain and a faster recovery.

[0098] Kinematic modeling

[0099] A joint kinematics model to map the joint space coordinates to the Cartesian spaceposition and orientation of the end tip of the robotic system was developed. The kinematics of the system were derived in two states: (A) when the prismatic joints of the minor cannulas are fully retracted, and (B) when the prismatic joints of the minor cannulas are advanced to expose the individual minor cannulas. All the frames can be defined with respect to the base frame, { F0}, of the robot, located at the base of the major cannula.

[0100] When the minor cannulas are fully retracted, the major cannula can be steered, and theorigin of the tool frame of the robot, {FM}, coincides with the center of the tip of the distal endB: F<9 @5>BD 75AAG?5& 4<9 @5>BD 75AAG?5 <5E FIB >B=AFE / 5 DBF5F=BA >B=AF "NR) and a bending joint"NS#$ @B89?98 5E 5 D9HB?GF9%CD=E@5F=7 "323# >B=AF I=F< C5D5@9F9DE Ns / 2$ Ncs$ 5A8 Ns / 2. Thecoordinate frames attached to the robotic system are shown in FIGs. 7A-B, when unactuated and actuated, respectively. The joints of the robotically steerable major cannula, and theirD9EC97F=H97BBD8=A5F9 :D5@9E 5D989:=A985E :B??BIE / 1B=AF 'M39HB?GF9 >B=AF I=F< DBF5F=BA NRabout the Z0-axis in the {F0L :D5@901B=AF (M39HB?GF9 >B=AF I=F< DBF5F=BA Ns / 2 about the Z1-axisin the{F1L :D5@90 1B=AF )M2D=E@5F=7 >B=AF I=F< FD5AE?5F=BA Ncs along the Z2-axis in the {F2}:D5@901B=AF *M39HB?GF9 >B=AF I=F< DBF5F=BA Ns / 2 about the Z3-axis in the{F3} frame.

[0101] The length of the non-steerable segment of the major cannula is L0, followed by asteerable segment of length, Ls, and a short segment at the distal end of length, Le. The total length of the major cannula is given by Lt, where Lt= L0+ Ls+ Le. The prismatic joint actuationB: F<9 69A8=A; >B=AF$ Ncs, is determined by the chord length connecting the ends of the curveand is given by:

[0102] The twist coordinate, ) - ,P, for a revolute joint is given by ) ; [:C x 6, C]Z and fora prismatic joint is given by ) ; [;, 0]Z, where ; is the velocity of a point attached to theprismatic joint moving with unit velocity. The unit angular velocity, C, for each revolute joint and the unit velocity, ;, for each prismatic joint, with respect to the base frame, {F0}, is given by: 0 CK = x0|1where the subscript in C_orcorresponds to Joint i. The position vector, q, of a point on the axis of rotation relative to the base frame, {F0}, for each revolute joint is given by:- 8.(3) for a prismatic joint- 8.(3) for a revolute jointwhere C^_ - 84(3) is the skew-symmetric representation- ,M. Through the twists, the forward kinematics of the major cannula can be determined through the product of exponentials and is given by:and position of the tool-frame, given in the base frame, {F0}, respectively. The homogeneous transformation matrix relating the tool-frame, {FM}, to the base frame, {F0}, when the major cannula is unactuated, FJY (0), is given by: 1 0 00 FJY (0) = ^0 1 00 0 0 1'h ^ - *$(3)0 0 01

[0105] The major cannula has two inner channels for the minor cannulas to bend along withthe major cannula. When the major cannula is steered to its desired configuration, the prismatic joints at the base of the minor cannulas can be advanced to expose the steerable section of the minor cannulas. When the minor cannulas are fully advanced, the origin of the tool-frame, {Fm1}, is located at the tip of minor cannula 1, and the origin of the tool-frame, {Fm2}, is located at the tip of minor cannula 2. FIG.7C shows the schematic of the steerable major cannula with the jth(j = 1, 2) minor cannula advanced out. For conciseness, the general analysis for a minor cannula is presented without the jthminor cannula labeling.

[0106] 4<9 =A8=H=8G5? @=ABD 75AAG?5 75A <5H9 :BGD >B=AFE / CD=E@5F=7 "Npris#$ DBF5F=BA "Nr),CDBJ=@5? 69A8=A; "@B89?985E 5A 323 >B=AF / Np / 2$ Ncp$ Np / 2), and distal bending (modeled as an323 >B=AF / Nd / 2$ Ncd$ Nd / 2) joints. In some implementations, the prismatic joint can be used onlyto advance and retract the minor cannula and hence is omitted from the kinematic modeling. The base of the jthminor cannula is at an offset ± <0in the x-direction from the center of the base frame, {F0}. The remaining joints and the coordinate frames {F4}–{Fmj}, attached to the minor cannula as shown in FIG. 7D are defined as follows: Joint 5—Revolute joint withDBF5F=BA Nr about the Z4-axis in the{F4L :D5@901B=AF +M39HB?GF9 >B=AF I=F< DBF5F=BA Np / 2 aboutthe Z5-axis in the {F5L :D5@901B=AF ,M2D=E@5F=7 >B=AF I=F< FD5AE?5F=BA Ncp along the Z6-axis inthe {F6L :D5@901B=AF -M39HB?GF9 >B=AF I=F< DBF5F=BA Np / 2 about the Z7-axis in the {F7} frame;1B=AF .M39HB?GF9 >B=AF I=F< DBF5F=BA Nd / 2 about the Z8-axis in the {F8} frame; Joint 10—2D=E@5F=7 >B=AF I=F< FD5AE?5F=BA Ncd along the Z9-axis in the {F9} frame; Joint 11—Revolute>B=AF I=F< DBF5F=BA Nd / 2 about the Z10-axis in the {F10} frame.

[0107] The link lengths of the minor cannula are shown in FIG. 7D, and it can be assumed thatF<9 CDBJ=@5? 5A88=EF5? 69A8=A; >B=AFE 69A8 I=F< 7BAEF5AF 7GDH5FGD9E$ D9EC97F=H9?K$ 5A8 Ncp andNcd are given by:

[0108] The joint parameters for the steerable section on the minor cannulas can be defined as4<9 GA=F 5A;G?5D H9?B7=FK$ P$ :BD 957< D9HB?GF9joint and the unit velocity, ;, for each prismatic joint, with respect to the base frame, {F0}, is given by:I<9D9 F<9 EG6E7D=CF =A Pi or ;i corresponds to Joint i. The position vector, q, of a point on theaxis of rotation relative to the base frame, {F0}, for each revolute joint is given by:where w0 denotes the offset of the jthminor cannula from the center of the base frame, {F0}, and can be negative (if the jthminor cannula is along the negative X0 axis in its home configuration) or positive (if the jthminor cannula is along the positive X0 axis in its home configuration). The resultant twist coordinates are given by:7D=CF =A Oj refers to the jth minor cannula. The homogeneous transformationmj} to {F0} for each minor cannula is given by:mj} refers to the end-effector frame of the jthminor cannula. The forward jth(j = 1, 2) minor cannula with respect to the base frame, {F0}, is given by:where EJZ br and ^5ir , 5jr , 5kr ^are the orientation and position of the tip of the jthminor cannula with respect to the base frame, {F0}, respectively. The system was tested to approximately bend up to the following angles: 30° bending of the steerable major cannula, 30° bending of the proximal joints of the steerable minor cannula, and 90° bending of the distal joints of the steerable minor cannula. Furthermore, approximately ±180° rotation motion of the steerable minor cannulas can be achieved. A purpose of the steerable major cannula is to allow for minor repositioning, if necessary, during the procedure. For a range of ±180° rotation of the major cannula and up to 30° bending of the major cannula, the simulated workspace of the major cannula is shown in blue in FIG. 7F. Furthermore, for a 45° rotation angle and 10° bending angle of the major cannula, the workspace of the two minor cannulas with the proximal joints bending up to 30°, distal joints bending up to 90°, and rotation of the minor cannulas in the range of ±180° are shown. The workspace of the two minor cannulas overlap, which shows the capability to achieve bimanual triangulation, a desired feature for several endoscopic surgeries.

[0110] The relationship between the tendon stroke and the desired joint angle for the proximalbending, distal bending, and torsion joints of the minor cannulas were derived. The derived joint static models relating the curvature to tendon stroke comprise kinematic and tendon elongation terms.

[0111] The kinematic and tendon elongation relationships are derived below assuming adeformation occurs in constant curvature arc for each segment.

[0112] The proximal joint of the minor cannula can comprise a UAN pattern and the kinematicterms, for the deflection of the proximal joint, Ae, is given by:where >e,his the moment arm of the proximal tendon shown in FIG.6A and is given by:where >teis the neutral axis location for a UAN joint.

[0113] Since significant force can be required to deflect the joint, tendon elongation can beconsidered. The tendon elongation term for the proximal joint is given by:where 'e,J is the length of the proximal tendon when unloaded, $ is the Young’s modulusof the material of the joint (e.g., NiTi tube), &eis the second moment of area of the notched cross-section of the proximal joint, $e,his the Young’s modulus of the proximal tendon, 7e,his the radius of the proximal tendon, and 2eis the length of the proximal joint.

[0114] The second moment of area of the notched cross-section of the proximal joint about theneutral axis is given by:

[0115] The model was experimentally validated.

[0116] For the distal joint, comprising a BAN pattern, the bending member is primarily themember between the two consecutive notches as shown in FIG.6B. The distal joint comprises3 notches resulting in (3 : *= bending members. The second moment of area along the lengthof the bending member is given by: 9M<(=) &]= 12 where, 9, is the thickness of the bending member and <(=) is the width of the bending member given by:where, =, is the length along the beam from the center of the bending member. The kinematic component of bending for the distal joint, '`_c(A]) is given by:where >],his the moment arm of the tendon as shown in FIG. 6C and A]is the deflection of the distal joint. The deflection of a single bending member is related to the total deflection of the joint by: 3: *A]= A 2[bwhere A[bis the deflection of a single bending member. Assuming small deflections of the individual bending members, the deflection of a single member is given by:where %]is the tension of the distal joint tendon and '[bis the length of the bending member is given by: '[b = 2(- : 7d)

[0117] As a result, the tendon elongation that occurs when achieving a desired bending angleis given by:where '],Jis the length of the distal tendon when unloaded, 7],his the radius of the distal tendon, and $],his the Young’s modulus of the distal tendon.

[0118] The model was experimentally validated.

[0119] For the rotation motion of the minor cannula, the tendon elongation term is omitted.This is because the tendon employed in this joint exhibits minimal elongation under lower forces. The kinematic term can be derived as follows: '`_c(Af) = 7Afwhere, 7, is the combined radius of the rigid tube (e.g., steel tube) with the heat shrink (e.g., PET heat shrink), and the diameter of the tendon (e.g., UHMWPE tendon), and Afis the rotation angle of the joint. The tendon slack can cause a deadband in the system. Thus, a backlash model can be used to relate the tendon stroke to the rotation angle of the joint. The backlash model has the deadband term that equals the tendon slack, and the slope term equal to the kinematic term given above. The tendon slack can be determined experimentally.

[0120] The models derived for the proximal joint, distal joint, and rotation joint were validatedexperimentally. A 6-DoF EM tracker (Aurora, Northern Digital Inc., Waterloo, Ontario, Canada) is attached to the end tips of the minor cannulas to collect bending angle and rotation angle data (FIG. 4A). All the joints are actuated individually by pulling the corresponding tendons. Sinusoidal input signals are applied to DC motors to actuate the joints. The quaternion data generated by the EM trackers was converted to the joint deflection using: )= )W h)hmA = 2arccos(6J)where Qhm - ,N and Qh - ,N, obtained from the EM tracker, and are the unit quaternions at time 9 and W J 9, respectively, )hmrepresent the conjugate of )hm, and A is the joint deflection withrespect to the initial joint configuration at 9J = 0.

[0121] FIGS. 4B-E provide graphs showing the verification of the modeling for the minorcannula joints. FIGS. 4B-E are graphs of the joint angle as a function of the tendon stroke for the BAN joint (FIG. 4B), UAN joint (FIG.4C), rotation joint minor cannula 1 (FIG. 4D), and rotation joint minor cannula 2 (FIG.4E).

[0122] Using the models developed to estimate the joint angle from a given tendon stroke, theBAN joints and UAN joints for both the minor cannulas (as shown in FIGS. 4B-C), respectively) are compared. The values of the parameters utilized in the models are given in Table 1. The $ of an NiTi tendon used was 34.6 GPa. For the NiTi tubes, $ was iteratively adjusted in the range provided by the manufacturer (40 GPa-45 GPa) and the value of 40 GPa was chosen and determined to the value that gave the least error between the model and the collected data. For the rotation joint, the tendon was loaded and unloaded at a speed of 1 mm / s for four different tendon stroke values (FIGS. 4D-E). The joints follow derived models with the root-mean-square error (RMSE) values given in the Table 2 (below).

[0123] To derive the relationship between the tendon stroke and bending angle of the majorcannula, the joint statics relation is experimentally derived.

[0124] FIG. 4F provides a graph of the measured bending angle as a function of the tendonstroke with the model ('b) fitted to the experimental data ('^ie). A quadratic model was fitted to the experimental data collected for the joint deflection versus tendon stroke, with an RMSE of 0.17°.

[0125] To verify the kinematic model of the robot derived, an EM tracker was attached to theend tip of the robot. Different tendon strokes were applied to the joints, and the maximum joint deflection for a given trajectory is indicated in Table 3. Based on the models derived, the joint angles are computed from the applied tendon strokes. The computed joint angles are used to compute the position of the tip using the derived robot kinematics model. The position change was estimated using the kinematic model, and the actual position change was measured using the data from the EM trackers. All the measured and estimated tip position values are with respect to the base frame of the robot.

[0126] Referring now to FIG. 5A, an illustration of an unactuated major cannula and actuatedminor cannulas is shown. FIGS. 5C-H are graphs showing the position of the end tips of actuated minor cannulas as a function of time, under different conditions where different minor cannula joints were actuated. The following joints were actuated to produce the graphed kinematic trajectories: minor cannula 1 BAN joint (FIG.5C), minor cannula 1 UAN joint (FIG. 5D), minor cannula 1 UAN and BAN joint (FIG. 5E), minor cannula 2 BAN joint (FIG. 5F), minor cannula 2 UAN joint (FIG.5G), and minor cannula 2 UAN and BAN joint (FIG.5H).

[0127] For the first six trajectories, as shown in FIGS. 5C-H, the major cannula was held in itshome configuration, while the minor cannulas were advanced out. The proximal and distal joints of each minor cannula are actuated. For these trajectories, the tendon stroke was applied as a sinusoidal signal. Also, the major cannula was not perfectly straight in its home configuration due to a pre-curvature induced in the UAN joint during micromachining. The pre-curvature of 3.5° was considered in the kinematic model and was estimated using imaging the UAN joint.

[0128] Referring now to FIG. 5B, an illustration of an actuated major cannula and actuatedminor cannulas is shown. FIGS.5I-N are graphs showing the position of the end tips of actuated minor cannulas as a function of time, under different conditions where different minor cannula joints were actuated and the major cannula bending joint was actuated to 23.4°. The following joints were actuated to produce the graphed kinematic trajectories: minor cannula 1 BAN joint (FIG. 5I), minor cannula 1 UAN joint (FIG. 5J), minor cannula 1 UAN and BAN joint (FIG. 5K), minor cannula 2 BAN joint (FIG.5L), minor cannula 2 UAN joint (FIG.5M), and minor cannula 2 UAN and BAN (FIG.5N).

[0129] For the next six trajectories, as shown in FIGS. 5I-N, the major cannula was actuatedto a desired angle. The minor cannulas were then advanced out using the prismatic motion of the joints. The minor cannula proximal and distal joints were then actuated using a joystick controller.

[0130] The sequence of all the twelve trajectories and the RMSE value from the desired andactual position measurements in the =, >, and ? directions are given in Table 2. FIGS. 5C-Hand FIGS. 5I-N show the experimental (=^b, >̂ b, ?^b), and the modeled (=b, >b, ?b) tipposition changes in the =, >, and ? directions. One can observe that the minor cannula positions can be controlled with an average RMSE of 0.66 mm and 0.98 mm for minor cannula 1 and minor cannula 2, respectively.

[0131] It is to be understood that the embodiments and claims disclosed herein are not limitedin their application to the details of construction and arrangement of the components set forth in the description and illustrated in the drawings. Rather, the description and the drawings provide examples of the embodiments envisioned. The embodiments and claims disclosed herein are further capable of other embodiments and of being practiced and carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein are for the purposes of description and should not be regarded as limiting the claims.

[0132] Accordingly, those skilled in the art will appreciate that the conception upon which theapplication and claims are based may be readily utilized as a basis for the design of other structures, methods, and systems for carrying out the several purposes of the embodiments and claims presented in this application. It is important, therefore, that the claims be regarded as including such equivalent constructions.

[0133] Furthermore, the purpose of the foregoing Abstract is to enable the United States Patentand Trademark Office and the public generally, and especially including the practitioners in the art who are not familiar with patent and legal terms or phraseology, to determine quickly from a cursory inspection the nature and essence of the technical disclosure of the application. The Abstract is neither intended to define the claims of the application, nor is it intended to be limiting to the scope of the claims in any way.

Claims

CLAIMS What is claimed is:

1. An apparatus for a robotic system, comprising:a major cannula comprising one or more major cannula joints that enable articulation of the major cannula, and one or more major cannula tendons operatively coupled with at least a portion of the one or more major cannula joints to control the articulation; a first guiding channel extending through at least a portion of the major cannula, the first guiding channel defining a first inlet for receiving a first minor cannula; a first minor cannula having a first end and a second end, wherein the first end is removably coupled to the first guiding channel, the first minor cannula comprising one or more minor cannula joints that enable articulation of the first minor cannula and one or more minor cannula tendons operably coupled with at least a portion of the one or more minor cannula joints to control the articulation.

2. The apparatus of claim 1, wherein the one or more major cannula tendons areoperatively coupled to a distal end of the one or more major cannula joints.

3. The apparatus of claim 1, wherein at least a portion of the one or more major cannulatendons is disposed within a portion of the one or more major cannula joints.

4. The apparatus of claim 1, wherein the first minor cannula is retractably disposed withinthe first guiding channel, such that a distal portion of the first minor cannula is configured to retractably extend out of the first inlet at a distal end of the major cannula.

5. The apparatus of claim 1, further comprising:a second guiding channel extending through at least a portion of the major cannula, the second guiding channel defining a second inlet for receiving a second minor cannula; a second minor cannula having a first end and a second end, wherein the first end is removably coupled to the second guiding channel, the second minor cannula comprising one or more minor cannula joints that enable articulation of the second minor cannula and one or more minor cannula tendons operably coupled with at least a portion of the one or more minor cannula joints to control the articulation.

6. The apparatus of claim 5, wherein the first and second minor cannulas are retractablydisposed within the first and second guiding channels, respectively, such that a distal portion of the first and second minor cannulas is configured to retractably extend out of the first and second inlets, respectively, at a distal end of the major cannula.

7. The apparatus of claim 6, wherein the first and second minor cannulas are configuredto retractably extend out of the first and second inlets, respectively, at a distal end of the major cannula, independently of one another.

8. The apparatus of claim 1, wherein each of the one or more major cannula joints and oneor more minor cannula joints is selected from the group consisting of: an active bending joint; a passive bending joint; a torsion or rotation joint; and a prismatic joint.

9. The apparatus of claim 1, wherein at least a portion of the one or more major cannulajoints and one or more minor cannula joints comprises a plurality of notches arranged in a pattern.

10. The apparatus of claim 9, wherein the pattern selected from the group consisting of: aunidirectional asymmetric notch (UAN) pattern; and a bidirectional symmetric notch (BSN) pattern; and a bidirectional asymmetric notch (BAN) pattern.

11. The apparatus of claim 1, further comprising an actuator system comprising a pluralityof joint actuators configured to independently actuate a respective major cannula joint or minor cannula joint.

12. The apparatus of claim 11, wherein the plurality of joint actuators comprises:a first actuator configured to actuate a first major cannula tendon in the one or more major cannula tendons to actuate a first major cannula joint in the one or more major cannula joints to articulate the major cannula; and a second actuator configured to actuate a first minor cannula tendon in the one or more minor cannula tendons to actuate a first minor cannula joint in the one or more minor cannula joints to articulate the minor cannula.

13. The apparatus of claim 12, wherein the first actuator is configured to rotate a first spoolto which the first major cannula tendon is operatively coupled, and wherein the second actuator is configured to rotate a second spool to which the first minor cannula tendon is operatively coupled.

14. The apparatus of claim 12, wherein the apparatus is configured to provide for movementwith at least nine degrees of freedom.

15. The apparatus of claim 1, further comprising a tool disposed at a distal end of the firstminor cannula.

16. The apparatus of claim 15, wherein the tool is selected from the group consisting of: acamera, a light source, an ablation probe, a knife, forceps, a brush, an injection needle, an ultrasound probe, a sensor, a grasper, and scissors.

17. An apparatus for a robotic system, comprising:a major cannula comprising: a plurality of major cannula joints disposed along a length of the major cannula, wherein actuation of the plurality of major cannula joints causes articulation of the major cannula; and first and second channels disposed along at least a portion of the interior of the major cannula; a first minor cannula disposed within at least a portion of the first channel, the first minor cannula comprising a first plurality of minor cannula joints disposed along a length of the first minor cannula, wherein actuation of the first plurality of minor joints causes articulation of the first minor cannula; and a second minor cannula disposed within at least a portion of the second channel, the second minor cannula comprising a second plurality of minor cannula joints disposed along a length of the second minor cannula, wherein actuation of the second plurality of minor cannula joints causes articulation of the second minor cannula.

18. The apparatus of claim 17, further comprising an actuator system comprising:a plurality of joint actuators; and a plurality of tendons having first ends and second ends, the first ends operatively coupled to a respective actuator in the plurality of actuators, the second ends operatively coupled to at least one minor or major cannula joint.

19. The apparatus of claim 18, wherein the second ends are operatively coupled to a distalend of at least one minor or major cannula joint.

20. The apparatus of claim 18, wherein at least a portion of the plurality of tendons aredisposed within a portion of the plurality of major cannula joints.

21. The apparatus of claim 18, wherein the plurality of joint actuators comprises:a first actuator configured to actuate a first tendon in the plurality of tendons to actuate a first major cannula joint in the plurality of major cannula joints to articulate the major cannula; a second actuator configured to actuate a second tendon in the plurality of tendons to actuate a first minor joint in the first plurality of minor cannula joints to articulate the first minor cannula; anda third actuator configured to actuate a third tendon in the plurality of tendons to actuate a first minor joint in the second plurality of minor cannula joints to articulate the second minor cannula.

22. The apparatus of claim 21, wherein the first actuator is configured to rotate a first spoolto which the first tendon is operatively coupled, the second actuator is configured to rotate a second spool to which the second tendon is operatively coupled, and the third actuator is configured to rotate a third spool to which the third tendon is operatively coupled.

23. The apparatus of claim 17, wherein the first and second minor cannulas are retractablydisposed within the first and second channels, respectively, such that distal portions of the first and second minor cannulas are configured to retractably extend, independently of one another, out of a distal end of the major cannula.

24. The apparatus of claim 17, wherein each of the pluralities of major and minor cannulajoints is selected from the group consisting of: an active bending joint; a passive bending joint; a torsion or rotation joint; and a prismatic joint.

25. The apparatus of claim 17, wherein at least a portion of the pluralities of major andminor cannula joints comprise a plurality of notches arranged in a pattern.

26. The apparatus of claim 23, wherein the pattern selected from the group consisting of:a unidirectional asymmetric notch (UAN) pattern; and a bidirectional symmetric notch (BSN) pattern; and a bidirectional asymmetric notch (BAN) pattern.

27. The apparatus of claim 17, wherein the apparatus is configured to provide for movementwith at least nine degrees of freedom.

28. The apparatus of claim 17, further comprising a first tool disposed at a distal end of thefirst minor cannula and a second tool disposed at a distal end of the second minor cannula.

29. The apparatus of claim 15, wherein the first and second tools are selected from thegroup consisting of: a camera, a light source, an ablation probe, a knife, forceps, a brush, an injection needle, an ultrasound probe, therapeutic device, diagnostic device, manipulation device, a sensor, a grasper, and scissors.

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