WO2013158978A1 - Procédé et système pour l'insertion souple de robots continuum - Google Patents

Procédé et système pour l'insertion souple de robots continuum Download PDF

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Publication number
WO2013158978A1
WO2013158978A1 PCT/US2013/037346 US2013037346W WO2013158978A1 WO 2013158978 A1 WO2013158978 A1 WO 2013158978A1 US 2013037346 W US2013037346 W US 2013037346W WO 2013158978 A1 WO2013158978 A1 WO 2013158978A1
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Prior art keywords
continuum robot
generalized force
segments
forces
controller
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PCT/US2013/037346
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English (en)
Inventor
Nabil Simaan
Roger E. GOLDMAN
Andrea BAJO
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Vanderbilt University
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Publication of WO2013158978A1 publication Critical patent/WO2013158978A1/fr
Priority to US14/271,418 priority Critical patent/US9539726B2/en
Priority to US15/399,902 priority patent/US10300599B2/en

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Classifications

    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/06—Programme-controlled manipulators characterised by multi-articulated arms
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B1/00—Instruments for performing medical examinations of the interior of cavities or tubes of the body by visual or photographical inspection, e.g. endoscopes; Illuminating arrangements therefor
    • A61B1/00002—Operational features of endoscopes
    • A61B1/00004—Operational features of endoscopes characterised by electronic signal processing
    • A61B1/00006—Operational features of endoscopes characterised by electronic signal processing of control signals
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B1/00—Instruments for performing medical examinations of the interior of cavities or tubes of the body by visual or photographical inspection, e.g. endoscopes; Illuminating arrangements therefor
    • A61B1/00147—Holding or positioning arrangements
    • A61B1/0016—Holding or positioning arrangements using motor drive units
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B1/00—Instruments for performing medical examinations of the interior of cavities or tubes of the body by visual or photographical inspection, e.g. endoscopes; Illuminating arrangements therefor
    • A61B1/005—Flexible endoscopes
    • A61B1/0051—Flexible endoscopes with controlled bending of insertion part
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/30—Surgical robots
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J13/00—Controls for manipulators
    • B25J13/08—Controls for manipulators by means of sensing devices, e.g. viewing or touching devices
    • B25J13/085—Force or torque sensors
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J18/00—Arms
    • B25J18/06—Arms flexible
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1615—Programme controls characterised by special kind of manipulator, e.g. planar, scara, gantry, cantilever, space, closed chain, passive/active joints and tendon driven manipulators
    • B25J9/1625—Truss-manipulator for snake-like motion
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/16—Programme controls
    • B25J9/1628—Programme controls characterised by the control loop
    • B25J9/1633—Programme controls characterised by the control loop compliant, force, torque control, e.g. combined with position control
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B17/00—Surgical instruments, devices or methods, e.g. tourniquets
    • A61B17/24—Surgical instruments, devices or methods, e.g. tourniquets for use in the oral cavity, larynx, bronchial passages or nose; Tongue scrapers
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B17/00—Surgical instruments, devices or methods, e.g. tourniquets
    • A61B17/00234—Surgical instruments, devices or methods, e.g. tourniquets for minimally invasive surgery
    • A61B2017/00292—Surgical instruments, devices or methods, e.g. tourniquets for minimally invasive surgery mounted on or guided by flexible, e.g. catheter-like, means
    • A61B2017/003—Steerable
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/30—Surgical robots
    • A61B2034/302—Surgical robots specifically adapted for manipulations within body cavities, e.g. within abdominal or thoracic cavities
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B34/00—Computer-aided surgery; Manipulators or robots specially adapted for use in surgery
    • A61B34/30—Surgical robots
    • A61B2034/305—Details of wrist mechanisms at distal ends of robotic arms
    • A61B2034/306—Wrists with multiple vertebrae
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B90/00—Instruments, implements or accessories specially adapted for surgery or diagnosis and not covered by any of the groups A61B1/00 - A61B50/00, e.g. for luxation treatment or for protecting wound edges
    • A61B90/06—Measuring instruments not otherwise provided for
    • A61B2090/064—Measuring instruments not otherwise provided for for measuring force, pressure or mechanical tension

Definitions

  • the present invention relates to systems and methods of controlling the position and pose of multi-segment continuum robots. More specifically, the present invention relates to systems and methods of compliant insertion of a continuum robot into a cavity of unknown size, dimensions, and structure.
  • Multi-segment continuum robots provide for snake-like movement and positioning by deformation of internal structures of the robotic mechanisms as opposed to the relative deformation of individual rigid links. As such, continuum robots can be used to extend deeper into cavities to perform functions including, for example, search and rescue in disaster relief, nuclear handling, and minimally invasive surgical procedures.
  • adoption of continuum robots has been limited due to a lack of controls methods to prevent damage to the robotic structure and the environment when the device is inserted into a cavity of unknown dimensions. During insertion into a complex environment, such as a surgical or disaster site, continuum robots must interact safely while being subject to a multitude of unknown contact sites along the robot arm length.
  • Passive compliance techniques have been proposed to achieve safe interaction without the need for additional sensing and complex control.
  • Passively compliant structures contain flexible members which comply with environment interaction forces without explicit compliant control. Though these systems have shown promise in providing a measure of safety, they suffer from a number of significant disadvantages for exploration and intervention in unstructured environments. By the very nature of their design, passive compliant systems are limited in their accuracy and the magnitude of forces that can be applied during environment interaction. Conversely, the measure of safety provided by passive compliance is limited by the flexibility of the system. Additionally, the compliance adds uncertainty and modeling difficulties that degrade trajectory tracking performance. Thus, a need exists for active compliant instrumentation that can safely interact with the surrounding environment while maintaining manipulation precision and delivering adequate forces for executing manipulation tasks.
  • the invention provides a method of compliant insertion of a continuum robot.
  • the continuum robot includes a plurality of independently controlled segments along a length of the continuum robot.
  • the continuum robot is inserted into a cavity of unknown dimensions.
  • a plurality of forces acting on the continuum robot are determined.
  • the plurality of forces includes a force acting on each of the plurality of segments along the length of the continuum robot.
  • Each force of the plurality of forces includes a magnitude and a direction. These forces result in a generalized force that captures the statics of the robot as described in its configuration space (a space describing the shape of each segment by two configuration space angles per a segment).
  • Each determined generalized force is compared to a respective expected generalized force for each of the plurality of segments.
  • the expected force for each segment is determined based on the position of the continuum robot.
  • the position of each segment of the continuum robot is adjusted based on a difference between the determined generalized force and the expected generalized force for the segment.
  • the method further includes repeating the acts of determining the plurality of forces, comparing each determined force to a respective expected force, and adjusting the position of each segment as the continuum robot is advanced further into the cavity.
  • the invention provides a controller for compliant insertion of a continuum robot into a cavity of unknown dimensions.
  • the continuum robot includes a plurality of independently controlled segments along the length of the continuum robot.
  • the controller includes a processor and memory storing instructions that are executable by the processor.
  • the controller is configured to determine a plurality of forces acting on the continuum robot.
  • the plurality of forces includes a generalized force acting on each of the plurality of segments along the length of the continuum robot.
  • Each generalized force includes a magnitude and a direction.
  • Each determined generalized force is then compared to a respective expected generalized force for each of the plurality of segments.
  • the expected generalized force is determined based on the position of the continuum robot.
  • the controller adjusts the position of each segment based on the difference between the determined generalized force and the expected generalized force for each of the plurality of segments.
  • the invention provides a robotic system including a continuum robot, a plurality of actuators, and a controller.
  • the continuum robot includes a plurality of independently controlled segments along the length of the continuum robot and a plurality of back-bone structures extending through the continuum robot.
  • Each actuator is connected to a different one of the plurality of back-bone structures and advances or retracts the back-bone structure to control the shape and end effector position of the continuum robot.
  • the controller includes a processor and a memory. The controller determines a plurality of forces acting on the continuum robot based on forces exerted on the plurality of back-bone structures by the plurality of actuators.
  • the determined forces include a generalized force acting on each of the plurality of segments along the length of the continuum robot.
  • Each generalized force includes a magnitude and a direction.
  • the controller compares each determined generalized force to a respective expected generalized force for each of the plurality of segments.
  • the expected generalized force is determined based on the position of the continuum robot.
  • the position of each segment is adjusted based on the difference between the determined generalized force and the expected generalized force for each segment.
  • the acts of determining the plurality of forces, comparing the generalized forces to a respective expected generalized force, and adjusting the position of each segment are repeated as the continuum robot is advanced into the cavity.
  • compliant motion control of the continuum robot is provided by mapping generalized forces into a configuration space of a robot.
  • Support vector regression techniques are used to provide sparse interpolation to estimate and cancel out effects of uncertainty in the generalized forces due to friction and uncertainty in material properties.
  • the compliant motion control methods are used to operate rapidly deployable handheld robotic devices that are inserted into the human anatomy for surgical operations such as trans-urethral bladder resection, trans-nasal surgery, and frontal sinus exploration/surgery.
  • the methods are also used to provide impedance control of continuum robots and to enable a method for bracing the continuum robot against the anatomical features inside the cavity once contact has been localized and detected.
  • Bracing techniques provide increased stability and increased accuracy for operations performed by a tool positioned at the distal end of the continuum robot.
  • Collaborative telemanipulation algorithms can be implemented to work with the compliant motion control methods to reduce the telemanipulation burden of high degree-of-freedom (DoF) surgical slave devices.
  • DoF degree-of-freedom
  • Continuum robots with compliant insertion functionality can be used, among other things, to perform a minimally invasive surgery (MIS) of the throat which typically requires full anesthesia and use of a laryngoscope. Additional examples of potential applications include frontal sinus exploration surgery and office-based sinus surgery treatment and monitoring of disease progression. This technology is can also be used, for example, for micro-surgical function restoration of paralyzed vocal cords, which requires control of the location and amount of material to inject inside the paralyzed vocal cord. Currently, surgeons guess the amount of material and adjust accordingly during a follow-up surgery (assuming they do not overfill the vocal cord). By avoiding the use of full anesthesia, cost of operation is reduced and surgeons can get feedback about surgical outcomes during the procedure. Relevance is also found in injection site targeting that currently pairs a trans-dermal injection with a microscope for visualizing the anatomy.
  • Fig. 1 is a perspective view of a multiple-segment continuum robot.
  • Fig. 2 is a perspective view of a single segment of the continuum robot of Fig. 1.
  • Fig. 3 is a block diagram of a controller for positioning the continuum robot of Fig. 1.
  • Fig. 4 is a perspective view of the continuum robot of Fig. 1 being inserted into the nasal passage of a human head.
  • Fig. 5 is a flowchart illustrating a method of adjusting the position of the continuum robot of Fig. 1 as the continuum robot is inserted into a cavity of unknown size and dimensions.
  • Fig. 6 is a flowchart illustrating a method of adjusting the position of a single segment of the multiple-segment continuum robot of Fig. 1 as the continuum robot is inserted into a cavity of unknown size and dimension.
  • Fig. 7 is a stiffness model for segment of the continuum robot of Fig. 1 with multiple back-bone structures.
  • Figs. 8 is a graph of sample training and estimation data for the uncertainty parameters in a multi-segment robot.
  • Fig. 9 is a graph of training and estimation data similar to the data provided in figure 8.
  • Fig. 10 is a functional block diagram of the operation of a controller providing for compliant insertion of the continuum robot of Fig. 1.
  • Fig. 11 is a perspective view of an experimental system for analyzing the sensitivity of a continuum robot utilizing compliant motion control.
  • Fig. 12 is a graph illustrating poses of the continuum robot during sensitivity analysis of the compliant motion controller using the experimental system of Fig. 11.
  • Fig. 13 is a table providing experimental data recording during sensitivity analysis of the compliant motion controller using the experimental system of Fig. 11.
  • Fig. 14 is a graph illustrating measured and theoretical minimum forces required for compliant motion during sensitivity analysis of the compliant motion controller using the experimental system of Fig. 11.
  • Fig. 15 is a table providing mean pose error and standard deviation of the nominal kinematics from magnetic sensor measurements during sensitivity analysis of the compliant motion controller using the experimental system of Fig. 11.
  • Fig. 16 is a series of images showing compliant insertion of a continuum robot into a cavity of unknown size and shape.
  • Fig. 17 is a series of graphs illustrating reaction data for the compliant insertion of Fig. 16.
  • Fig. 1 illustrates a multiple-segment continuum robot 100 with multiple back-bone structures to control the movement and position of the continuum robot 100.
  • the multiple- segment continuum robot 100 of Fig. 1 includes three independent segments 101, 102, and 103. However, other continuum robots may include more or fewer segments.
  • a tool or other device would be extended through the continuum robot and would emerge at the distal end of the continuum robot (e.g., the open end of segment 103).
  • the other labels and vectors illustrated in Fig. 1 are referred to below in describing the kinematics of the continuum robot.
  • Fig. 2 provides a more detailed view of a single segment 101 of the continuum robot 100.
  • the continuum robot 100 includes a single central back-bone 121 and multiple secondary back-bones 123.
  • Each segment 101 includes a base disc 125 at the proximate end of the segment and an end disc 127 at the distal end of the segment.
  • a plurality of spacer discs 129 are positioned between the base disc 125 and the end disc 127.
  • the secondary back-bones 123 are super elastic NiTi tubes circumferentially distributed around the central back-bone 121.
  • the end disc 127 is attached to all of the back-bones 121, 123.
  • the base disc 125 is connected only to the central backbone 121.
  • the spacer discs 129 area separated by elastomeric spacers (not pictured) and float along the central backbone 121 while maintaining a fixed radial distance between the central backbone 121 and all secondary backbones 123.
  • two degrees of freedom (DoF) per segment are controlled by pushing and pulling on the secondary backbones 123 to bend the segment in a circular arc.
  • the inset 131 of Fig. 2 illustrates a top view of the discs 125, 127, and 129.
  • a single hole 133 is positioned at the center of each disc.
  • the central backbone 121 extends through the hole 133.
  • Each disc in this example also includes a plurality of holes 135 positioned around the circumference of the disc.
  • the secondary backbones 123 extend through these holes 135.
  • Each disc also includes one or more larger holes 137. Instruments such as, for example, grabbers, cameras, light sources, laser ablation tools, imaging probes (e.g. ultrasound or optical coherence tomography) can be extended through the continuum robot via these larger holes 137 and will emerge from the distal end of the continuum robot 100.
  • the additional labels and vectors illustrated in Fig. 2 are referred to below in describing the kinematics of the continuum robot.
  • Fig. 3 illustrates a control system for the continuum robot 101 of Fig. 1.
  • the control system includes a controller 301 with a processor 303 and a memory 305.
  • the memory 305 stores instructions that can be executed by the processor 303 to cause the controller to control the operation of the continuum robot.
  • Multiple actuators 307, 309, 311 are connected to and operated by the controller 301. As described above, the actuators 307, 309, 311 each push and pull on one of the secondary backbones 123 of the continuum robot 100 to adjust the position and pose of the continuum robot 100.
  • a continuum robot 100 can be inserted into various cavities to reach a target location. Once the distal end of the continuum robot 100 is positioned at the target location, tools emerging from the distal end of the continuum robot 100 are used to perform operations.
  • Fig. 4 illustrates an example of a continuum robot 100 inserted into the nasal passage of a human head 400.
  • the target location for the distal end of the continuum robot is the upper sinuses.
  • the exact dimensions and size of the nasal passages extending from the nose to the upper sinus may not be known.
  • the compliant insertion methods described herein enable the continuum robot 100 to adapt its shape and position to comply with the shape of the nasal passages as the continuum robot 100 is advanced into the nasal passage.
  • Fig. 5 describes a method of adjusting the position and shape of the continuum robot to adapt to the shape of the cavity in which it has been inserted.
  • the continuum robot 100 is pushed further into the cavity to advance the position of the distal end (step 501).
  • the forces exerted along the length of the continuum robot 100 are measured (step 503).
  • each determined force indicates the generalized forces applied to the end disc 127 of each segment of the continuum robot.
  • These measured forces include both the forces required to position the continuum robot in its current shape and external forces, or wrenches, applied to the continuum robot 100 by the surfaces of the cavity.
  • the measured generalized forces along the length of the continuum robot are compared to expected generalized forces that would be detected on the continuum robot if it were positioned in its current shape without the presence of external wrenches (step 505).
  • the positions of the continuum robot segments are then adjusted to minimize the difference between the measured generalized forces and the expected generalized forces (step 507).
  • the shape of the continuum robot is adjusted to minimize the affect of external wrenches on the continuum robot structure along the length of the continuum robot 100.
  • Fig. 6 illustrates in further detail how the controller 301 adjusts a single segment of the continuum robot 100.
  • the method illustrated in Fig. 6 is performed concurrently and repeatedly for each segment of the continuum robot 100 as it is inserted into the cavity.
  • the controller measures the forces on each of the controlled secondary backbone structures 123 (step 603).
  • the forces are measured at the actuator units and, again represent the forces required to position the continuum robot in its current position and external wrench applied to the continuum robot structure by the surfaces of the cavity.
  • the controller further determines a generalized force applied to the end disc of each individual segment of the continuum robot (step 605).
  • the determined generalized force is compared with an expected generalized force (step 607) to determine the magnitude and direction of the external wrench applied to the continuum robot at the end disc of each segment. If the difference between the measured generalized force and the expected generalized force (e.g., the magnitude of the wrench) is greater than a threshold, the controller determines the direction of the wrench (step 611) and adjusts the position of the segment accordingly (step 613). If the magnitude of the wrench does not exceed the threshold, the controller continues to monitor forces (step 603) without changing the position of the continuum robot.
  • the threshold applied in step 609 is adjusted in real-time during insertion of the continuum robot into the cavity to account for elastic cavity surfaces such as internal body tissues.
  • the same compliant insertion techniques can be used to brace the continuum robot against the surfaces of the cavity. Bracing the continuum robot provides additional stability and allows for more accurate placement and maneuvering of the tools emerging from the distal end of the continuum robot.
  • the controller 301 adjusts the position of each segment of the continuum robot to increase the difference between the measured generalized force and the expected generalized force on each end disc 127. To prevent damage to the continuum robot structure, the controller 301 ensures that the difference between the expected generalized force and the measured generalized force (i.e., the magnitude of the wrench) does not exceed a defined threshold.
  • the following nomenclature is used to describe the kinematics of the continuum robot, the mathematical modeling, and the specific techniques used to map external wrenches to a generalize force to provide for compliant insertion:
  • N The number of training data for the SVR optimization ⁇ ( ⁇ ) High dimensional mapping of the input feature space of the support
  • (-)(k) denotes a variable associated with the k* segment.
  • 9(k) defines the bending angle of the segment measured from the plane defined by the base disk, ( A Ub(k), A Vb(k) ⁇ , and the direction normal to the end disk A w g (k).
  • 5(k) defines the orientation of the bending plane of the segment as measured from the plane to the A Ub(k) about A Wb(k
  • the direct kinematics of the k segment is given by the position b(k)Pb(k)g(k) and ⁇ orientation b(k)Rg(k) of the segment end disk with respect to its base disk.
  • the kinematics takes the form
  • Vt/ (i) the gradient of the potential energy
  • w e , (k) the external wrench applied to the end disk of the k th continuum segment.
  • the energy gradient Vt/ (i) is calculated with respect to a virtual displacement in configuration space
  • the statics expression (13) projects both the actuation forces and perturbation wrench w e (k) w into the configuration space of the continuum segment,
  • the projected generalized force on the segment resides in the vector space controllable within the framework of the single-segment kinematics of equation (1).
  • This projection eliminates the requirements for explicit determination of wrenches required by conventional compliance algorithms and casts the interaction force minimization problem into the configuration space of the continuum segment.
  • the elements of the stiffness matrix (18) can be expanded as
  • the first term of the configuration space stiffness is the Hessian of the elastic energy of the segment given by
  • the third term of equation (19) can be expanded by applying a simplifying assumption based on the relative geometry of the backbones in remote actuated continuum system configurations.
  • the stiffness of the continuum robot as measured from the actuation forces at the proximal end of the actuation lines, is a function of strain throughout the length of the actuation lines. As illustrated in Fig. 7, the contributions to the axial stiffness are divided into the stiffnesses, fa and fa, corresponding to the bending, L b , and non-bending, L c , regions of the actuation lines connecting the working distal end to the actuation unit.
  • a compliant motion controller can be constructed to minimize the difference between the expected and measured actuation forces in the secondary backbones.
  • the controller provides compliant motion control of each continuum segment subject to a perturbing wrench at the end disk of the segment. This wrench approximates a multitude of small perturbation forces acting along the length of a continuum segment during an insertion through a tortuous path (e.g., a cavity of unknown size, shape, and dimensions).
  • the configuration space stiffness of an individual segment is generalized as the following to result in the augmented configuration space stiffness of the multi-segment contin m robot
  • An error function is defined as the distance in configuration space from the current configuration, ⁇ & to the desired configuration ⁇ , as
  • the estimated generalized force is calculated using the idealized statics model of f a based on the estimate of the energy and measured actuation forced as in equation (16). This estimate is contaminated by an error ⁇ due to un- modeled friction and strain along the actuation lines, perturbations from circulate-b ending shape of individual segments, deviations in the cross-section of the backbones during bending, and uncertainties in the elastic properties of the NiTi backbones.
  • the generalized force estimate takes the form
  • SV Support Vector
  • An augmented compliant motion controller taking into account the estimates of the un-modeled error, , takes the form
  • ⁇ and A correspond respectively to positive definite scalar and matrix gains to be chosen by the operator.
  • a Lyapunov function candidate of the error system for compliant control can be defined as where P is any symmetric positive definite matrix. Differentiating equation (43) with respect to time and accounting for equation (42) yields
  • the block diagonal matrix is constructed of the sub-matrices, as in equation
  • Lyapunov function candidate is negative definite.
  • the input to the controller is filtered such that estimation error does not drive accidental motion.
  • a dead-band filter is used to ensure that the controller acts for deviation above a reasonable bound for the estimation error.
  • the performance compromise of applying this filter is a reduction in the sensitivity of the controller.
  • Bounds for the sensitivity of the compliant motion controller are limited by the error in canceling the generalized force uncertainties,, ⁇ — ⁇
  • the errors in the generalized force, ⁇ are well approximated by a function of the robot pose in configuration space lf/ a and the trajectory leading to this pose,. / a
  • the trajectory required to achieve a pose influences the friction and backlash in the system at the current pose.
  • the performance of the controller depends on canceling deviations from the idealized model. As specified in equation (39), this cancellation is carried out by a feed- forward term, ⁇ that is obtained though off-line training and online estimation of the model error via support vector regression (SVR).
  • SVR support vector regression
  • SV machines provide a method for nonlinear regression through mapping of the input vectors into a higher dimensional feature space. Parameters for the estimation are learned by application of empirical risk minimization in this feature space through convex optimization. A subset of the training data forms the support vectors which define the parameters for regression. The robustness and favorable generalization properties with noisy data, coupled with a compact structure which allows real-time function estimation during motion control motivate the choice of a SV machine.
  • v-SVR v-SV Regression
  • the training set for the v-SVR contains input pairs
  • x[j] y [j] For the 1 th component of the generalized force, the input is given as
  • v-SVR Given these training input vector pairs, v-SVR provides a method for estimating the function
  • the SVR algorithm allows mapping of the input space to a higher dimensional vector space.
  • Uncertainties in predicting the generalized force, including friction and non-linear bending, are modeled by exponential functions.
  • a Gaussian radial basis function (RBF) kernel is modeled by Gaussian radial basis function (RBF) kernel
  • the v-SVR displays good generalization to the untrained data.
  • the compensation provides a minimum of 1.4 times reduction in the RMS error for ⁇ 4 and a maximum of 2.5 times reduction for ⁇ . While the v-SVR reduces errors on average, the compensation is locally imperfect as can be seen by maxima in the error in the ⁇ directions exceeding the measured errors, Fig. 8.
  • the magnitude of the predicted v-SVR values exceed the measured values, e.g. Fig. 9 for ⁇ , producing local increases in the compensated predicted force given by f > in equation (39). Filtering is applied to smooth outliers in the prediction values.
  • Fig. 10 illustrates an example of a real-time controller for the compliant motion algorithm.
  • This multi-rate controller can be implemented utilizing the Matlab xPC computing environment.
  • the main control loop updating the control values at the joint level runs at 1 kHz. Joint forces are measured at 5 kHz and smoothed with a moving average filter and down- sampled to the 1 kHz control loop.
  • the support vector regression (SVR) is run at 100 Hz.
  • a moving average filter smoothes outliers in the estimate provided by the support vector regression functions of equation (51).
  • Joint force sensors 701 provide actuation force measurements for individual segments of the continuum robot, 7( m ).
  • the actuation forces are utilized to determine a Jacobian matrix linearly mapping the configuration space velocities to joint velocities (step 703).
  • the Jacobian matrix 703 is multiplied by the energy gradient 705 at step 707.
  • the estimated augmented generalized force errors 709 are filtered by a low pass filter 711.
  • the filtered force error is multiplied by the combination of the Jacobian matrix 703 and the energy gradient 705 to provide an estimated augmented force, F a .
  • a dead-band filter 715 is applied to the estimated generalized force to reduce joint motion due to uncompensated errors.
  • the inverse of the configuration space stiffness 717 is applied to determine difference, ⁇ ⁇ , in the configuration space between the current configuration of the continuum robot and the desired configuration.
  • the controller determines the configuration space vector for an equilibrium pose of the continuum robot (step 719).
  • the Jacobian matrix mapping configuration space velocities to joint velocities is applied to the determined equilibrium pose of the continuum robot (step 721) to determine joint positions, q, for the equilibrium pose.
  • An integral 723 is applied and the output provided to a Joint PID controller 725 that adjusts the position of the continuum robot segments to conform to the detected forces.
  • the compliant motion controller uses a feed forward term for compensation of model uncertainties.
  • the sum of the uncertainty estimate and the expected generalized force are filtered through a dead-band to prevent motion by the controller due to errors in the compensation.
  • generalized forces less than the threshold of the deadband filter will be neglected and the threshold for this filter therefore forms a tradeoff between the sensitivity to external perturbations and insensitivity to errors in the model and compensation.
  • Fig. 11 illustrates an experimental system that is used to evaluated the sensitivity of the continuum robot.
  • a wrench was applied at the end disk of the segment 1101 by a Kevlar thread 1105 , attached through a pulley system 1106 to calibrated weights 1107 .
  • the load direction at each pose was quantified relative to the base of the robot by an optical tracking system 1109 with a specified accuracy of 0.20mm RMS.
  • Optical markers 1104 mounted to the Kevlar thread 1105 and to the base of the continuum robot 1103 serve to specify the direction of the applied force.
  • the weight of the thread and markers is less than 1 gram and is therefore negligible with respect to the loads required to initiate the compliant motion.
  • the optical tracking system 1109 provides a specification for the linear accuracy of the device while the experiment requires an orientation prediction.
  • the linear accuracy can be used to estimate the orientation accuracy of the optical tracking system 1 109 by noting the orientation of a vector that is calculated based on the position of two marker points.
  • the smallest linear distance between marker points of 48.5 mm used for the orientation estimation occurs at the base marker system 1103.
  • An RMS error of 0.2 mm at a moment of 24.25 mm corresponds to an orientation error of less than 0.5°.
  • the segment was guided into position by manually applying an external wrench and allowing the continuum structure to comply to the sampled configuration.
  • the pose estimate was measured via the nominal kinematics and was verified by an embedded magnetic tracker system 1 108 with an RMS orientation accuracy of 0.5°.
  • the load direction was measured via the optical trackers after a 10 gram weight was applied to the Kevlar thread to straighten the thread length between the optical markers.
  • the sensitivity measurements provide an opportunity to evaluate the contribution of the model uncertainties and the compensation by v-SVR.
  • equation (15) the applied force required to induced motion can be estimated as the minimum force required to exceed the motion threshold defined by equation (52).
  • the minimum force required to exceed the threshold in the direction of the applied force measured for each pose based on the idealized model is provided in addition to the measured force in Fig. 14.
  • the average difference between the measured and ideal force was 0.37 N with a standard deviation of 0.14 N.
  • the compliant controller for this robot demonstrated adequate sensitivity for this application.
  • Average interaction forces for functional endoscopic sinus surgery have been measured at 2.21 N and forces required to breach the sinus walls ranged between 6.06 N and 17.08 N.
  • the compliant motion controller demonstrated in these experiments obtains a comfortable margin of safety for exploration and interaction.
  • a two segment continuum robot was inserted into an acrylic tube with a three-dimensional shape comprised of multiple out of plane bends.
  • the tube was mounted to an insertion stage that autonomously brought the tube into contact with the robot in a manner analogous to blind insertion into a cavity and subsequent retraction.
  • the controller had no prior knowledge of the geometry of the tube or the path plan of the insertion stage. As illustrated in Fig. 16, the controller successfully complied with the confined complex shape despite a moving contact location unknown to the controller.
  • the generalized force estimates during insertion and retraction are presented in Fig. 17.
  • the data display the effect of the threshold on the motion of the system when subject to external perturbations.
  • Generalized force magnitudes below the threshold for motion denoted by the dashed lines in Fig. 17, are filtered and do not cause motion of the continuum robot.
  • the controller rapidly moves to reduce the force to a level below the threshold. It should be noted that the controller is agnostic to the location of contact and does not therefore require location information for minimization of the environment contact.
  • the results demonstrate the utility of the algorithm for compliant motion control at unknown locations along the length of a continuum robot.
  • the invention provides, among other things, systems and methods for controlling the pose of a multi-segmented continuum robot structure to adapt to the unknown dimensions of a cavity.
  • the shape and position of the individual segments of the continuum robot are continually adjusted as the continuum robot is advanced further into the cavity, thereby providing for compliant insertion of a continuum robot into an unknown cavity.

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  • Life Sciences & Earth Sciences (AREA)
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Abstract

L'invention concerne des procédés et systèmes pour l'insertion souple d'un robot continuum dans une cavité de dimensions inconnues. Le robot continuum comprend une pluralité de segments commandés indépendamment sur la longueur du robot continuum. Une pluralité de forces agissant sur le robot continuum sont déterminées, y compris une force agissant sur chaque segment de la pluralité de segments. Chaque force déterminée comprend une amplitude et une direction. Chaque force déterminée est comparée à une force prévue respective pour chaque segment de la pluralité de segments. La position de chaque segment du robot continuum est ajustée en fonction de la différence entre la force déterminée et la force prévue pour chaque segment. Les segments sont continuellement positionnés de manière à réduire au minimum la différence entre les forces déterminées et les forces prévues à mesure que le robot continuum est avancé dans la cavité.
PCT/US2013/037346 2012-04-20 2013-04-19 Procédé et système pour l'insertion souple de robots continuum WO2013158978A1 (fr)

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