WO2022083173A1 - 基于双闭环三维路径跟踪的微机器人磁驱装置和控制方法 - Google Patents

基于双闭环三维路径跟踪的微机器人磁驱装置和控制方法 Download PDF

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WO2022083173A1
WO2022083173A1 PCT/CN2021/104466 CN2021104466W WO2022083173A1 WO 2022083173 A1 WO2022083173 A1 WO 2022083173A1 CN 2021104466 W CN2021104466 W CN 2021104466W WO 2022083173 A1 WO2022083173 A1 WO 2022083173A1
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robot
micro
magnetic
loop
magnetic field
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PCT/CN2021/104466
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English (en)
French (fr)
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樊启高
陈伟
谢林柏
朱一昕
杨国锋
李岳阳
毕恺韬
黄文涛
罗海驰
赵正青
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江南大学
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Priority to US17/522,676 priority Critical patent/US11938629B2/en
Publication of WO2022083173A1 publication Critical patent/WO2022083173A1/zh

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    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/10—Programme-controlled manipulators characterised by positioning means for manipulator elements
    • B25J9/12—Programme-controlled manipulators characterised by positioning means for manipulator elements electric
    • B25J9/126—Rotary actuators
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance
    • 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
    • A61B1/04—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 combined with photographic or television appliances
    • A61B1/041—Capsule endoscopes for imaging
    • 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
    • A61B1/00158—Holding or positioning arrangements using magnetic field
    • 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
    • A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
    • 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
    • A61B34/70—Manipulators specially adapted for use in surgery
    • A61B34/72—Micromanipulators
    • 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
    • A61B34/70—Manipulators specially adapted for use in surgery
    • A61B34/73—Manipulators for magnetic surgery
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/06—Devices, other than using radiation, for detecting or locating foreign bodies ; determining position of probes within or on the body of the patient
    • A61B5/061—Determining position of a probe within the body employing means separate from the probe, e.g. sensing internal probe position employing impedance electrodes on the surface of the body
    • A61B5/062—Determining position of a probe within the body employing means separate from the probe, e.g. sensing internal probe position employing impedance electrodes on the surface of the body using magnetic field
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J7/00—Micromanipulators
    • 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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • 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
    • B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
    • B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
    • 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
    • B25J9/1694—Programme controls characterised by use of sensors other than normal servo-feedback from position, speed or acceleration sensors, perception control, multi-sensor controlled systems, sensor fusion
    • B25J9/1697—Vision controlled systems
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02P—CONTROL OR REGULATION OF ELECTRIC MOTORS, ELECTRIC GENERATORS OR DYNAMO-ELECTRIC CONVERTERS; CONTROLLING TRANSFORMERS, REACTORS OR CHOKE COILS
    • H02P27/00—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage
    • H02P27/04—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage
    • H02P27/06—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters
    • H02P27/08—Arrangements or methods for the control of AC motors characterised by the kind of supply voltage using variable-frequency supply voltage, e.g. inverter or converter supply voltage using dc to ac converters or inverters with pulse width modulation
    • 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
    • A61B2017/00345—Micromachines, nanomachines, microsystems
    • 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
    • A61B34/20—Surgical navigation systems; Devices for tracking or guiding surgical instruments, e.g. for frameless stereotaxis
    • A61B2034/2046—Tracking techniques
    • A61B2034/2065—Tracking using image or pattern recognition

Definitions

  • the invention relates to the technical field of micro-nano robot control, in particular to a micro-robot magnetic drive device and a control method based on double closed-loop three-dimensional path tracking.
  • Electromagnetically driven magnetic microrobots can be used in medical environments, and magnetic microrobots can be used to carry and transport drugs without harming the human body. Minimally invasive treat. In order to perform such tasks, the magnetic microrobot should be able to achieve the tracking of the desired path.
  • the path tracking control of the existing magnetic micro-robots is mostly applied in the plane range, and single closed-loop path tracking is mostly used, that is, the position and attitude information of the magnetic micro-machine in the plane is obtained through the visual feedback of the camera, and the position closed-loop is established to realize the tracking in the plane range. There are certain problems of response delay and low adaptability.
  • the present inventor proposes a micro-robot magnetic drive device and control method based on double closed-loop three-dimensional path tracking, which can achieve accurate and timely tracking of a given three-dimensional desired tracking path, and overcome the problem of magnetic drive under high frequency conditions. Due to the slow response speed of the device, the double closed-loop control of position feedback and current feedback improves the accuracy and rapidity of three-dimensional path tracking.
  • a micro-robot magnetic drive device based on double closed-loop three-dimensional path tracking comprising an electromagnetic coil module, a DC current source module, a PWM inverter circuit, a current sensor, a host computer, and two cameras, and the electromagnetic coil module includes six belts.
  • the primary iron core of the trapezoidal probe, the Helmholtz coil arranged on the primary iron core and the coil support, each pair of the primary iron core with the trapezoidal probe and its corresponding Helmholtz coil are arranged in parallel, and the coil support It is used to fix three pairs of primary iron cores with trapezoidal probes and three pairs of Helmholtz coils.
  • the area formed by the two pairs of trapezoidal probes is orthogonal to each other, and the area formed by the inner side of the three pairs of trapezoidal probes is used as the working space of the magnetic micro robot.
  • Each DC current source provides AC power to a pair or one Helmholtz coil after passing through the PWM inverter circuit, and the host computer is connected to the PWM respectively.
  • Inverter circuit, current sensor and camera The current sensor is used to detect the output current of the Helmholtz coil.
  • the two cameras are arranged outside the coil bracket and are orthogonally distributed.
  • the host computer sends a control signal to the PWM inverter circuit to output frequency and amplitude.
  • the alternating current with adjustable value, the Helmholtz coil generates a rotating magnetic field and then controls the magnetic micro-robot to move three-dimensionally along the axis of the rotating magnetic field. three-dimensional movement.
  • the coil support includes a base, a support and a hollow baffle that are arranged oppositely up and down, each base is provided with three triangular inclined blocks along the axis direction, and the inclined surfaces of a pair of triangular inclined blocks in the axial direction are arranged in parallel. And it is used to place the first-level iron core with trapezoidal probe.
  • the bracket is arranged between the bases to play a supporting role.
  • the hollow baffle is arranged in the middle of the bracket and is parallel to the base.
  • the hollow baffle divides the space enclosed by the base into the upper area and In the lower area, one of each pair of primary iron cores with trapezoidal probes and their corresponding Helmholtz coils is arranged on the hollow baffle and located in the upper area, and the other is located in the lower area, and the hollow area of the hollow baffle is at least equal to Magnetic microrobots have the same workspace area.
  • the primary iron core is a cylindrical iron core made of DT4-E material, with a diameter of 50mm and a thickness of 30mm, the number of turns of the Helmholtz coil is 190, and the end of the trapezoidal probe is a square with a side length of 35mm.
  • the front end is a rectangle with a length of 16mm and a width of 2mm
  • the working space is a spherical space with a radius of 16mm
  • the magnetic micro robot is a spiral shape.
  • a micro-robot control method based on double closed-loop three-dimensional path tracking includes:
  • the actual axis direction and the desired motion direction, the three-dimensional coordinates of the centroid and the three-dimensional coordinates of the desired position point are processed respectively to obtain the direction error and position error.
  • the direction error includes the pitch angle error and the direction angle error
  • the position error includes the horizontal distance and vertical distance between the two. ;
  • the state space equation is obtained by modeling the 3D kinematics of the desired tracking path according to the curvature, torsion, orientation error and position error;
  • the position closed-loop controller is designed through the state space equation to obtain the required rotating magnetic field, and the rotating magnetic field is input to the established current closed-loop magnetic field controller to output the desired magnetic field, so as to realize the double closed-loop three-dimensional motion control of the magnetic micro-robot;
  • the camera acquires the current pose information of the magnetic micro-robot and feeds it back to the host computer to obtain the three-dimensional coordinates of the centroid and the actual axis direction of the magnetic micro-robot, including:
  • ct h t represents the normal vector of the top camera plane
  • cs h s represents the normal vector of the side camera plane
  • ct h s represents the transformation of the normal vector of the side camera plane to the top camera plane
  • ct R cs represents the side camera coordinate system to The rotation matrix of the top camera coordinate system
  • X B represents the actual axis direction of the magnetic micro-robot in the world coordinate system
  • the three-dimensional coordinates of the center of mass of the magnetic microrobot in the world coordinate system are calculated by the following formula:
  • cs G represents the coordinates of the center of mass in the side camera plane
  • ct t cs represents the translation matrix from the side camera coordinate system to the top camera coordinate system
  • G represents the three-dimensional coordinates of the center of mass in the world coordinate system.
  • s represents the three-dimensional coordinates of the desired position point
  • v represents the actual motion speed
  • ⁇ de represents the heading angle error
  • ⁇ ie represents the pitch angle error
  • c represents the curvature
  • ⁇ represents the torsion rate
  • dy represents the vertical distance
  • d z represents the horizontal distance
  • ⁇ y represents the angular velocity component of the magnetic microrobot on the Y axis
  • ⁇ z represents the angular velocity component of the magnetic microrobot on the Z axis
  • ⁇ ⁇ i represents the compensation pitch angle
  • ⁇ ⁇ d represents the compensation direction angle
  • the state space equation is linearized to obtain the input of the position closed-loop controller:
  • k d1 , k t1 , k d2 , and k t2 are control gains and are positive;
  • the path tracking task is to make the heading angle error, pitch angle error, vertical distance and horizontal distance converge to zero;
  • the output of the position closed-loop controller is:
  • B ⁇ is the magnetic field perpendicular to the axis and used to provide rotation for the magnetic microrobot
  • is the magnetic field parallel to the axis and used to provide steering for the magnetic microrobot
  • B 0 is the magnetic flux density at the center of the workspace
  • f is the rotation frequency
  • t is the rotation time
  • y b , z b are the basis vectors of the X B plane perpendicular to the actual axis direction of the magnetic microrobot
  • ⁇ is the control gain
  • ⁇ is the output of the position closed-loop controller
  • ⁇ [ ⁇ x ⁇ y ⁇ z ], I 1 represents the third-order identity matrix.
  • the current closed-loop magnetic field controller analyzes the direction of the rotating magnetic field and the coil output current fed back by the current sensor, and outputs a control signal to the PWM inverter circuit, which outputs the desired current to the Helmholtz coil to generate the desired magnetic field;
  • B X , B Y , and B Z are the components of the magnetic field B in the three axial directions, and n x , ny , and nz are the unit directions of the three planes of XOY, XOZ , and YOZ;
  • the magnetic field is decomposed into the three axes of X, Y, and Z, and the mapping relationship between the magnetic field and the current between the axes is as follows:
  • ⁇ 0 is the dielectric constant of the magnetic field
  • N is the number of turns of the Helmholtz coil
  • a is the radius of the Helmholtz coil
  • I is the desired current passing through the coil.
  • the desired motion direction of the magnetic micro-robot is its axis direction in the undisturbed condition
  • the desired motion direction is represented by the first direction angle and the first pitch angle
  • the first direction angle is the vector v p to the XOY plane.
  • the angle between the projection of , and the x-axis, the first pitch angle is the angle between the vector v p and the XOY plane
  • the actual axis direction of the magnetic micro-robot is represented by the second direction angle and the second pitch angle due to the action of gravity and disturbance
  • ⁇ d1 is the second direction angle
  • ⁇ d is the first direction angle
  • ⁇ ⁇ d is the compensation direction angle of the lateral plane
  • the lateral plane is the XOY plane
  • ⁇ i1 is the second pitch angle
  • ⁇ i is the first pitch angle
  • ⁇ ⁇ i is the compensation pitch angle of the vertical plane
  • the vertical plane is the plane perpendicular to the XOY plane;
  • the actual motion speed of the running magnetic microrobot is:
  • v p is the expected movement speed
  • v is the actual movement speed
  • the desired tracking path curve coordinate system is established with the desired position point as the origin, the tangent direction of the desired position point, the main normal direction, and the secondary normal direction as the coordinate axes, and the tangent direction is the desired movement direction.
  • the conversion relationship between the actual axis direction of the magnetic micro-robot and the first direction angle and the first pitch angle is obtained by using the following formula:
  • the magnetic drive device provided in this application can generate a rotating magnetic field, and realizes the control of the magnetic micro-robot in any direction in three-dimensional space.
  • the camera, the position closed-loop controller and the current closed-loop magnetic field controller integrated in the upper computer cooperate with the real-time monitoring and control of the magnetic micro-robot.
  • the PWM inverter circuit can shorten the establishment time of the desired magnetic field and make the desired magnetic field more stable, and the upper function can quickly give the coordinates of the desired position point and the running track information of the magnetic micro-robot; current closed-loop magnetic field controller, PWM inverter circuit , Helmholtz coil and current sensor form the first closed-loop control.
  • the current closed-loop magnetic field controller analyzes the direction of the rotating magnetic field and the output current fed back by the current sensor, and outputs the control signal to the PWM inverter.
  • the PWM inverter circuit outputs the desired current to the Helmholtz coil to generate the desired magnetic field
  • the position closed-loop controller, the current closed-loop magnetic field controller, the PWM inverter circuit, the Helmholtz coil, the magnetic micro-robot and the camera form the second Heavy closed-loop control
  • the position closed-loop controller is designed according to the error between the pose information fed back by the camera and the desired motion path to obtain the required rotating magnetic field. Accurate and fast path tracing in environments.
  • FIG. 1 is a schematic diagram of a magnetic drive device provided by the present application.
  • FIG. 2 is a front view of the overall assembly of the electromagnetic coil module provided by the present application.
  • FIG. 3 is an assembly diagram of the electromagnetic coil module provided by the present application with a base and a bracket removed.
  • FIG. 4 is a schematic diagram of a base with a triangular inclined block provided by the present application.
  • FIG. 5 is a combined three views of a trapezoidal probe, a primary iron core and a secondary iron core provided by the present application.
  • FIG. 6 is a flowchart of the control method provided by the present application.
  • FIG. 7 is a schematic diagram of angle compensation of the magnetic microrobot provided by the present application when it moves in a three-dimensional space.
  • FIG. 8 is a schematic diagram of the principle of obtaining the three-dimensional coordinates of the centroid of the magnetic microrobot and the actual axis direction provided by the present application.
  • FIG. 9 is a model diagram of a desired tracking path of the magnetic microrobot provided by the present application in the tracking path curve coordinate system.
  • FIG. 10 is a partial circuit diagram of the first re-closed-loop control provided by the present application.
  • FIG. 1 shows the principle diagram of the magnetic drive device.
  • the magnetic drive device includes an electromagnetic coil module, a DC current source module, and a PWM inverter circuit. , current sensor, host computer, two cameras.
  • the PWM inverter circuit can shorten the establishment time of the desired magnetic field and make the desired magnetic field more stable, and the host computer can quickly give the coordinates of the desired position point and the running track information of the magnetic micro-robot.
  • the electromagnetic coil module includes six primary iron cores 2 with trapezoidal probes 1, Helmholtz coils 3 arranged on the primary iron core 2, and coil supports, each pair of which has a trapezoidal shape.
  • the primary iron core 2 of the probe 1 and its corresponding Helmholtz coil 3 are arranged in parallel.
  • the coil support includes a base 401, a support 402 and a hollow baffle 403 that are arranged opposite each other up and down.
  • Each base 401 is provided with three triangular inclined blocks 404 along the axis direction, and the inclined surfaces of a pair of triangular inclined blocks 404 in the axial direction are parallel to each other. It is arranged and used to place the primary iron core 2 with the trapezoidal probe 1.
  • the bracket 402 is arranged between the bases 401 to play a supporting role.
  • the hollow baffle 403 is arranged in the middle of the bracket 402 and is parallel to the base 401.
  • the space enclosed by the base 401 is divided into an upper layer area and a lower layer area, and one of each pair of the primary iron core 2 with the trapezoidal probe 1 and its corresponding Helmholtz coil 3 is arranged on the hollow baffle 403 and is located in the upper layer area, The other is in the lower area.
  • the three pairs of primary iron cores 2 with trapezoidal probes 1 are orthogonal to each other along the axis direction, and the three pairs of Helmholtz coils 3 are orthogonal to each other along the axis direction.
  • the hollow area of the hollow baffle 403 is at least the same as the workspace area of the magnetic micro-robot.
  • Each DC current source provides alternating current for a pair or one Helmholtz coil 3 after passing through the PWM inverter circuit, that is, there are at least six and at most twelve DC current sources in this application.
  • the host computer is respectively connected to the PWM inverter circuit, the current sensor and the camera.
  • the current sensor is used to detect the output current of the Helmholtz coil 3.
  • the two cameras are arranged outside the coil bracket 402 and are orthogonally distributed.
  • the host computer sends a control signal to the PWM
  • the inverter circuit outputs alternating current with adjustable frequency and amplitude.
  • the Helmholtz coil 3 generates a rotating magnetic field and controls the magnetic micro-robot to move in three dimensions along the axis of the rotating magnetic field.
  • the camera obtains the position information of the magnetic micro-robot and transmits it to the upper position.
  • the machine realizes closed-loop control of the three-dimensional motion of the magnetic microrobot.
  • the electromagnetic coil module also includes six secondary iron cores 5 and a trapezoidal coil 6 arranged around it, and the secondary iron core 5 is arranged on one side of the primary iron core 2 without the trapezoidal probe 1, Similarly, each pair of secondary iron cores 5 is arranged in parallel and placed on the triangular inclined block 404, three pairs of secondary iron cores 5 are orthogonal to each other along the axis direction, and three pairs of trapezoidal coils 6 are orthogonal to each other along the axis direction.
  • the probe 1, the primary iron core 2 and the secondary iron core 5 are arranged in steps.
  • Figure 5(a) is a front view of the combination of the probe and the iron core
  • Figure 5(b) is a side view of the combination of the probe and the iron core
  • Figure 5(c) is the probe and the iron core.
  • the primary iron core 2 and the secondary iron core 5 are cylindrical iron cores made of DT4-E material.
  • the diameter of the primary iron core 2 is 50 mm and the thickness is 30 mm.
  • the number of turns of the Helmholtz coil 3 is 190.
  • the diameter of the iron core 5 is 70mm and the thickness is 35mm.
  • the number of turns of the trapezoidal coil 6 is 610. The corresponding two coils are connected in series.
  • the magnetic microrobot is in a spiral shape as shown in FIG. 7 .
  • the present application also discloses a micro-robot control method based on double-closed-loop three-dimensional path tracking, which can be applied to the above-mentioned magnetic drive device.
  • the flow chart of the control method is shown in FIG. 6 and includes the following steps:
  • Step 1 Input the desired tracking path in the host computer to obtain the desired motion direction, and the camera obtains the current pose information of the magnetic micro-robot and feeds it back to the host computer to obtain the three-dimensional coordinates of the magnetic micro-robot's center of mass and the actual axis direction.
  • the desired motion direction of the magnetic micro-robot is its axis direction under the undisturbed condition, and the desired motion direction is represented by the first direction angle and the first pitch angle, and the first direction angle is the vector v p to the XOY plane.
  • the angle between the projection and the x-axis, the first pitch angle is the angle between the vector v p and the XOY plane.
  • ⁇ d1 is the second direction angle
  • ⁇ d is the first direction angle
  • ⁇ ⁇ d is the compensation direction angle of the lateral plane
  • the lateral plane is the XOY plane
  • ⁇ i1 is the second pitch angle
  • ⁇ i is the first pitch angle
  • ⁇ ⁇ i is the compensation pitch angle of the vertical plane
  • the vertical plane is the plane perpendicular to the XOY plane.
  • the actual motion speed of the running magnetic microrobot is:
  • v p is the expected movement speed
  • v is the actual movement speed
  • the camera obtains the current pose information of the magnetic micro-robot and feeds it back to the host computer to obtain the three-dimensional coordinates of the center of mass and the actual axis direction of the magnetic micro-robot, as shown in Figure 8, including:
  • ct h t represents the normal vector of the top camera plane 701
  • cs h s represents the normal vector of the side camera plane 702
  • ct h s represents the transformation of the normal vector of the side camera plane 702 to the top camera plane 701
  • ct R cs represents the side The rotation matrix from the camera coordinate system to the top camera coordinate system
  • X B represents the actual axis direction of the magnetic microrobot in the world coordinate system.
  • the three-dimensional coordinates of the center of mass of the magnetic microrobot in the world coordinate system are calculated by the following formula:
  • cs G represents the coordinates of the center of mass in the side camera plane 702
  • ct t cs represents the translation matrix from the side camera coordinate system to the top camera coordinate system
  • G represents the three-dimensional coordinates of the center of mass in the world coordinate system.
  • Step 2 Find the desired position point with the smallest distance from the center of mass on the desired tracking path, establish the desired tracking path curve coordinate system to obtain the three-dimensional coordinates of the desired position point, and the curvature and torsion of the desired tracking path curve.
  • the desired tracking path curve coordinate system takes the desired position point s as the origin, the tangent direction X F of the desired position point, the main normal direction Y F , and the secondary normal direction Z F as the coordinate axes to establish the SF coordinate system Obtained, the tangential direction X F is the desired motion direction, and the conversion relationship between the actual axis direction of the magnetic micro-robot and the first direction angle and the first pitch angle is obtained by using the following formula:
  • Step 3 Process the actual axis direction and the desired motion direction, the three-dimensional coordinates of the centroid and the three-dimensional coordinates of the desired position point respectively to obtain the direction error and position error.
  • the direction error includes the pitch angle error and the direction angle error
  • the position error includes the horizontal distance between the two. and vertical distance.
  • ⁇ de ⁇ d1 - ⁇ dc , where ⁇ dc is the desired direction angle.
  • the horizontal distance d z and the vertical distance dy are the Euclidean distances between the three-dimensional coordinates of the desired position point and the three-dimensional coordinates of the centroid.
  • Step 4 According to the curvature, torsion, orientation error and position error, the three-dimensional kinematics modeling of the desired tracking path is obtained to obtain the state space equation.
  • s represents the three-dimensional coordinates of the desired position point
  • v represents the actual motion speed
  • ⁇ de represents the heading angle error
  • ⁇ ie represents the pitch angle error
  • c represents the curvature
  • ⁇ represents the torsion rate
  • dy represents the vertical distance
  • d z represents the horizontal distance
  • ⁇ y represents the angular velocity component of the magnetic microrobot on the Y axis
  • ⁇ z represents the angular velocity component of the magnetic microrobot on the Z axis
  • ⁇ ⁇ i represents the compensation pitch angle
  • ⁇ ⁇ d represents the compensation direction angle
  • Step 5 Design the position closed-loop controller through the state space equation to obtain the required rotating magnetic field, input the rotating magnetic field to the established current closed-loop magnetic field controller to output the desired magnetic field, and realize the double closed-loop three-dimensional motion control of the magnetic micro-robot.
  • the state space equation is linearized to obtain the input of the position closed-loop controller:
  • k d1 , k t1 , k d2 , and k t2 are control gains and are positive.
  • the path tracking task is to converge the yaw error, pitch error, vertical distance and horizontal distance to zero.
  • the output of the position closed-loop controller is:
  • B ⁇ is the magnetic field perpendicular to the axis and used to provide rotation for the magnetic microrobot
  • is the magnetic field parallel to the axis and used to provide steering for the magnetic microrobot
  • B 0 is the magnetic flux density at the center of the workspace
  • f is the rotation frequency
  • t is the rotation time
  • y b , z b are the basis vectors of the X B plane perpendicular to the actual axis direction of the magnetic microrobot
  • ⁇ is the control gain
  • ⁇ is the output of the position closed-loop controller
  • ⁇ [ ⁇ x ⁇ y ⁇ z ], I 1 represents the third-order identity matrix.
  • Figure 10 shows part of the circuit diagram of the first closed-loop control.
  • the current closed-loop magnetic field controller analyzes the direction of the rotating magnetic field and the coil output current fed back by the current sensor, and outputs a PWM control signal to the PWM inverter circuit.
  • the output of the PWM inverter circuit is expected Current is passed to the Helmholtz coil 3 to generate the desired magnetic field.
  • B X , B Y , and B Z are the components of the magnetic field B in the three axial directions
  • n x , ny , and nz are the unit directions of the three planes of XOY, XOZ , and YOZ.
  • the magnetic field is decomposed into the three axes of X, Y, and Z, and the mapping relationship between the magnetic field and the current between the axes is as follows:
  • ⁇ 0 is the dielectric constant of the magnetic field
  • N represents the number of turns of the Helmholtz coil 3
  • a represents the radius of the Helmholtz coil 3
  • I represents the desired current flowing into the coil.
  • Step 6 Re-execute the steps of obtaining the current pose information of the magnetic micro-robot by the camera and feeding it back to the host computer to obtain the three-dimensional coordinates of the magnetic micro-robot's center of mass and the actual axis direction, until the tracking of the entire desired tracking path is completed.
  • the current closed-loop magnetic field controller and the position closed-loop controller are designed in the host computer.
  • the current closed-loop magnetic field controller, PWM inverter circuit, Helmholtz coil and current sensor form the first closed-loop control.
  • the current closed-loop magnetic field controller outputs a control signal to the PWM inverter circuit, and the PWM inverter circuit outputs the desired current to the Helmholtz coil to generate the desired magnetic field; position closed-loop controller, current closed-loop magnetic field controller, PWM inverter
  • the variable circuit, Helmholtz coil, magnetic micro-robot and camera form the second closed-loop control.
  • the position closed-loop controller is designed according to the position and attitude information fed back by the camera to calculate the error with the desired motion path.
  • the required rotating magnetic field through the double closed-loop control method, realizes the accurate and fast path tracking of the magnetic microrobot in the three-dimensional environment.

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Abstract

基于双闭环三维路径跟踪的微机器人磁驱装置和控制方法，涉及微机器人控制技术领域，方法包括：输入期望跟踪路径，通过摄像机获取磁性微机器人的当前位姿信息进而计算得到质心位置、实际轴线方向（X B）、期望跟踪路径上距离质心最近的期望位置点（s）坐标以及此点（s）的切线方向（X F）；根据实际轴线方向（X B）和切线方向（X F）以及扰动补偿计算出两点的水平距离（d z）、垂直距离（d y）、方向角误差（θ de）、俯仰角误差（θ ie）；根据设计的位置闭环控制器求得所需的旋转磁场，电流闭环磁场控制器根据旋转磁场和反馈的线圈输出电流闭环控制亥姆霍兹线圈（3）产生期望磁场，使磁性微机器人完成对期望跟踪路径的跟踪。采用位置和电流反馈的双闭环控制能够精准的完成对三维路径的跟踪。

Description

基于双闭环三维路径跟踪的微机器人磁驱装置和控制方法 技术领域
本发明涉及微纳机器人控制技术领域，尤其是基于双闭环三维路径跟踪的微机器人磁驱装置和控制方法。
背景技术
机器人的小型化为复杂和危险环境下的多种应用提供了解决方案，电磁驱动的磁性微机器人可以应用于医学环境，在不伤害人体的情况下磁性微机器人可以用于携带运输药物实现微创治疗。为了执行这样的任务磁性微机器人应该能实现对期望路径的跟踪。现有磁性微机器人的路径跟踪控制大多应用于平面范围，而且多采用单闭环路径跟踪即通过摄像机的视觉反馈获取磁性微机器在平面内的位姿信息建立位置闭环实现平面范围内的跟踪，然而这其中存在一定的响应延迟和适应性低的问题。一方面在高频环境下由于磁场发生装置的响应延迟问题，所使用的驱动装置往往不能及时准确的建立所需磁场造成响应速度慢。另一方面对复杂的人体环境我们更希望的是磁性微机器人能够完成对三维路径的跟踪，在平面路径跟踪控制领域上述方法可行，但应用于三维环境下的路径跟踪上述的控制方法便失去作用。
发明内容
本发明人针对上述问题及技术需求，提出了基于双闭环三维路径跟踪的微机器人磁驱装置和控制方法，实现对给定的三维期望跟踪路径准确及时的跟踪，克服在高频条件下磁驱装置响应速度慢的问题，采用位置反馈和电流反馈的双闭环控制提高了三维路径跟踪的准确性和快速性。
本发明的技术方案如下：
一种基于双闭环三维路径跟踪的微机器人磁驱装置，包括电磁线圈模组、直流电流源模组、PWM逆变电路、电流传感器、上位机、两个摄像头，电磁线圈模组包括六个带梯形探头的一级铁芯、设置在一级铁芯上的亥姆霍兹线圈以及线圈支架，每对带梯形探头的一级铁芯及其相应的亥姆霍兹线圈均平行设置，线圈支架用于固定三对带梯形探头的一级铁芯和三对亥姆霍兹线圈，三对 带梯形探头的一级铁芯沿轴线方向两两正交，三对亥姆霍兹线圈沿轴线方向两两正交，三对梯形探头内侧形成的区域作为磁性微机器人的工作空间，每个直流电流源通过PWM逆变电路后为一对或一个亥姆霍兹线圈提供交流电，上位机分别连接PWM逆变电路、电流传感器和摄像头，电流传感器用于检测亥姆霍兹线圈的输出电流，两个摄像头设置在线圈支架外侧并且正交分布，上位机发送控制信号到PWM逆变电路输出频率和幅值可调的交流电，亥姆霍兹线圈产生旋转磁场进而控制磁性微机器人沿着旋转磁场的轴线方向进行三维运动，摄像头获取磁性微机器人的位置信息并传送至上位机实现闭环控制磁性微机器人的三维运动。
其进一步的技术方案为，线圈支架包括上下相对设置的底座、支架和中空挡板，每个底座沿轴线方向上均设有三个三角斜块，轴向上的一对三角斜块的斜面平行设置且用于放置带梯形探头的一级铁芯，支架设置在底座之间起到支撑作用，中空挡板设置在支架的中部并与底座平行，中空挡板将底座围成的空间分成上层区域和下层区域，每对带梯形探头的一级铁芯及其相应的亥姆霍兹线圈中的一个设置在中空挡板上且位于上层区域、另一个位于下层区域，中空挡板的中空面积至少与磁性微机器人的工作空间面积相同。
其进一步的技术方案为，一级铁芯为DT4-E材料制成的圆柱铁芯，直径50mm、厚30mm，亥姆霍兹线圈的匝数为190，梯形探头的末端为边长35mm的正方形，前端为长16mm、宽2mm的矩形，工作空间为半径16mm的球形空间，磁性微机器人为螺旋形状。
基于双闭环三维路径跟踪的微机器人控制方法，控制方法包括：
在上位机中输入期望跟踪路径得到期望运动方向，摄像机获取磁性微机器人的当前位姿信息并反馈给上位机得到磁性微机器人的质心三维坐标和实际轴线方向；
在期望跟踪路径上寻找与质心距离最小的期望位置点，建立期望跟踪路径曲线坐标系获取期望位置点三维坐标、期望跟踪路径曲线的曲率和挠率；
将实际轴线方向与期望运动方向、质心三维坐标与期望位置点三维坐标分别进行处理得到方向误差和位置误差，方向误差包括俯仰角误差和方向角误差，位置误差包括两者的水平距离和垂直距离；
根据曲率、挠率、方向误差和位置误差对期望跟踪路径的三维运动学建模得到状态空间方程；
通过状态空间方程设计位置闭环控制器得到所需旋转磁场，将旋转磁场输入至建立的电流闭环磁场控制器输出期望磁场，实现对磁性微机器人的双闭环三维运动控制；
重新执行摄像机获取磁性微机器人的当前位姿信息并反馈给上位机得到磁性微机器人的质心三维坐标和实际轴线方向的步骤，直至完成整个期望跟踪路径的跟踪。
其进一步的技术方案为，摄像机获取磁性微机器人的当前位姿信息并反馈给上位机得到磁性微机器人的质心三维坐标和实际轴线方向，包括：
利用侧面摄像机和顶部摄像机对磁性微机器人的当前位姿信息进行检测，把顶部摄像机坐标系固定为世界坐标系，通过下式计算磁性微机器人在世界坐标系中的实际轴线方向：X B＝ cth t× cth s＝ cth t×( ctR cs csh s)
其中， cth t表示顶部摄像机平面的法向量， csh s表示侧面摄像机平面的法向量， cth s表示侧面摄像机平面的法向量到顶部摄像机平面的变换， ctR cs表示侧面摄像机坐标系到顶部摄像机坐标系的旋转矩阵，X B表示磁性微机器人在世界坐标系中的实际轴线方向；
通过下式计算磁性微机器人的质心在世界坐标系中的三维坐标：
G＝ ctR cs csG+ ctt cs
其中， csG表示质心在侧面摄像机平面的坐标， ctt cs表示侧面摄像机坐标系到顶部摄像机坐标系的平移矩阵，G表示质心在世界坐标系中的三维坐标。
其进一步的技术方案为，状态空间方程为：
Figure PCTCN2021104466-appb-000001
其中，s表示期望位置点三维坐标，v表示实际运动速度，θ de表示方向角误差，θ ie表示俯仰角误差，c表示曲率，τ表示挠率，d y表示垂直距离，d z表示水平距离，Ω y表示磁性微机器人在Y轴上的角速度分量，Ω z表示磁性微机器人在Z轴上的角速度分量，δ θi表示补偿俯仰角，δ θd表示补偿方向角。
其进一步的技术方案为，通过状态空间方程设计位置闭环控制器得到所需旋转磁场，包括：
根据链式法则和路径跟踪任务对状态空间方程做线性化处理得到位置闭环控制器的输入量为：
Figure PCTCN2021104466-appb-000002
其中，k d1、k t1、k d2、k t2为控制增益且为正；
路径跟踪任务为使方向角误差、俯仰角误差、垂直距离和水平距离收敛至零；
位置闭环控制器的输出量为：
Figure PCTCN2021104466-appb-000003
其中，γ 21、γ 22、γ 31、γ 32、γ 33的具体表达式为：
Figure PCTCN2021104466-appb-000004
通过下式计算所需旋转磁场为：
B ⊥＝B 0cos(2πft)y b+B 0sin(2πft)z b
B ||＝-sgn((B ⊥×Ω)X B)λ||(I 1-X BX B T)Ω||X B
B＝B ||+B ⊥
其中，B ⊥为垂直于轴线方向的磁场并用于为磁性微机器人提供自转，B ||为平行于轴线方向的磁场并用于为磁性微机器人提供转向，B 0是工作空间中心的磁通密度，f是旋转频率，t是旋转时间，y b、z b是垂直于磁性微机器人的实际轴线方向X B平面的基向量，λ是控制增益，Ω是位置闭环控制器的输出量，且Ω＝[Ω x Ω y Ω z]，I 1表示三阶单位矩阵。
其进一步的技术方案为，将旋转磁场输入至建立的电流闭环磁场控制器输出期望磁场，包括：
电流闭环磁场控制器对旋转磁场的方向和电流传感器反馈的线圈输出电流进行分析输出控制信号给PWM逆变电路，PWM逆变电路输出期望电流至亥姆霍兹线圈从而生成期望磁场；
Figure PCTCN2021104466-appb-000005
其中，B X、B Y、B Z为磁场B在三个轴向上的分量，n x、n y、n z为XOY、XOZ、YOZ三个平面的单位方向量；
将磁场分解到X、Y、Z三轴，则各轴之间的磁场与电流的映射关系如下式：
Figure PCTCN2021104466-appb-000006
其中，μ 0为磁场介电常数，N表示亥姆霍兹线圈的匝数，a表示亥姆霍兹线圈的半径，I表示通入线圈的期望电流。
其进一步的技术方案为，在无扰动状况下磁性微机器人的期望运动方向为其轴线方向，期望运动方向由第一方向角和第一俯仰角表示，第一方向角为向量v p到XOY平面的投影与x轴的夹角，第一俯仰角为向量v p与XOY平面的夹角，由于受到重力及扰动的作用磁性微机器人的实际轴线方向由第二方向角和第二俯仰角表示，则对运行的磁性微机器人进行方向补偿，得到实际轴线方向与期望运动方向的对应关系为：θ d1＝θ d-δ θd；θ i1＝θ i-δ θi
其中，θ d1为第二方向角，θ d为第一方向角，δ θd为横向平面的补偿方向角，横向平面为XOY平面，θ i1为第二俯仰角，θ i为第一俯仰角，δ θi为垂直平面的补偿俯仰角，垂直平面为与XOY平面垂直的面；
则方向角误差为：θ de＝θ d1-θ dc，其中，θ dc为期望方向角；
俯仰角误差为：θ ie＝θ i-δ θi-θ ic，其中，θ ic为期望俯仰角；
运行的磁性微机器人的实际运动速度为：
Figure PCTCN2021104466-appb-000007
其中，v p为期望运动速度，v为实际运动速度。
其进一步的技术方案为，期望跟踪路径曲线坐标系是以期望位置点为原点、期望位置点的切线方向、主法线方向、次法线方向为坐标轴建立得到的，切线 方向为期望运动方向，利用下述公式获取磁性微机器人的实际轴线方向与第一方向角、第一俯仰角之间的转换关系为：
Figure PCTCN2021104466-appb-000008
本发明的有益技术效果是：
本申请提供的磁驱装置能够产生旋转磁场，实现了磁性微机器人在三维空间任意方向的控制，摄像机和集成在上位机中的位置闭环控制器、电流闭环磁场控制器配合实时监测和控制磁性微机器人的运动，PWM逆变电路能够缩短期望磁场的建立时间且使期望磁场更加稳定，上位机能快速给出期望位置点坐标以及磁性微机器人的运行轨迹信息；电流闭环磁场控制器、PWM逆变电路、亥姆霍兹线圈和电流传感器形成第一重闭环控制，在第一重闭环控制中，电流闭环磁场控制器对旋转磁场的方向和电流传感器反馈的输出电流进行分析输出控制信号给PWM逆变电路，PWM逆变电路输出期望电流至亥姆霍兹线圈从而生成期望磁场，位置闭环控制器、电流闭环磁场控制器、PWM逆变电路、亥姆霍兹线圈、磁性微机器人和摄像机形成第二重闭环控制，在第二重闭环控制中，根据摄像机反馈的位姿信息计算与期望运动路径的误差来设计位置闭环控制器得到所需旋转磁场，通过双闭环控制方法实现了磁性微机器人在三维环境下的准确、快速的路径跟踪。
附图说明
图1是本申请提供的磁驱装置原理图。
图2是本申请提供的电磁线圈模组整体装配正视图。
图3是本申请提供的去掉一个底座和支架的电磁线圈模组装配图。
图4是本申请提供的带三角斜块的底座示意图。
图5是本申请提供梯形探头、一级铁芯和二级铁芯的组合三视图。
图6是本申请提供的控制方法流程图。
图7是本申请提供的磁性微机器人在三维空间下运动的角度补偿示意图。
图8是本申请提供的获取磁性微机器人质心三维坐标和实际轴线方向的原理示意图。
图9是本申请提供的磁性微机器人在跟踪路径曲线坐标系下的期望跟踪路径模型图。
图10是本申请提供的第一重闭环控制的部分电路图。
具体实施方式
下面结合附图对本发明的具体实施方式做进一步说明。
本申请公开了一种基于双闭环三维路径跟踪的微机器人磁驱装置，图1示出了磁驱装置的原理图，磁驱装置包括电磁线圈模组、直流电流源模组、PWM逆变电路、电流传感器、上位机、两个摄像头。PWM逆变电路能够缩短期望磁场的建立时间且使期望磁场更加稳定，上位机能快速给出期望位置点坐标以及磁性微机器人的运行轨迹信息。结合图2-图4所示，电磁线圈模组包括六个带梯形探头1的一级铁芯2、设置在一级铁芯2上的亥姆霍兹线圈3以及线圈支架，每对带梯形探头1的一级铁芯2及其相应的亥姆霍兹线圈3均平行设置，线圈支架用于固定三对带梯形探头1的一级铁芯2和三对亥姆霍兹线圈3，具体的，线圈支架包括上下相对设置的底座401、支架402和中空挡板403，每个底座401沿轴线方向上均设有三个三角斜块404，轴向上的一对三角斜块404的斜面平行设置且用于放置带梯形探头1的一级铁芯2，支架402设置在底座401之间起到支撑作用，中空挡板403设置在支架402的中部并与底座401平行，中空挡板403将底座401围成的空间分成上层区域和下层区域，每对带梯形探头1的一级铁芯2及其相应的亥姆霍兹线圈3中的一个设置在中空挡板403上且位于上层区域、另一个位于下层区域。
三对带梯形探头1的一级铁芯2沿轴线方向两两正交，三对亥姆霍兹线圈3沿轴线方向两两正交，三对梯形探头1内侧形成的区域作为磁性微机器人的工作空间，中空挡板403的中空面积至少与磁性微机器人的工作空间面积相同。每个直流电流源通过PWM逆变电路后为一对或一个亥姆霍兹线圈3提供交流电，也即本申请的直流电流源至少为六个，至多为十二个。上位机分别连接PWM逆变电路、电流传感器和摄像头，电流传感器用于检测亥姆霍兹线圈3的输出电流，两个摄像头设置在线圈支架402外侧并且正交分布，上位机发送控制信号到PWM逆变电路输出频率和幅值可调的交流电，亥姆霍兹线圈3产生旋转磁场进而控制磁性微机器人沿着旋转磁场的轴线方向进行三维运动，摄像头获取磁性微机器人的位置信息并传送至上位机实现闭环控制磁性微机器人的三维运动。
可选的，电磁线圈模组还包括六个二级铁芯5以及围绕其设置的梯形线圈6，二级铁芯5设置在未设有梯形探头1的一级铁芯2的一侧上，同理，每对二级铁芯5平行设置且放置在三角斜块404上，三对二级铁芯5沿轴线方向两两 正交，三对梯形线圈6沿轴线方向两两正交，梯形探头1、一级铁芯2和二级铁芯5呈阶梯状排列。
可选的，如图5所示，图5(a)为探头和铁芯组合的正视图，图5(b)为探头和铁芯组合的侧视图，图5(c)为探头和铁芯组合的俯视图。一级铁芯2和二级铁芯5均为DT4-E材料制成的圆柱铁芯，一级铁芯2的直径50mm、厚30mm，亥姆霍兹线圈3的匝数为190，二级铁芯5的直径70mm、厚35mm，梯形线圈6的匝数为610，对应的两个线圈串联通电，梯形探头1的末端为边长35mm的正方形，前端为长16mm、宽2mm的矩形。
可选的，根据上述带梯形探头1的一级铁芯2围成的工作空间为半径16mm的球形空间，磁性微机器人如图7所示为螺旋形状。
本申请还公开了一种基于双闭环三维路径跟踪的微机器人控制方法，能够应用在上述的磁驱装置中，该控制方法的流程图如图6所示，包括如下步骤：
步骤1：在上位机中输入期望跟踪路径得到期望运动方向，摄像机获取磁性微机器人的当前位姿信息并反馈给上位机得到磁性微机器人的质心三维坐标和实际轴线方向。
如图7所示，在无扰动状况下磁性微机器人的期望运动方向为其轴线方向，期望运动方向由第一方向角和第一俯仰角表示，第一方向角为向量v p到XOY平面的投影与x轴的夹角，第一俯仰角为向量v p与XOY平面的夹角。由于受到重力及扰动的作用磁性微机器人的实际轴线方向由第二方向角和第二俯仰角表示，则对运行的磁性微机器人进行方向补偿，得到实际轴线方向与期望运动方向的对应关系为：θ d1＝θ d-δ θd；θ i1＝θ i-δ θi
其中，θ d1为第二方向角，θ d为第一方向角，δ θd为横向平面的补偿方向角，横向平面为XOY平面，θ i1为第二俯仰角，θ i为第一俯仰角，δ θi为垂直平面的补偿俯仰角，垂直平面为与XOY平面垂直的面。
运行的磁性微机器人的实际运动速度为：
Figure PCTCN2021104466-appb-000009
其中，v p为期望运动速度，v为实际运动速度。
摄像机获取磁性微机器人的当前位姿信息并反馈给上位机得到磁性微机器人的质心三维坐标和实际轴线方向，如图8所示，包括：
利用侧面摄像机和顶部摄像机对磁性微机器人的当前位姿信息进行检测，把顶部摄像机坐标系固定为世界坐标系，通过下式计算磁性微机器人在世界坐 标系中的实际轴线方向：X B＝ cth t× cth s＝ cth t×( ctR cs csh s)
其中， cth t表示顶部摄像机平面701的法向量， csh s表示侧面摄像机平面702的法向量， cth s表示侧面摄像机平面702的法向量到顶部摄像机平面701的变换， ctR cs表示侧面摄像机坐标系到顶部摄像机坐标系的旋转矩阵，X B表示磁性微机器人在世界坐标系中的实际轴线方向。
通过下式计算磁性微机器人的质心在世界坐标系中的三维坐标：
G＝ ctR cs csG+ ctt cs
其中， csG表示质心在侧面摄像机平面702的坐标， ctt cs表示侧面摄像机坐标系到顶部摄像机坐标系的平移矩阵，G表示质心在世界坐标系中的三维坐标。
步骤2：在期望跟踪路径上寻找与质心距离最小的期望位置点，建立期望跟踪路径曲线坐标系获取期望位置点三维坐标、期望跟踪路径曲线的曲率和挠率。
如图9所示，期望跟踪路径曲线坐标系是以期望位置点s为原点、期望位置点的切线方向X F、主法线方向Y F、次法线方向Z F为坐标轴建立SF坐标系得到的，切线方向X F为期望运动方向，利用下述公式获取磁性微机器人的实际轴线方向与第一方向角、第一俯仰角之间的转换关系为：
Figure PCTCN2021104466-appb-000010
步骤3：将实际轴线方向与期望运动方向、质心三维坐标与期望位置点三维坐标分别进行处理得到方向误差和位置误差，方向误差包括俯仰角误差和方向角误差，位置误差包括两者的水平距离和垂直距离。
则方向角误差为：θ de＝θ d1-θ dc，其中，θ dc为期望方向角。
俯仰角误差为：θ ie＝θ i-δ θi-θ ic，其中，θ ic为期望俯仰角。
水平距离d z和垂直距离d y为期望位置点三维坐标与质心三维坐标的欧式距离。
步骤4：根据曲率、挠率、方向误差和位置误差对期望跟踪路径的三维运动学建模得到状态空间方程。
则状态空间方程为：
Figure PCTCN2021104466-appb-000011
其中，s表示期望位置点三维坐标，v表示实际运动速度，θ de表示方向角误差，θ ie表示俯仰角误差，c表示曲率，τ表示挠率，d y表示垂直距离，d z表示水平距离，Ω y表示磁性微机器人在Y轴上的角速度分量，Ω z表示磁性微机器人在Z轴上的角速度分量，δ θi表示补偿俯仰角，δ θd表示补偿方向角。
步骤5：通过状态空间方程设计位置闭环控制器得到所需旋转磁场，将旋转磁场输入至建立的电流闭环磁场控制器输出期望磁场，实现对磁性微机器人的双闭环三维运动控制。
根据链式法则和路径跟踪任务对状态空间方程做线性化处理得到位置闭环控制器的输入量为：
Figure PCTCN2021104466-appb-000012
其中，k d1、k t1、k d2、k t2为控制增益且为正。
路径跟踪任务为使所述方向角误差、俯仰角误差、垂直距离和水平距离收敛至零。
位置闭环控制器的输出量为：
Figure PCTCN2021104466-appb-000013
其中，γ 21、γ 22、γ 31、γ 32、γ 33的具体表达式为：
Figure PCTCN2021104466-appb-000014
通过下式计算所需旋转磁场为：
B ⊥＝B 0cos(2πft)y b+B 0sin(2πft)z b
B ||＝-sgn((B ⊥×Ω)X B)λ||(I 1-X BX B T)Ω||X B
B＝B ||+B ⊥
其中，B ⊥为垂直于轴线方向的磁场并用于为磁性微机器人提供自转，B ||为平行于轴线方向的磁场并用于为磁性微机器人提供转向，B 0是工作空间中心的磁通密度，f是旋转频率，t是旋转时间，y b、z b是垂直于磁性微机器人的实际轴线方向X B平面的基向量，λ是控制增益，Ω是位置闭环控制器的输出量，且Ω＝[Ω x Ω y Ω z]，I 1表示三阶单位矩阵。
图10示出了第一重闭环控制的部分电路图，电流闭环磁场控制器对旋转磁场的方向和电流传感器反馈的线圈输出电流进行分析输出PWM控制信号给PWM逆变电路，PWM逆变电路输出期望电流至亥姆霍兹线圈3从而生成期望磁场。
Figure PCTCN2021104466-appb-000015
其中，B X、B Y、B Z为磁场B在三个轴向上的分量，n x、n y、n z为XOY、XOZ、YOZ三个平面的单位方向量。
将磁场分解到X、Y、Z三轴，则各轴之间的磁场与电流的映射关系如下式：
Figure PCTCN2021104466-appb-000016
其中，μ 0为磁场介电常数，N表示亥姆霍兹线圈3的匝数，a表示亥姆霍兹线圈3的半径，I表示通入线圈的期望电流。
步骤6：重新执行摄像机获取磁性微机器人的当前位姿信息并反馈给上位机得到磁性微机器人的质心三维坐标和实际轴线方向的步骤，直至完成整个期 望跟踪路径的跟踪。
在本申请中，在上位机中设计电流闭环磁场控制器和位置闭环控制器，电流闭环磁场控制器、PWM逆变电路、亥姆霍兹线圈和电流传感器形成第一重闭环控制，在第一重闭环控制中，电流闭环磁场控制器输出控制信号给PWM逆变电路，PWM逆变电路输出期望电流至亥姆霍兹线圈从而生成期望磁场；位置闭环控制器、电流闭环磁场控制器、PWM逆变电路、亥姆霍兹线圈、磁性微机器人和摄像机形成第二重闭环控制，在第二重闭环控制中，根据摄像机反馈的位姿信息计算与期望运动路径的误差来设计位置闭环控制器得到所需旋转磁场，通过双闭环控制方法实现了磁性微机器人在三维环境下的准确、快速的路径跟踪。
以上所述的仅是本申请的优选实施方式，本发明不限于以上实施例。可以理解，本领域技术人员在不脱离本发明的精神和构思的前提下直接导出或联想到的其他改进和变化，均应认为包含在本发明的保护范围之内。

Claims (10)

  1. 基于双闭环三维路径跟踪的微机器人磁驱装置，其特征在于，所述磁驱装置包括电磁线圈模组、直流电流源模组、PWM逆变电路、电流传感器、上位机、两个摄像头，所述电磁线圈模组包括六个带梯形探头的一级铁芯、设置在所述一级铁芯上的亥姆霍兹线圈以及线圈支架，每对带梯形探头的一级铁芯及其相应的亥姆霍兹线圈均平行设置，所述线圈支架用于固定三对带梯形探头的一级铁芯和三对亥姆霍兹线圈，所述三对带梯形探头的一级铁芯沿轴线方向两两正交，所述三对亥姆霍兹线圈沿轴线方向两两正交，三对梯形探头内侧形成的区域作为磁性微机器人的工作空间，每个直流电流源通过所述PWM逆变电路后为一对或一个所述亥姆霍兹线圈提供交流电，所述上位机分别连接所述PWM逆变电路、电流传感器和摄像头，所述电流传感器用于检测所述亥姆霍兹线圈的输出电流，两个所述摄像头设置在所述线圈支架外侧并且正交分布，所述上位机发送控制信号到所述PWM逆变电路输出频率和幅值可调的交流电，所述亥姆霍兹线圈产生旋转磁场进而控制所述磁性微机器人沿着所述旋转磁场的轴线方向进行三维运动，所述摄像头获取所述磁性微机器人的位置信息并传送至所述上位机实现闭环控制所述磁性微机器人的三维运动。
  2. 根据权利要求1所述的基于双闭环三维路径跟踪的微机器人磁驱装置，其特征在于，所述线圈支架包括上下相对设置的底座、支架和中空挡板，每个所述底座沿轴线方向上均设有三个三角斜块，轴向上的一对所述三角斜块的斜面平行设置且用于放置所述带梯形探头的一级铁芯，所述支架设置在所述底座之间起到支撑作用，所述中空挡板设置在所述支架的中部并与所述底座平行，所述中空挡板将所述底座围成的空间分成上层区域和下层区域，每对所述带梯形探头的一级铁芯及其相应的亥姆霍兹线圈中的一个设置在所述中空挡板上且位于所述上层区域、另一个位于所述下层区域，所述中空挡板的中空面积至少与所述磁性微机器人的工作空间面积相同。
  3. 根据权利要求1或2所述的基于双闭环三维路径跟踪的微机器人磁驱装置，其特征在于，所述一级铁芯为DT4-E材料制成的圆柱铁芯，直径50mm、厚30mm，所述亥姆霍兹线圈的匝数为190，所述梯形探头的末端为边长35mm的正方形，前端为长16mm、宽2mm的矩形，所述工作空间为半径16mm的球 形空间，所述磁性微机器人为螺旋形状。
  4. 基于双闭环三维路径跟踪的微机器人控制方法，其特征在于，应用于如权利要求1-3任一所述的磁驱装置，所述控制方法包括：
    在所述上位机中输入期望跟踪路径得到期望运动方向，所述摄像机获取所述磁性微机器人的当前位姿信息并反馈给所述上位机得到所述磁性微机器人的质心三维坐标和实际轴线方向；
    在所述期望跟踪路径上寻找与质心距离最小的期望位置点，建立期望跟踪路径曲线坐标系获取所述期望位置点三维坐标、期望跟踪路径曲线的曲率和挠率；
    将所述实际轴线方向与所述期望运动方向、所述质心三维坐标与所述期望位置点三维坐标分别进行处理得到方向误差和位置误差，所述方向误差包括俯仰角误差和方向角误差，所述位置误差包括两者的水平距离和垂直距离；
    根据所述曲率、挠率、方向误差和位置误差对所述期望跟踪路径的三维运动学建模得到状态空间方程；
    通过所述状态空间方程设计位置闭环控制器得到所需旋转磁场，将所述旋转磁场输入至建立的电流闭环磁场控制器输出期望磁场，实现对所述磁性微机器人的双闭环三维运动控制；
    重新执行所述摄像机获取所述磁性微机器人的当前位姿信息并反馈给所述上位机得到所述磁性微机器人的质心三维坐标和实际轴线方向的步骤，直至完成整个所述期望跟踪路径的跟踪。
  5. 根据权利要求4所述的基于双闭环三维路径跟踪的微机器人控制方法，其特征在于，所述摄像机获取所述磁性微机器人的当前位姿信息并反馈给所述上位机得到所述磁性微机器人的质心三维坐标和实际轴线方向，包括：
    利用侧面摄像机和顶部摄像机对所述磁性微机器人的当前位姿信息进行检测，把顶部摄像机坐标系固定为世界坐标系，通过下式计算所述磁性微机器人在所述世界坐标系中的实际轴线方向：X B＝ cth t× cth s＝ cth t×( ctR cs csh s)
    其中， cth t表示顶部摄像机平面的法向量， csh s表示侧面摄像机平面的法向量， cth s表示所述侧面摄像机平面的法向量到所述顶部摄像机平面的变换， ctR cs表示侧面摄像机坐标系到顶部摄像机坐标系的旋转矩阵，X B表示所述磁性微机器人在所述世界坐标系中的实际轴线方向；
    通过下式计算所述磁性微机器人的质心在所述世界坐标系中的三维坐标：
    G＝ ctR cs csG+ ctt cs
    其中， csG表示质心在所述侧面摄像机平面的坐标， ctt cs表示侧面摄像机坐标系到顶部摄像机坐标系的平移矩阵，G表示质心在所述世界坐标系中的三维坐标。
  6. 根据权利要求4所述的基于双闭环三维路径跟踪的微机器人控制方法，其特征在于，所述状态空间方程为：
    Figure PCTCN2021104466-appb-100001
    其中，s表示所述期望位置点三维坐标，v表示实际运动速度，θ de表示所述方向角误差，θ ie表示所述俯仰角误差，c表示所述曲率，τ表示所述挠率，d y表示所述垂直距离，d z表示所述水平距离，Ω y表示所述磁性微机器人在Y轴上的角速度分量，Ω z表示所述磁性微机器人在Z轴上的角速度分量，δ θi表示补偿俯仰角，δ θd表示补偿方向角。
  7. 根据权利要求6所述的基于双闭环三维路径跟踪的微机器人控制方法，其特征在于，所述通过所述状态空间方程设计位置闭环控制器得到所需旋转磁场，包括：
    根据链式法则和路径跟踪任务对所述状态空间方程做线性化处理得到所述位置闭环控制器的输入量为：
    Figure PCTCN2021104466-appb-100002
    其中，k d1、k t1、k d2、k t2为控制增益且为正；
    所述路径跟踪任务为使所述方向角误差、俯仰角误差、垂直距离和水平距离收敛至零；
    所述位置闭环控制器的输出量为：
    Figure PCTCN2021104466-appb-100003
    其中，γ 21、γ 22、γ 31、γ 32、γ 33的具体表达式为：
    Figure PCTCN2021104466-appb-100004
    通过下式计算所述所需旋转磁场为：
    B ⊥＝B 0cos(2πft)y b+B 0sin(2πft)z b
    B ||＝-sgn((B ⊥×Ω)X B)λ||(I 1-X BX B T)Ω||X B
    B＝B ||+B ⊥
    其中，B ⊥为垂直于轴线方向的磁场并用于为所述磁性微机器人提供自转，B ||为平行于轴线方向的磁场并用于为所述磁性微机器人提供转向，B 0是工作空间中心的磁通密度，f是旋转频率，t是旋转时间，y b、z b是垂直于所述磁性微机器人的实际轴线方向X B平面的基向量，λ是控制增益，Ω是所述位置闭环控制器的输出量，且Ω＝[Ω x Ω y Ω z]，I 1表示三阶单位矩阵。
  8. 根据权利要求7所述的基于双闭环三维路径跟踪的微机器人控制方法，其特征在于，所述将所述旋转磁场输入至建立的电流闭环磁场控制器输出期望磁场，包括：
    所述电流闭环磁场控制器对所述旋转磁场的方向和所述电流传感器反馈的线圈输出电流进行分析输出所述控制信号给所述PWM逆变电路，所述PWM逆变电路输出期望电流至所述亥姆霍兹线圈从而生成所述期望磁场；
    Figure PCTCN2021104466-appb-100005
    其中，B X、B Y、B Z为磁场B在三个轴向上的分量，n x、n y、n z为XOY、XOZ、YOZ三个平面的单位方向量；
    将磁场分解到X、Y、Z三轴，则各轴之间的磁场与电流的映射关系如下 式：
    Figure PCTCN2021104466-appb-100006
    其中，μ 0为磁场介电常数，N表示亥姆霍兹线圈的匝数，a表示亥姆霍兹线圈的半径，I表示通入线圈的期望电流。
  9. 根据权利要求6或7所述的基于双闭环三维路径跟踪的微机器人控制方法，其特征在于，在无扰动状况下所述磁性微机器人的期望运动方向为其轴线方向，所述期望运动方向由第一方向角和第一俯仰角表示，所述第一方向角为向量v p到XOY平面的投影与x轴的夹角，所述第一俯仰角为向量v p与XOY平面的夹角，由于受到重力及扰动的作用所述磁性微机器人的实际轴线方向由第二方向角和第二俯仰角表示，则对运行的所述磁性微机器人进行方向补偿，得到所述实际轴线方向与期望运动方向的对应关系为：θ d1＝θ d-δ θd；θ i1＝θ i-δ θi
    其中，θ d1为所述第二方向角，θ d为所述第一方向角，δ θd为横向平面的所述补偿方向角，所述横向平面为XOY平面，θ i1为所述第二俯仰角，θ i为所述第一俯仰角，δ θi为垂直平面的补偿俯仰角，所述垂直平面为与所述XOY平面垂直的面；
    则所述方向角误差为：θ de＝θ d1-θ dc，其中，θ dc为期望方向角；
    所述俯仰角误差为：θ ie＝θ i-δ θi-θ ic，其中，θ ic为期望俯仰角；
    运行的所述磁性微机器人的实际运动速度为：
    Figure PCTCN2021104466-appb-100007
    其中，v p为期望运动速度，v为实际运动速度。
  10. 根据权利要求5所述的基于双闭环三维路径跟踪的微机器人控制方法，其特征在于，所述期望跟踪路径曲线坐标系是以所述期望位置点为原点、所述期望位置点的切线方向、主法线方向、次法线方向为坐标轴建立得到的，所述切线方向为所述期望运动方向，利用下述公式获取所述磁性微机器人的实际轴线方向与第一方向角、第一俯仰角之间的转换关系为：
    Figure PCTCN2021104466-appb-100008
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