CN116852363A - Method for controlling pose of tail end of continuum mechanical arm, computer equipment and readable storage medium - Google Patents

Method for controlling pose of tail end of continuum mechanical arm, computer equipment and readable storage medium Download PDF

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Publication number
CN116852363A
CN116852363A CN202310871299.7A CN202310871299A CN116852363A CN 116852363 A CN116852363 A CN 116852363A CN 202310871299 A CN202310871299 A CN 202310871299A CN 116852363 A CN116852363 A CN 116852363A
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pose
mechanical arm
continuum
end effector
matrix
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齐鹏
刘文杰
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Tongji University
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Tongji University
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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
    • B25J9/16—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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

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  • Engineering & Computer Science (AREA)
  • Robotics (AREA)
  • Mechanical Engineering (AREA)
  • Automation & Control Theory (AREA)
  • Physics & Mathematics (AREA)
  • Artificial Intelligence (AREA)
  • Evolutionary Computation (AREA)
  • Fuzzy Systems (AREA)
  • Mathematical Physics (AREA)
  • Software Systems (AREA)
  • Numerical Control (AREA)

Abstract

The invention discloses a method for controlling the pose of the tail end of a continuum mechanical arm, which comprises the following steps: calculating a pose error between a current pose matrix and a target pose matrix of the continuous body mechanical arm end effector; judging whether the pose error meets the preset condition, if not, acquiring pose correction parameters of the end effector according to the pose error, acquiring an updated control law function according to the pose correction parameters, a preset target control function and a speed jacobian matrix of the end effector, inputting the pose error into the updated control law function to obtain joint driving increment of the end effector of the continuous mechanical arm, and driving the continuous mechanical arm to displace by utilizing the joint driving increment; then updating the current joint quantity and the velocity jacobian matrix through joint driving increment, further obtaining the current pose matrix of the end effector of the continuum mechanical arm, and returning to the step of calculating pose errors; the method realizes the accurate control of the pose of the tail end of the continuum mechanical arm.

Description

Method for controlling pose of tail end of continuum mechanical arm, computer equipment and readable storage medium
Technical Field
The invention relates to the technical field of medical surgical robots, in particular to a method for controlling the pose of the tail end of a continuum mechanical arm, computer equipment and a readable storage medium.
Background
In recent years, robots have affected human life in many ways. The manufacturing industry is shaved, and robots have also entered the application fields of agriculture, aerospace, and the like. Robots have been increasingly stepping into the medical field over the last decade, frequently found in operating rooms around the world, and used to assist or complete a variety of minimally invasive surgical procedures. It can reduce postoperative discomfort and hospitalization time of patients. Robotics brings precision, speed and stability to the surgical procedure.
In order to improve the flexibility of the mechanical arm in the minimally invasive surgery, researchers propose a novel medical mechanical arm, namely a continuous body surgery mechanical arm. The continuum robot arm has a radically different structure than a conventional robot arm consisting of articulating discrete rigid links. The continuum manipulator consists of a continuum torso with its degree of freedom increasing with the number of consecutive segments of itself. Therefore, the continuum manipulator can have higher degrees of freedom, and each segment of continuum manipulator can be driven by a driver to generate bending changes so as to change the position and the posture of the end effector.
In order to meet the requirements of minimally invasive surgery, the pose control of the continuum manipulator end effector must meet the accuracy requirements. Nowadays, the continuum robot arm mostly adopts a constant curvature kinematic model, namely, each segment of continuum robot arm bending variation is assumed to be a standard bending circular arc. For control of a single segment continuum arm, we can control its end position by directly solving for its inverse kinematics' position resolution.
However, for the control of a two-stage continuum arm with multiple degrees of freedom (e.g., 6 degrees of freedom), we cannot directly solve for the inverse solution of the end pose control due to the positive kinematic nonlinearity. The original analysis solution of inverse kinematics can be obtained based on the jacobian iteration method and the newton-Lawson iteration method, but the methods involve a large amount of mathematical operations and have the defects of high iteration times, difficult convergence, no solution and the like. In addition, in order to solve the problems, some researchers start from a mechanical structure, optimize the structure of a multi-section continuous body arm, and realize the end pose separation of the continuous body mechanical arm by adding an intermediate continuous body section. The inverse solution of the terminal pose of the multi-section continuum arm is solved by a quaternion interpolation method, but the control effect cannot be well achieved.
Disclosure of Invention
In order to solve the problem of motion control of the tail end pose of a continuous mechanical arm, the invention discloses a method for controlling the tail end pose of the continuous mechanical arm, which aims to solve the problem that the two-stage continuous mechanical arm with multiple degrees of freedom in the prior art cannot always obtain pose motion analysis solution through inverse kinematics due to nonlinear factors in control, so that the required control precision cannot be achieved.
The utility model provides a continuum arm terminal position appearance control method, continuum arm includes two sections continuum arms and a rigid straight-bar, control method includes:
step S1, calculating a pose error between a current pose matrix of the continuous body mechanical arm end effector and an input target pose matrix of the continuous body mechanical arm end effector;
step S2, judging whether the pose error meets a preset condition, if so, inputting a target pose matrix of a target pose control point of the end effector of the next continuum mechanical arm as the target pose matrix of the end effector of the continuum mechanical arm, returning to the step S1, and if not, continuing to carry out the step S3;
step S3, acquiring pose correction parameters of the end effector of the continuous mechanical arm according to the pose errors, and obtaining an updated control law function according to the pose correction parameters, a preset target control function and a velocity jacobian matrix of the end effector of the continuous mechanical arm, wherein the target control function is used for restraining the minimum difference between the current pose and the target pose of the end effector;
s4, inputting the pose error into the updated control law function to obtain a joint driving increment of the end effector of the continuous mechanical arm, and driving the continuous mechanical arm to displace by using the joint driving increment;
and S5, updating the current joint quantity of the end effector of the continuous mechanical arm and the velocity jacobian matrix of the end effector of the continuous mechanical arm through joint driving increment, further obtaining the current pose matrix of the end effector of the continuous mechanical arm, and returning to the step S1.
In some of these embodiments, before performing the step S1, the control method further includes:
and establishing a base coordinate system and a local coordinate system on the continuum mechanical arm to obtain an end effector pose matrix when the continuum mechanical arm is bent.
In some of these embodiments, the step of establishing the base coordinate system and the local coordinate system on the continuum robot arm is specifically:
a base coordinate system is established at the base of the continuum manipulator, and a local coordinate system is established at the end of the rigid straight rod and the end face of the end of each segment of continuum manipulator.
In some embodiments, a velocity jacobian matrix of the continuum manipulator end effector is derived from the end effector pose matrix when the continuum manipulator is bent to obtain a mapping relationship of the end pose change velocity and the joint change velocity of the continuum manipulator.
In some embodiments, determining whether the pose error meets a preset condition specifically includes:
judging whether the two norm values of the position error vector of the end effector of the continuum manipulator are smaller than a first preset value or not;
judging whether the two norms of the attitude error vector of the end effector of the continuum mechanical arm are smaller than a second preset value.
In some of these embodiments, the continuum robot is a two-stage continuum robot having 6 degrees of freedom.
In some of these embodiments, the method further comprises the step of performing simulation experiment verification of the control method.
In some of these embodiments, the control method is validated in a software matlab by simulation experiments.
In another aspect, the present invention also discloses a computer device, including:
at least one processor; the method comprises the steps of,
a memory communicatively coupled to the at least one processor; wherein,,
the memory stores computer readable instructions, and the processor implements the method for controlling the pose of the end of the continuum manipulator when executing the computer readable instructions.
In still another aspect, the invention further discloses a computer readable storage medium, on which computer readable instructions are stored, the computer readable instructions implementing the above-mentioned method for controlling the pose of the end of the continuum manipulator when executed by a processor.
Compared with the prior art, the invention has at least one of the following advantages or beneficial effects:
the invention provides a method for controlling the tail end pose of a continuum mechanical arm, which can obtain a motion analysis solution more quickly and realize tail end pose control and track tracking tasks; according to the control method, the actual iteration times can be greatly reduced by setting the self-adaptive pose correction parameters, and meanwhile, the iteration times are kept uniform each time, so that the pose of the tail end of the continuous mechanical arm converges more quickly, and the parameter calculation is more stable; therefore, the problem of controlling the terminal pose of the multi-degree-of-freedom continuum mechanical arm can be well solved, and a good control strategy is provided for the multi-section continuum mechanical arm in the control field.
Drawings
The invention and its features, aspects and advantages will become more apparent from the detailed description of non-limiting embodiments with reference to the following drawings. Like numbers refer to like parts throughout. The drawings may not be to scale, emphasis instead being placed upon illustrating the principles of the invention.
FIG. 1 is a flow chart of a method for controlling the pose of the tail end of a continuum manipulator in an embodiment of the invention;
FIG. 2 is a diagram illustrating an overall configuration of a continuum robot in an embodiment of the present invention;
FIG. 3 is a schematic diagram of motion analysis of a single segment continuum arm in an embodiment of the invention;
FIG. 4 is a diagram showing the verification of the simulation result of the position tracking control error in the simulation experiment of the present invention;
fig. 5 is a verification chart of simulation experiment results of an attitude tracking control error in a simulation experiment of the present invention.
Detailed Description
The invention will now be further described with reference to the accompanying drawings and specific examples, which are not intended to limit the invention.
As shown in FIG. 1, the invention discloses a method for controlling the terminal pose of a continuous mechanical arm, wherein the main body of the continuous mechanical arm consists of two sections of continuous mechanical arms and a rigid straight bar which cannot be bent, and the total number of degrees of freedom is 6, including linear propulsion, integral torsion, proximal bending and distal bending of the continuous mechanical arm; specifically, the control method comprises the following steps:
step S1, calculating the pose error between the current pose matrix of the continuous body mechanical arm end effector and the input target pose matrix of the continuous body mechanical arm end effector.
In an embodiment of the present invention, before performing the step S1, the control method further includes: and establishing a base coordinate system at the base of the continuous mechanical arm, establishing a local coordinate system at the tail end of the rigid straight rod and the tail end face of each section of continuous mechanical arm to obtain an end effector pose matrix when the continuous mechanical arm is bent, and deducing a velocity jacobian matrix of the end effector of the continuous mechanical arm according to the end effector pose matrix when the continuous mechanical arm is bent to obtain a mapping relation of the change velocity of the end pose of the continuous mechanical arm and the change velocity of the joint.
Specifically, first, fig. 2 shows the basic structure and basic movement of the continuum robot arm in the present method. Fig. 3 depicts the joint configuration when a single segment continuum arm is flexed. Let the length of the single segment continuum arm be L, with 2 degrees of freedom. The coordinate system and joint variables are shown in fig. 3. In the figure, a base coordinate system O, Z is established at the base of the continuum manipulator o The direction is the axial direction of the continuous body arm, X o To point to the direction of the first driving line, Y o The direction satisfies the right rule. A coordinate system e is established on the end face of the end of the single-section continuous body arm, and when no bending change occurs, the coordinate systems O and e are parallel. When the continuum manipulator is flexed,it can be assumed that its curvature is in the form of an ideal circular arc, i.e. its curvature plane and X o Z o Plane surface isThe angle, the bending angle is theta angle. The relationship between the base coordinate system O to the terminal end face coordinate system l when bent can be converted by the following changes, specifically:
the base coordinate system O rotates around the Z axisThe angle is used for obtaining a coordinate system m;
the coordinate system m is translated along the z axis and the x axis successively, rsin theta and R (1-cos theta) are translated, and then the coordinate system n is obtained by rotating the coordinate system m around the y axis of the coordinate system m by theta angles;
the coordinate system n rotates about its own z-axisThe angle, the terminal face coordinate system l is obtained.
From this, the pose conversion matrix of the terminal end face coordinate system I relative to the base coordinate system O can be obtainedThe linear velocity and the angular velocity of the terminal end face coordinate system I relative to the base coordinate system O are +.>，/>The jacobian matrix of the terminal end face coordinate system l relative to the base coordinate system O is +.>。
Wherein->
The kinematic modeling based on the single-segment continuum manipulator can be applied to the multi-segment continuum manipulator. As shown in fig. 2, the first degree of freedom of the two-stage continuum manipulator is linear motion d, the second degree of freedom is an overall torsion angle α, and the third and fourth degrees of freedom are proximal torsion angles of the continuum manipulator, respectivelyAnd a bending angle theta 1 The fifth and sixth degrees of freedom are distributed as the distal torsion angle of the continuum manipulator +.>And a bending angle theta 2 . Wherein the proximal and distal lengths are both L.
The kinematic relationships of the overall continuum robotic arm are as follows:
in the method, a control method based on a jacobian matrix is adopted, and a velocity jacobian matrix J derivation formula of the whole end effector of the continuum mechanical arm is as follows:
J w1 ＝[0,0,0] T J w2 ＝[0,0,1] T
J＝[J v ；J w ]；
therefore, a velocity jacobian matrix (comprising a linear velocity and an angular velocity jacobian matrix of the end effector of the continuous body mechanical arm) of the end effector of the continuous body mechanical arm can be deduced according to the pose matrix of the end effector when the continuous body mechanical arm is bent, so that a mapping relation between the change velocity of the end pose of the continuous body mechanical arm and the change velocity of the joint can be obtained.
Specifically, in actual control, an initial current pose matrix of the end effector of the continuum manipulator is set asThe input target pose matrix is T d 。
And then T diff ＝T init -1 T d -I 4×4 ，T diff Is obtained by combining differential movement and differential rotation, which describes the pose error relation between the current pose and the target pose, and obtains the pose error e= [ d ] x ,d y ,d z ,δ x ,δ y ,δ z ] T Wherein d is x ,d y ,d z Delta as position error x ,δ y ,δ z Is an attitude error.
And S2, judging whether the pose error meets the preset condition, if so, inputting a target pose matrix of a target pose control point of the end effector of the next continuum mechanical arm as the target pose matrix of the end effector of the continuum mechanical arm, returning to the step S1 to judge the pose error again, and if not, continuing to the step S3.
The step of judging whether the pose error meets the preset condition specifically comprises the following steps: judging whether the two norm values of the position error vector of the end effector of the continuum mechanical arm are smaller than a first preset value Lpmm or not; judging whether the two norms of the attitude error vector of the continuous body mechanical arm end effector are smaller than a second preset value La radian, if the two norms of the attitude error vector are all smaller than the second preset value La radian, substituting a target pose matrix of a next pose target point (namely, a target pose matrix of a target pose control point of the next continuous body mechanical arm end effector), and carrying out pose error judgment again.
And S3, acquiring pose correction parameters of the end effector of the continuum mechanical arm according to the pose errors (namely, determining the position correction parameters according to the position error values, and determining the pose correction parameters according to the pose error values), and obtaining an updated control law function according to the pose correction parameters, a preset target control function and a velocity jacobian matrix of the end effector of the continuum mechanical arm, wherein the target control function is used for restraining the minimum difference between the current pose and the target pose of the end effector (the target control function aims to enable each control error to trend to 0, and the joint driving increment is as small as possible so as to enable movement to be smoother).
Specifically, an objective control function min J (q) dq-Ke|| is set 2 +μ 2 ||dq|| 2 Where e is pose error, dq is joint drive increment, μ 1 ,μ 2 For correcting parameters of position, k 1 ,k 2 Is a posture correction parameter.
And setting a jacobian correction matrix M and an error correction matrix K.
The method comprises the following steps of performing formula deformation on an objective control function, inputting pose correction parameters into the objective control function, and combining a jacobian matrix of the speed of a continuous mechanical arm end effector to obtain an updated control law function (namely a function of a joint driving law dq):
dq＝J T (q)[J(q)J T (q)+M] -1 Ke。
and S4, inputting the pose error into the updated control law function to obtain a joint driving increment dq of the end effector of the continuous mechanical arm, and driving the continuous mechanical arm to displace by using the joint driving increment dq (namely, driving the end of the continuous mechanical arm to displace in the direction of reducing the pose error).
Step S5, updating the current joint amount of the end effector of the continuous mechanical arm (the current joint amount is the original joint amount+the joint driving amount) and the velocity jacobian matrix of the end effector of the continuous mechanical arm (i.e. updating both the current joint amount of the end effector of the continuous mechanical arm and the velocity jacobian matrix of the end effector of the continuous mechanical arm) through joint driving increment, thereby obtaining the current pose matrix T of the end effector of the continuous mechanical arm unit (i.e. by positive kinematic model T 4 0 Current pose matrix T for end effector unit Update is performed), and returns to step S1.
And finally, when the tracking of all target points of the target track reaches a convergence state, namely the tracking task is ended.
In a preferred embodiment of the present invention, the method further comprises a step of performing simulation experiment verification on the control method in the software matlab.
In particular, program simulations were used to verify the inventive method. The simulation experiment uses software matlab, simulation data is input as a track, and the track consists of a group of 40 target pose control points. In the simulation, the first preset value Lp is set to be 0.3mm, and the second preset value La radian is set to be 0.05rad. The simulation results are shown in fig. 4 and 5, and the actual iteration times in the control of the pose correction parameters are compared, so that the actual iteration times when each target point reaches convergence after the self-adaptive pose error compensation are less and the iteration times are more uniform. And under the same error setting, the iteration times of the method are obviously less than those of the Newton Lawson iteration method. Therefore, the control method of the invention has faster calculation speed and better convergence in actual control.
In summary, compared with the previous control method for solving the inverse kinematics solution based on Jacobian matrix iteration, the control method for the pose of the tail end of the continuous mechanical arm disclosed by the invention can obtain the motion analysis solution faster, realizes the pose control and track tracking tasks of the continuous mechanical arm, and verifies the feasibility of the method through actual simulation.
In another aspect, the present invention also discloses a computer device, which includes:
at least one processor; and a memory communicatively coupled to the at least one processor; wherein,,
the memory stores computer readable instructions, and the processor implements the method for controlling the pose of the end of the continuum manipulator when executing the computer readable instructions.
In still another aspect, the present invention further discloses a computer readable storage medium, where computer readable instructions are stored, where the computer readable instructions implement the method for controlling the pose of the end of the continuum manipulator described above when executed by a processor.
Those skilled in the art will understand that the skilled person can implement the modification in combination with the prior art and the above embodiments, and this will not be repeated here. Such modifications do not affect the essence of the present invention, and are not described herein.
The preferred embodiments of the present invention have been described above. It is to be understood that the invention is not limited to the specific embodiments described above, wherein devices and structures not described in detail are to be understood as being implemented in a manner common in the art; any person skilled in the art can make many possible variations and modifications to the technical solution of the present invention or modifications to equivalent embodiments without departing from the scope of the technical solution of the present invention, using the methods and technical contents disclosed above, without affecting the essential content of the present invention. Therefore, any simple modification, equivalent variation and modification of the above embodiments according to the technical substance of the present invention still fall within the scope of the technical solution of the present invention.

Claims (10)

1. The utility model provides a continuum arm terminal position appearance control method, continuum arm includes two sections continuum arms and a rigid straight-bar, its characterized in that, control method includes:
step S1, calculating a pose error between a current pose matrix of the continuous body mechanical arm end effector and an input target pose matrix of the continuous body mechanical arm end effector;
step S2, judging whether the pose error meets a preset condition, if so, inputting a target pose matrix of a target pose control point of the end effector of the next continuum mechanical arm as the target pose matrix of the end effector of the continuum mechanical arm, returning to the step S1, and if not, continuing to carry out the step S3;
step S3, acquiring pose correction parameters of the end effector of the continuous mechanical arm according to the pose errors, and obtaining an updated control law function according to the pose correction parameters, a preset target control function and a velocity jacobian matrix of the end effector of the continuous mechanical arm, wherein the target control function is used for restraining the minimum difference between the current pose and the target pose of the end effector of the continuous mechanical arm;
s4, inputting the pose error into the updated control law function to obtain a joint driving increment of the end effector of the continuous mechanical arm, and driving the continuous mechanical arm to displace by using the joint driving increment;
and S5, updating the current joint quantity of the end effector of the continuous mechanical arm and the velocity jacobian matrix of the end effector of the continuous mechanical arm through joint driving increment, further obtaining the current pose matrix of the end effector of the continuous mechanical arm, and returning to the step S1.
2. The method according to claim 1, characterized in that before performing the step S1, the control method further comprises:
and establishing a base coordinate system and a local coordinate system on the continuum mechanical arm to obtain an end effector pose matrix when the continuum mechanical arm is bent.
3. The method for controlling the end pose of a continuum manipulator according to claim 2, wherein the step of establishing a base coordinate system and a local coordinate system on the continuum manipulator comprises the steps of:
a base coordinate system is established at the base of the continuum manipulator, and a local coordinate system is established at the end of the rigid straight rod and the end face of the end of each segment of continuum manipulator.
4. The method according to claim 2, wherein a velocity jacobian matrix of the end effector of the continuum robot is derived from the end effector pose matrix when the continuum robot is bent to obtain a mapping relationship between the end pose change velocity and the joint change velocity of the continuum robot.
5. The method for controlling the pose of the end of the continuum manipulator according to claim 1, wherein determining whether the pose error satisfies a preset condition specifically comprises:
judging whether the two norm values of the position error vector of the end effector of the continuum manipulator are smaller than a first preset value or not;
judging whether the two norms of the attitude error vector of the end effector of the continuum mechanical arm are smaller than a second preset value.
6. The method for controlling the end pose of a continuum robot of claim 1, wherein the continuum robot is a two-stage continuum robot having 6 degrees of freedom.
7. The method for controlling the pose of the end of a continuum manipulator according to claim 1, further comprising the step of performing simulation experiment verification of the control method.
8. The method for controlling the terminal pose of the continuous body mechanical arm according to claim 1, wherein simulation experiment verification is performed on the control method in software matlab.
9. A computer device, characterized by: the computer device includes:
at least one processor; the method comprises the steps of,
a memory communicatively coupled to the at least one processor; wherein,,
the memory stores computer readable instructions, and the processor executes the computer readable instructions to implement the continuum manipulator end pose control method according to any one of claims 1 to 8.
10. A computer-readable storage medium, characterized by: the computer readable storage medium stores thereon computer readable instructions that when executed by a processor implement the continuum robot arm end pose control method according to any one of claims 1 to 8.
CN202310871299.7A 2023-07-15 2023-07-15 Method for controlling pose of tail end of continuum mechanical arm, computer equipment and readable storage medium Pending CN116852363A (en)

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