WO2022141160A1 - 并联平台的主从映射方法、机械臂系统和存储介质 - Google Patents

并联平台的主从映射方法、机械臂系统和存储介质 Download PDF

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Publication number
WO2022141160A1
WO2022141160A1 PCT/CN2020/141274 CN2020141274W WO2022141160A1 WO 2022141160 A1 WO2022141160 A1 WO 2022141160A1 CN 2020141274 W CN2020141274 W CN 2020141274W WO 2022141160 A1 WO2022141160 A1 WO 2022141160A1
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WIPO (PCT)
Prior art keywords
coordinate system
joint
slave
master
platform
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PCT/CN2020/141274
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English (en)
French (fr)
Inventor
黄善灯
柏龙
陈晓红
潘鲁锋
柳建飞
Original Assignee
诺创智能医疗科技(杭州)有限公司
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Priority to EP20967505.7A priority Critical patent/EP4272904A1/en
Priority to PCT/CN2020/141274 priority patent/WO2022141160A1/zh
Publication of WO2022141160A1 publication Critical patent/WO2022141160A1/zh
Priority to US18/346,076 priority patent/US20230347516A1/en

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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
    • B25J13/00—Controls for manipulators
    • B25J13/02—Hand grip control means
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J17/00—Joints
    • B25J17/02—Wrist joints
    • B25J17/0258—Two-dimensional joints
    • B25J17/0266—Two-dimensional joints comprising more than two actuating or connecting rods
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J18/00—Arms
    • B25J18/02—Arms extensible
    • B25J18/025—Arms extensible telescopic
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J3/00—Manipulators of master-slave type, i.e. both controlling unit and controlled unit perform corresponding spatial movements
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/0009—Constructional details, e.g. manipulator supports, bases
    • B25J9/0018—Bases fixed on ceiling, i.e. upside down manipulators
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/0084—Programme-controlled manipulators comprising a plurality of manipulators
    • B25J9/0087—Dual arms
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
    • B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
    • B25J9/00—Programme-controlled manipulators
    • B25J9/02—Programme-controlled manipulators characterised by movement of the arms, e.g. cartesian coordinate type
    • B25J9/04—Programme-controlled manipulators characterised by movement of the arms, e.g. cartesian coordinate type by rotating at least one arm, excluding the head movement itself, e.g. cylindrical coordinate type or polar coordinate type
    • B25J9/045—Polar coordinate type
    • 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
    • B25J9/1607—Calculation of inertia, jacobian matrixes and inverses
    • 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
    • B25J9/1623—Parallel manipulator, Stewart platform, links are attached to a common base and to a common platform, plate which is moved parallel to the base
    • 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
    • B25J9/1679—Programme controls characterised by the tasks executed
    • B25J9/1682—Dual arm manipulator; Coordination of several manipulators
    • 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
    • B25J9/1679—Programme controls characterised by the tasks executed
    • B25J9/1689—Teleoperation
    • 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
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/40—Robotics, robotics mapping to robotics vision
    • G05B2219/40146—Telepresence, teletaction, sensor feedback from slave to operator
    • 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
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/40—Robotics, robotics mapping to robotics vision
    • G05B2219/40195—Tele-operation, computer assisted manual operation
    • 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
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/45—Nc applications
    • G05B2219/45117—Medical, radio surgery manipulator

Definitions

  • the present application relates to the field of control, and in particular to a master-slave mapping method, a robotic arm system and a storage medium of a parallel platform.
  • a master-slave mapping method of a parallel platform is provided, which is applied to a robotic arm system, the robotic arm system includes a parallel platform and a master operator, and the parallel platform includes a static platform, a moving platform, and a A plurality of telescopic rods arranged between the static platform and the moving platform
  • the master-slave mapping method of the parallel platform includes: establishing a calculation coordinate system of the parallel platform on the static platform, establishing a slave on the static platform
  • the user coordinate system and the master user coordinate system established on the master operator, wherein the calculated coordinate system coincides with the origin of the slave user coordinate system, and the Z of the slave user coordinate system and the master user coordinate system
  • the axes are all parallel to the Z axis of the reference coordinate system; the first conversion relationship between the slave user coordinate system and the calculation coordinate system is obtained; the displacement of the end of the master operator in the master user coordinate system is calculated as follows: Setting the scale factor to map to the end of the moving platform in the slave user coordinate system to obtain
  • the above-mentioned master-slave mapping method of a parallel platform has the following advantages: compared with the related art, the master-slave mapping method of the parallel platform, the robotic arm system and the storage medium provided by the embodiments of the present application solve the problem of complex robotic arm control in the related art , which reduces the control complexity of the robotic arm.
  • the parallel platform in this embodiment can realize motion with multiple degrees of freedom.
  • the Stewart parallel platform includes a static platform, a moving platform, and a plurality of telescopic and retractable platforms arranged between the static platform and the moving platform.
  • the component can realize six degrees of freedom movement in space, namely displacement along the X axis, displacement along the Y axis, displacement along the Z axis, rotation around the X axis, rotation around the Y axis, and rotation around the Z axis.
  • the Stewart parallel platform is supported by 6 telescopic components. Compared with the passive arm using the cantilever beam structure in series, the rigidity is higher and the structure is stable.
  • the parallel structure Due to the high rigidity, the parallel structure has a higher self-weight or volume than the series structure. Carrying capacity.
  • the error at the end of the passive arm using the cantilever beam structure in series is the accumulation and amplification of the errors of each joint, so the error is large and the precision is low. Precision surgical operation.
  • the inverse solution of the parallel platform is very easy, and it is easy to obtain the motion posture of each telescopic component of the parallel platform according to the coordinate position.
  • the control amount of the master operator in the master user coordinate system is mapped to the slave user in the form of displacement.
  • the position information of the second target position in the calculation coordinate system can be obtained through the conversion from the user coordinate system and the calculation coordinate system.
  • the forward kinematics is used to solve the position information of the end of the parallel platform. The above method greatly reduces the computational complexity, improves the control efficiency, and saves computational resources.
  • the acquiring a first transformation relationship between the secondary user coordinate system and the calculated coordinate system includes: acquiring a second transformation relationship between the reference coordinate system and the secondary user coordinate system, and Acquire a third transformation relationship between the reference coordinate system and the calculated coordinate system; and determine the first transformation relationship according to the second transformation relationship and the third transformation relationship.
  • the reference coordinate system is the base coordinate system of the manipulator system; the manipulator system further includes a serial manipulator, and the parallel platform is mounted on the end of the serial manipulator;
  • acquiring the third conversion relationship between the reference coordinate system and the calculation coordinate system includes: establishing a joint coordinate system of each joint in the serial robotic arm; acquiring joint coordinates of the first joint in the serial robotic arm.
  • the DH parameters of the reference coordinate system and the reference coordinate system determine the conversion relationship between the reference coordinate system and the joint coordinate system of the first joint
  • the first joint is a joint directly connected to the base, and the DH parameter is a traditional DH parameter or an improved DH parameter; obtain the joint coordinate system of the i-th joint in the serial robotic arm and the i-th
  • the serial manipulator includes a rotation joint and a moving joint; wherein the Z axis of the joint coordinate system of the rotating joint is set along the rotation axis, and the Z axis of the joint coordinate system of the moving joint is along the rotation axis.
  • the movement direction is set, the reference coordinate system and the joint coordinate system of each joint are both left-handed or right-handed systems, and when the joint before the rotating joint is a moving joint, the origin of the joint coordinate system of the rotating joint is the same as the moving joint. The origin of the joint coordinate system is coincident.
  • the rotation angle of the Z axis in the DH parameter of the rotary joint in the serial robotic arm is not 0 or 2 ⁇ .
  • the acquiring the second transformation relationship between the reference coordinate system and the secondary user coordinate system includes: acquiring a viewing angle value of the user relative to the robotic arm system; The third conversion relationship is determined, and the second conversion relationship between the reference coordinate system and the secondary user coordinate system is determined.
  • the viewing angle value is determined based on configuration information input by a user when the robotic arm system operates with a single arm.
  • the acquiring of the reference coordinate system and the second coordinate system from the user coordinate system are performed.
  • the conversion relationship includes: establishing a first slave user coordinate system of the first serial manipulator and a second slave user coordinate system of the second serial manipulator, wherein the X-axis direction of the first slave user coordinate system is the same as that of the first slave user coordinate system.
  • the X-axis directions of the second slave user coordinate system are the same and collinear, and the origin of the first slave user coordinate system coincides with the origin of the calculation coordinate system of the first serial manipulator.
  • the origin of the coordinate system is coincident with the origin of the calculation coordinate system of the second serial manipulator; determine the angle between the X-axis direction of the first slave user coordinate system and the X-axis direction of the reference coordinate system, and according to this The included angle and the conversion relationship between the reference coordinate system and the calculated coordinate system of each serial manipulator, determine that the reference coordinate system is respectively the second from the first slave user coordinate system and the second slave user coordinate system. conversion relationship.
  • a robotic arm system including a parallel platform, a master operator, a memory, and a controller
  • the parallel platform includes a static platform, a moving platform, and a plurality of For the telescopic rod between the moving platforms
  • a computer program is stored in the memory
  • the controller is configured to run the computer program to execute the master-slave mapping method for parallel platforms provided by the embodiments of the present application.
  • the robotic arm system further includes a serial robotic arm, and the parallel platform is mounted on the end of the serial robotic arm.
  • a storage medium is provided, where a computer program is stored in the storage medium, wherein the computer program is configured to execute the master-slave mapping method for parallel platforms provided by the embodiments of the present application when running. .
  • FIG. 1 is a flowchart of a master-slave mapping method of a parallel platform according to an embodiment of the present application.
  • FIG. 2 is a flowchart of a coordinate conversion method according to an embodiment of the present application.
  • FIG. 3 is a schematic structural diagram of a robotic arm system provided by a preferred embodiment of the present application.
  • FIG. 4 is a schematic diagram of a reference coordinate system and a joint coordinate system of a robotic arm system provided by a preferred embodiment of the present application.
  • FIG. 5 is a schematic diagram of the user coordinate system when the two arms of the manipulator system provided by the preferred embodiment of the present application work.
  • FIG. 6 is a schematic diagram of a master-slave mapping method of a parallel platform according to a preferred embodiment of the present application.
  • This embodiment provides a master-slave mapping method for parallel platforms.
  • the master-slave mapping method of the parallel platform is applied to a manipulator system including a parallel platform and a master operator.
  • the parallel platform includes a static platform, a moving platform and a plurality of telescopic rods arranged between the static platform and the moving platform.
  • FIG. 1 is a flowchart of a master-slave mapping method for a parallel platform according to an embodiment of the present application. As shown in FIG. 1 , the flowchart includes the following steps.
  • Step S101 establishing the calculation coordinate system of the parallel platform on the static platform, establishing the slave user coordinate system on the static platform, and establishing the master user coordinate system on the master operator, wherein the calculation coordinate system coincides with the origin of the slave user coordinate system, and the slave user coordinate system coincides with the origin of the slave user coordinate system.
  • the Z-axis of both the coordinate system and the primary user coordinate system are parallel to the Z-axis of the reference coordinate system.
  • Step S102 Obtain a first transformation relationship between the user coordinate system and the calculation coordinate system.
  • Step S103 Map the displacement of the end of the main operator in the main user coordinate system to the end of the moving platform in the slave user coordinate system according to the set proportional coefficient, and obtain the first position of the end of the moving platform in the slave user coordinate system. target location.
  • Step S104 According to the first conversion relationship and the first target position, determine the second target position of the end of the moving platform in the calculation coordinate system.
  • Step S105 According to the second target position, the motion amount of each telescopic rod of the parallel platform is solved through an inverse kinematics algorithm, and the motion of the parallel platform is controlled according to the motion amount of each telescopic rod.
  • the parallel platform in this embodiment can realize motion with multiple degrees of freedom.
  • the Stewart parallel platform includes a static platform, a moving platform, and a plurality of telescopic and retractable platforms arranged between the static platform and the moving platform.
  • the component can realize six degrees of freedom movement in space, namely displacement along the X axis, displacement along the Y axis, displacement along the Z axis, rotation around the X axis, rotation around the Y axis, and rotation around the Z axis.
  • the Stewart parallel platform is supported by 6 telescopic components. Compared with the passive arm using the cantilever beam structure in series, the rigidity is higher and the structure is stable.
  • the parallel structure Due to the high rigidity, the parallel structure has a higher self-weight or volume than the series structure. Carrying capacity.
  • the error at the end of the passive arm using the cantilever beam structure in series is the accumulation and amplification of the errors of each joint, so the error is large and the precision is low, while the parallel platform does not have such an error accumulation and amplification relationship. Precision surgical operation.
  • the inverse solution of the parallel platform is very easy, and it is easy to obtain the motion posture of each telescopic component of the parallel platform according to the coordinate position.
  • the control amount of the master operator in the master user coordinate system is mapped to the slave user in the form of displacement.
  • the position information of the second target position in the calculation coordinate system can be obtained through the conversion from the user coordinate system and the calculation coordinate system.
  • the forward kinematics is used to solve the position information of the end of the parallel platform. The above method greatly reduces the computational complexity, improves the control efficiency, and saves computational resources.
  • the above-mentioned reference coordinate system is also called the global coordinate system, and the coordinate system can be selected arbitrarily.
  • the base coordinate system established at the center of the base bottom of the robotic arm system is selected as the reference coordinate system in the embodiment of the present application.
  • the master user coordinate system and the slave user coordinate system may be the same coordinate system, or may be different coordinate systems.
  • the origin of the master user coordinate system and the slave user coordinate system and each coordinate axis are completely coincident, that is, the coordinate origin of the master user coordinate system also coincides with the calculation coordinate system on the static platform.
  • the coordinate origin of the master user coordinate system can be set at the end of the master operator, for example, and each coordinate axis is parallel to each coordinate axis of the slave user coordinate system, so as to facilitate the calculation.
  • the first transformation relationship between the user coordinate system and the calculated coordinate system may be obtained by the following methods: obtaining a second transformation relationship between the reference coordinate system and the slave user coordinate system, and obtaining the reference coordinate system and the calculated coordinate
  • the third conversion relationship of the system is determined; the first conversion relationship is determined according to the second conversion relationship and the third conversion relationship.
  • the reference coordinate system is the base coordinate system of the manipulator system; the manipulator system further includes a serial manipulator, and the parallel platform is mounted on the end of the serial manipulator.
  • FIG. 2 is a coordinate conversion method according to an embodiment of the present application. As shown in FIG. 2 , the flow chart of obtaining the third transformation relationship between the reference coordinate system and the calculation coordinate system includes the following steps.
  • Step S201 establishing a joint coordinate system of each joint in the serial robotic arm.
  • the control of serial manipulators is usually based on DH parameters or modified DH parameters for coordinate system transformation.
  • Two connected joints are adjacent joints.
  • the transformation of the joint coordinate system of two adjacent joints is usually represented by a DH parameter or an improved DH parameter.
  • a DH parameter as an example, two adjacent joint coordinate systems can overlap each other by rotating ⁇ around the Z axis and translating d, and then rotating ⁇ around the X axis and translating a.
  • ⁇ , d, ⁇ and a are DH parameters. It can be seen from this that the simpler the DH parameter is, the simpler the transformation of two adjacent joint coordinate systems will be.
  • the Z axis of the joint coordinate system of the rotating joint is set along the rotation axis
  • the Z axis of the joint coordinate system of the moving joint is set along the moving direction
  • the reference coordinate system is the same as the joint coordinate system of each joint. It is a left-handed system or a right-handed system, and when the joint before the rotating joint is a moving joint, the origin of the joint coordinate system of the rotating joint coincides with the origin of the joint coordinate system of the moving joint.
  • a rotary joint In a serial manipulator, in most cases, when a rotary joint receives a command with a rotation angle of 0 or 2 ⁇ , it may not be necessary to distinguish between the two, but it will not rotate according to a preset setting or rotate by 2 ⁇ in a set direction. However, in some cases, it is necessary to distinguish between these two corners. In the case where the 0 or 2 ⁇ rotation angle needs to be distinguished, the rotation angle of the Z axis in the DH parameter of the rotary joint is not 0 or 2 ⁇ , so as to avoid confusing the rotation angle of 0 or 2 ⁇ .
  • Step S202 Obtain the DH parameters of the joint coordinate system of the first joint in the serial manipulator and the reference coordinate system, and determine the conversion relationship between the reference coordinate system and the joint coordinate system of the first joint Among them, the first joint is the joint directly connected to the base, and the DH parameter is the traditional DH parameter or the improved DH parameter.
  • Step S204 According to the conversion relationship and conversion relationship Determine the transformation relationship between the reference coordinate system and the joint coordinate system of the Nth joint That is, the third conversion relationship, in which the joint coordinate system of the Nth joint completely coincides with the calculation coordinate system.
  • the DH parameters between adjacent joints can be obtained in turn, and according to the DH parameters, the conversion relationship between the reference coordinate system of the manipulator system and the calculation coordinate system of the serial manipulator can be determined.
  • the homogeneous transformation from the coordinates of the i-1th joint to the coordinates of the ith joint is constructed as a sequence with two rotations and two transformations, which can be expressed as follows using a matrix:
  • the DH parameter of the first joint of the serial manipulator is the transformation of the coordinate system between the first joint and the reference coordinate system, denoted as Then the transformation relationship between the reference coordinate system and the joint coordinate system of the first joint:
  • the transformation matrix from the 0th coordinate system (reference coordinate system) to the joint coordinate system of the Nth joint can be expressed as:
  • the Nth joint is the end joint.
  • step S204 It represents the coordinate conversion relationship between the reference coordinate system and the calculation coordinate system. According to the conversion relationship, the coordinate conversion between the reference coordinate system and the calculation coordinate system can be realized.
  • FIG. 3 is a schematic structural diagram of a robotic arm system provided by a preferred embodiment of the present application.
  • the robotic arm system shown in FIG. 3 includes a serial robotic arm, which in turn includes a moving joint 1, a rotating joint 2, a moving joint 3, a rotating joint The joint 4 , the rotating joint 5 , the moving joint 6 , the rotating joint 7 , the moving joint 8 , the rotating joint 9 and the moving joint 10 , in addition, the robotic arm system further includes a base 11 fixedly connected with the moving joint 1 .
  • FIG. 4 is a schematic diagram of a reference coordinate system and a joint coordinate system of a robotic arm system provided by a preferred embodiment of the present application. Referring to FIG. 4 , the master-slave mapping method for parallel platforms in this preferred embodiment includes the following steps.
  • Step 1 According to the rules of the world coordinate system, establish a reference coordinate system at the base of the serial manipulator, as well as the joint coordinate system of each joint.
  • the reference coordinate system F 0 -X 0 Y 0 0 Z 0 The origin of the coordinate system F 0 is fixed at the base of the manipulator, the Z 0 axis points from F 0 to the moving joint 1, and the Y 0 axis points from the base F 0 to the serial manipulator , the X 0 axis points to a right-handed coordinate system.
  • the origin L 1 of the joint coordinate system L 1 -X 1 Y 1 Z 1 of the mobile joint 1 is fixedly connected to the mobile joint 1 , and the orientation of each coordinate axis is the same as that of the corresponding axis of the reference coordinate system.
  • the origin of the joint coordinate system R 2 -X 2 Y 2 Z 2 of the rotary joint 2 is fixed on the rotary joint 2 and coincides with L 1.
  • the Z 2 and Z 1 axes point in the same direction, the X 2 axis and the Y 2 axis The directions are opposite to the X 1 axis and Y 1 axis respectively.
  • the joint coordinate system L 3 -X 3 Y 3 Z 3 of the mobile joint 3 is fixed at the origin L 3 of the mobile joint 3, the Z 3 axis points from the L 1 point to the L 3 point, and the X 3 axis and the Y 3 axis are respectively connected with the X 2 Axis and Z 2 axis point the same.
  • the origin of the joint coordinate system R 4 -X 4 Y 4 Z 4 of the rotary joint 4 is fixed on the rotary joint 4 and coincides with the point L 3 (Fig. 4 is a clear indication of the joint coordinate system of the mobile joint 3 and the rotary joint 4).
  • the joint coordinate system of L 3 and R 4 are marked separately, the same below), the Z 4 axis points to the opposite direction to the Y 3 axis, initially, the X 4 axis and the Y 4 axis point to the X 3 axis and the Z 3 axis respectively. on the contrary.
  • the joint coordinate system R 5 -X 5 Y 5 Z 5 of the rotary joint 5 is fixed at the origin R 5 of the rotary joint 5.
  • the direction of the Z 5 axis and the Z 4 axis are the same. Initially, the X 5 axis and the Y 5 axis point respectively.
  • the X 4 -axis and Y 4 -axis point opposite.
  • the joint coordinate system L 6 -X 6 Y 6 Z 6 of the mobile joint 6 is fixed at the origin L 6 of the mobile joint 6.
  • the Z 6 axis points from the R 5 point to the L 6 point, and the X 6 axis and the Y 6 axis point to the X axis respectively.
  • the 5 -axis and the Z 5 -axis point the same.
  • the joint coordinate system R 7 -X 7 Y 7 Z 7 of the rotary joint 7 is fixed at the origin R 7 of the rotary joint 7 and coincides with the L 6 point. Initially, the Z 7 axis and the Y 7 axis point to the Y 6 axis respectively. The X 7 axis and the Z 6 axis point in the same direction, as opposed to the X 6 axis.
  • the origin of the joint coordinate system L 8 -X 8 Y 8 Z 8 of the mobile joint 8 is fixed on the mobile joint 8.
  • the Z 8 axis points from the L 8 point to the R 7 point, and the directions of the X 8 and Y 8 axes are respectively the same as The X 7 and Y 7 axes point the same.
  • the origin of the joint coordinate system R9 - X9Y9Z9 of the rotary joint 9 is fixed on the rotary joint 9 and coincides with the L8 point.
  • the direction of the Z9 axis is opposite to the direction of the Y8 axis.
  • the direction of the X 9 axis is opposite to the direction of the Z 8 axis, and the direction of the Y 9 axis is the same as the direction of the X8 axis.
  • the origin of the joint coordinate system L 10 -X 10 Y 10 Z 10 of the mobile joint 10 is fixed on the mobile joint 10.
  • the Z 10 axis points from the R 9 point to the L 10 point, and the X 10 axis and the Y 10 axis point respectively. The same point as the X 9 and Z 9 axes.
  • the length of F 0 R 2 is l 1
  • the length of R 2 R 4 is l 2
  • the length of R 4 R 5 is l 3
  • the length of R 5 R 7 is l 4
  • the length of R 7 R 9 is l 5
  • the length of R 9 L 10 is l 6
  • the points L 1 , R 2 , L 3 , R 4 , R 5 , L 6 and R 7 are located on the same horizontal plane.
  • Step 2 Obtain the DH parameters and calculate the transformation relationship from the reference coordinate system to the end joint of the serial manipulator.
  • DH parameters are shown in Table 1.
  • Table 1 in order to avoid confusing the rotation angles of the revolute joints 0 and 2 ⁇ , in the DH parameter, the rotation angle of the Z axis avoids the two positions of 0 and 2 ⁇ .
  • the transformation matrix from the mth joint (containing the m degree of freedom) to the nth joint can be expressed as:
  • transformation matrix of a single serial manipulator from the base to the static platform of the Stewart platform can be solved That is, the transformation matrix from the reference coordinate system to the Stewart calculation coordinate system is named T trans_mach_st , and the transformation matrix from the Stewart calculation coordinate system to the reference coordinate system is the inverse matrix
  • Step 3 Perform coordinate transformation between the reference coordinate system and the Stewart-calculated coordinate system according to the transformation matrix and the inverse matrix of the transformation matrix.
  • the user coordinate system is established to simplify the motion mapping of the master-slave control.
  • the master-slave mapping method of the parallel platform in this preferred embodiment further includes the following steps.
  • Step S205 Establish a slave user coordinate system, wherein the XY coordinate plane of the slave user coordinate system is parallel to the XY plane of the reference coordinate system, and the origin of the slave user coordinate system coincides with the origin of the calculation coordinate system.
  • Step S206 Obtain the viewing angle value input by the user, and determine the conversion relationship between the secondary user coordinate system and the reference coordinate system according to the viewing angle value and the conversion relationship between the reference coordinate system and the calculation coordinate system.
  • the rotation angle around the Z axis from the XY coordinate plane of the user coordinate system established in step S205 is the viewing angle value.
  • the viewing angle value is input by the user according to the viewing angle, named ⁇ theta_mach_user .
  • the transformation matrix from the user coordinate system to the reference coordinate system can be obtained:
  • FIG. 5 is a schematic diagram of the user coordinate system when the two arms of the robotic arm system provided by the preferred embodiment of the present application work.
  • the reference coordinate system is O 0 -X 0 Y 0 Z 0
  • the Stewart calculation coordinate system is O S -X S Y S Z S
  • from the user coordinate system is O P -X P Y P Z P .
  • the master-slave mapping method of the parallel platform in this preferred embodiment further includes the following steps.
  • Step S207 Establish the first slave user coordinate system of the first serial manipulator and the second slave user coordinate system of the second serial manipulator, wherein the X-axis direction of the first slave user coordinate system is the same as the second slave user coordinate system.
  • the X-axis directions are the same and collinear, and the origin of the first slave user coordinate system coincides with the origin of the calculation coordinate system of the first serial manipulator, and the origin of the second slave user coordinate system and the calculation coordinate system of the second serial manipulator The origin coincides.
  • the left-hand side is the left serial manipulator
  • the right-hand side is the right serial manipulator.
  • input the DH parameters of the left and right arms respectively, and the respective transformation matrices T trans_mach_st_left and T trans_mach_st_right of the left and right arms can be obtained.
  • the coordinates of the origin of the static platform of the two serial manipulators in the reference coordinate system are:
  • C coord_mach_st_left [T trans_mach_st_left (1, 4) T trans_mach_st_left (2, 4) T trans_mach_st_left (3, 4) 1] T ;
  • C coord_mach_st_right [T trans_mach_st_right (1, 4) T trans_mach_st_right (2, 4) T trans_mach_st_right (3, 4) 1] T .
  • Step S208 Determine the angle between the X-axis direction of the first slave user coordinate system and the X-axis direction of the reference coordinate system, and determine the conversion relationship between the angle and the reference coordinate system and the calculation coordinate system of each serial manipulator.
  • the reference coordinate system has a second transformation relationship with the first slave user coordinate system and the second slave user coordinate system, respectively.
  • the angle ⁇ theta_mach_user between the X axis and the reference coordinate system can be calculated by the following formula:
  • ⁇ atan2(y,x), which is a built-in function in MATLAB or C language library. Therefore, the transformation matrix from the user coordinate system corresponding to the left and right serial manipulators can be obtained by a method similar to the single-arm transformation matrix:
  • the transformation matrix T trans_user_st from the user coordinate system to the Stewart calculated coordinate system can be calculated by the following formula:
  • T trans_user_st T trans_mach_user ⁇ 1 ⁇ T trans_mach_st .
  • the transformation matrix from the Stewart-calculated coordinate system to the user coordinate system is the inverse matrix
  • the conversion relationship between the user coordinate system and the reference coordinate system is determined by the viewing angle value input by the user; when the manipulator system works with two arms, because each single arm is The slave user coordinate system is established. Therefore, after setting the X-axis directions of the two slave user coordinate systems to be the same and collinear, the angle between the X-axis direction of the slave user coordinate system and the X-axis direction of the reference coordinate system can be determined. As the viewing angle value, the conversion relationship between the slave user coordinate system and the reference coordinate system of each single arm is then determined.
  • the slave coordinate system After obtaining the transformation relationship between the slave user coordinate system and the reference coordinate system, the slave coordinate system can be determined according to the transformation relationship between the reference coordinate system and the calculation coordinate system, and the transformation relationship between the slave user coordinate system and the reference coordinate system. The conversion relationship between the user coordinate system and the calculated coordinate system of the serial manipulator.
  • FIG. 6 is a schematic diagram of a master-slave mapping method of a parallel platform according to a preferred embodiment of the present application. As shown in FIG. 6 , the left picture is the passive arm, and the right picture is the master operator. Referring to FIG. 6 , specifically, the master-slave mapping method for parallel platforms provided by this preferred embodiment may include the following steps.
  • Step 1 From the moment the operator holds the main operator until the operator's hand leaves the main operator, it is regarded as a working cycle T.
  • the operator holds the main operator and starts to operate at time T(0), and the position coordinate of the main operator at this time is set as the origin M0 (0, 0, 0); the end point of the operating instrument installed on the moving platform at this time is at
  • the position coordinate from the user coordinate system is S0 (X0, Y0, Z0), the system calculates and saves S0 (X0, Y0, Z0) as a known value, denoted as C coord_now_user .
  • Step 2 At any time t in the working cycle, set the position coordinates of the end point of the master hand as M t (X mt , Y mt , Z mt ), denoted as C coord_offset_mas :
  • the position coordinates S t (X t , Y t , Z t ) of the device end point in the moving target point from the user coordinate system can be obtained through M t (X mt , Y mt , Z mt ) through the displacement scaling factor K 0 :
  • the master hand will send the current coordinate M t (X mt , Y mt , Z mt ) to solve the coordinate S t (X t , Y t , Z t ) of the end point of the instrument in the slave user coordinate system at this moment, denoted as C coord_new_user :
  • C coord_new_user C coord_now_user +K 0 ⁇ C coord_offset_mas .
  • Step 3 Convert the end point of the instrument at the coordinates S t (X t , Y t , Z t ) from the user coordinate system to the Stewart calculation coordinate system through the transformation matrix from the user coordinate system to the Stewart calculation coordinate system, denoted as C coord_new_st :
  • T trans_st_user is the transformation matrix from the user coordinate system to the Stewart calculation coordinate system.
  • Step 4 Knowing the coordinates of the end point of the device in the Stewart calculation coordinate system, the motion amount of each joint of the platform can be calculated through the inverse kinematics of the Stewart platform to complete the master-slave motion mapping.
  • the preset displacement proportional coefficient K 0 can be adjusted, and the value may be a value greater than 1 or a value less than 1; wherein, the preset displacement proportional coefficient K 0 is less than 1.
  • the value is set, high-precision control of the passive arm can be realized, and the shaking of the operator's hand during the operation can be eliminated to improve the operation reliability.
  • the motion mapping control of the relative zero position is adopted, which avoids the accumulation of errors and improves the control precision and operation safety.
  • This embodiment also provides a robotic arm system, including a parallel platform, a main operator, a memory, and a controller.
  • the parallel platform includes a static platform, a moving platform, and a plurality of telescopic rods disposed between the static platform and the moving platform.
  • the memory A computer program is stored in the controller, and the controller is configured to run the computer program to execute the master-slave mapping method of any one of the parallel platforms in the above-mentioned embodiments.
  • the embodiments of the present application further provide a computer-readable storage medium for implementation.
  • Computer program instructions are stored on the computer-readable storage medium; when the computer program instructions are executed by the processor, any one of the master-slave mapping methods for parallel platforms in the foregoing embodiments is implemented.

Abstract

本申请涉及并联平台的主从映射方法、机械臂系统和存储介质，通过获取用户坐标系与计算坐标系的第一转换关系；将主操作手的末端在主用户坐标系内的位移量按照设定比例系数映射到动平台的末端，得到动平台的末端的第一目标位置；根据第一转换关系和第一目标位置，确定动平台的末端的第二目标位置；根据第二目标位置通过逆运动学算法解得并联平台的各伸缩杆的运动量，并根据各伸缩杆的运动量控制并联平台的运动，简化了机械臂的控制。

Description

并联平台的主从映射方法、机械臂系统和存储介质 技术领域
本申请涉及控制领域，特别是涉及并联平台的主从映射方法、机械臂系统和存储介质。
背景技术
要实现机械臂的主从控制，需解算主手的运动学、从手的运动学，以及主手到从手的运动映射算法，而运动学的解算依赖于坐标系的建立，坐标系建立的方式，会影响运动学算法的复杂程度。
发明内容
根据本申请的各种实施例，提供一种并联平台的主从映射方法，应用于机械臂系统，所述机械臂系统包括并联平台和主操作手，所述并联平台包括静平台、动平台和多个设置在所述静平台和所述动平台之间的伸缩杆，所述并联平台的主从映射方法包括：在所述静平台建立并联平台的计算坐标系，在所述静平台建立从用户坐标系以及在所述主操作手建立主用户坐标系，其中，所述计算坐标系与所述从用户坐标系的原点重合，且所述从用户坐标系和所述主用户坐标系的Z轴均与参考坐标系的Z轴平行；获取所述从用户坐标系与所述计算坐标系的第一转换关系；将所述主操作手的末端在所述主用户坐标系内的位移量按照设定比例系数映射到所述动平台的末端在所述从用户坐标系内，得到所述动平台的末端在所述从用户坐标系内的第一目标位置；根据所述第一转换关系和所述第一目标位置，确定所述动平台的末端在所述计算坐标系内的第二目标位置；根据所述第二目标位置，通过逆运动学算法解得所述并联平台的各伸缩杆的运动量，并根据各所述伸缩杆的运动量控制所述并联平台的运动。
上述并联平台的主从映射方法具有以下优点：相比于相关技术，本申请实施例提供的并联平台的主从映射方法、机械臂系统和存储介质，解决了相关技术中机械臂控制复杂的问题，降低了机械臂的控制复杂程度。
本实施例的并联平台可以实现多个自由度的运动，以具有六自由度的Stewart并联平台为例，Stewart并联平台包括静平台、动平台和多个设置在静平台与动平台之间的伸缩组件，可以实现空间上六个自由度的运动，分别为沿X轴位移、沿Y轴位移、沿Z轴位移、绕X轴转动、绕Y轴转动和绕Z轴转动。Stewart并联平台由6根伸缩组件支撑，与采用串联的悬臂梁结构的被动臂相比刚度大，结构稳定，并且由于刚度大，并联结构较串联结构在相同的 自重或体积下，有较高的承载能力。采用串联的悬臂梁结构的被动臂末端的误差是各个关节误差的积累和放大，因而误差大、精度低，而并联平台则没有那样的误差积累和放大关系，微动精度高，更适宜执行高精度的手术操作。此外，在位置求解上，并联平台的逆解非常容易，容易根据坐标位置求得并联平台各伸缩组件的运动姿态。
正是基于并联平台逆解非常容易的特点，在上述步骤中通过建立主用户坐标系和从用户坐标系，将主操作手在主用户坐标系内的控制量通过位移量的形式映射到从用户坐标系内，再通过从用户坐标系与计算坐标系的转换从而得到第二目标位置在计算坐标系内的位置信息，根据该位置信息通过逆解就能够很容易地得到并联平台各伸缩组件的运动姿态，相对于相关技术中通过正运动学求解并联平台末端的位置信息，上述方式大大降低了运算复杂度，提高了控制效率，节约了运算资源。
在其中的一些实施例中，所述获取所述从用户坐标系与所述计算坐标系的第一转换关系包括：获取所述参考坐标系与所述从用户坐标系的第二转换关系，以及获取所述参考坐标系与所述计算坐标系的第三转换关系；根据所述第二转换关系和所述第三转换关系，确定所述第一转换关系。
在其中的一些实施例中，所述参考坐标系为所述机械臂系统的基座坐标系；所述机械臂系统还包括串联机械臂，所述并联平台搭载于所述串联机械臂的末端；其中，所述获取所述参考坐标系与所述计算坐标系的第三转换关系包括：建立所述串联机械臂中各关节的关节坐标系；获取所述串联机械臂中首个关节的关节坐标系与所述参考坐标系的DH参数，确定所述参考坐标系与所述首个关节的关节坐标系的转换关系
Figure PCTCN2020141274-appb-000001
其中，所述首个关节是与基座直接连接的关节，所述DH参数为传统的DH参数或改进的DH参数；获取所述串联机械臂中第i个关节的关节坐标系与第i-1个关节的关节坐标系的DH参数，确定第i-1个关节的关节坐标系与第i个关节的关节坐标系的转换关系
Figure PCTCN2020141274-appb-000002
其中，i＝2,3,4,…,N；N为所述串联机械臂的关节的总数量；根据转换关系
Figure PCTCN2020141274-appb-000003
和转换关系
Figure PCTCN2020141274-appb-000004
确定所述参考坐标系与第N个关节的关节坐标系的转换关系
Figure PCTCN2020141274-appb-000005
即为所述第三转换关系，其中，第N个关节的关节坐标系与所述计算坐标系完全重合。
在其中的一些实施例中，所述串联机械臂包括旋转关节和移动关节；其中，所述旋转关节的关节坐标系的Z轴沿旋转轴设置，所述移动关节的关节坐标系的Z轴沿移动方向设置，所述参考坐标系与各关节的关节坐标系同为左手系或右手系，且当旋转关节之前的关节为移 动关节时，所述旋转关节的关节坐标系的原点与该移动关节的关节坐标系的原点重合。
在其中的一些实施例中，所述串联机械臂中旋转关节的DH参数中Z轴的旋转角度不为0或2π。
在其中的一些实施例中，所述获取所述参考坐标系与所述从用户坐标系的第二转换关系包括：获取用户相对于所述机械臂系统的视角值；根据所述视角值和所述第三转换关系，确定所述参考坐标系与所述从用户坐标系的第二转换关系。
在其中的一些实施例中，在所述机械臂系统单臂工作的情况下，所述视角值基于用户输入的配置信息确定。
在其中的一些实施例中，在所述机械臂系统中第一串联机械臂和第二串联机械臂同时工作的情况下，所述获取所述参考坐标系与所述从用户坐标系的第二转换关系包括：建立所述第一串联机械臂的第一从用户坐标系和所述第二串联机械臂的第二从用户坐标系，其中，所述第一从用户坐标系的X轴方向与所述第二从用户坐标系的X轴方向相同且共线，且所述第一从用户坐标系的原点与所述第一串联机械臂的计算坐标系的原点重合，所述第二从用户坐标系的原点与所述第二串联机械臂的计算坐标系的原点重合；确定所述第一从用户坐标系的X轴方向与所述参考坐标系的X轴方向的夹角，并根据该夹角和所述参考坐标系与每条串联机械臂的计算坐标系的转换关系，确定所述参考坐标系分别与所述第一从用户坐标系以及所述第二从用户坐标系的第二转换关系。
根据本申请的各种实施例，提供一种机械臂系统，包括并联平台、主操作手、存储器和控制器，所述并联平台包括静平台、动平台和多个设置在所述静平台和所述动平台之间的伸缩杆，所述存储器中存储有计算机程序，所述控制器被设置为运行所述计算机程序以执行本申请实施例提供的并联平台的主从映射方法。
在其中的一些实施例中，所述机械臂系统还包括串联机械臂，所述并联平台搭载于所述串联机械臂的末端。
根据本申请的各种实施例，提供一种存储介质，所述存储介质中存储有计算机程序，其中，所述计算机程序被设置为运行时执行本申请实施例提供的并联平台的主从映射方法。
附图说明
为了更好地描述和说明这里公开的那些发明的实施例和/或示例，可以参考一幅或多幅附图。用于描述附图的附加细节或示例不应当被认为是对所公开的发明、目前描述的实施例和/或示例以及目前理解的这些发明的最佳模式中的任何一者的范围的限制。
图1是本申请实施例的并联平台的主从映射方法的流程图。
图2是本申请实施例的坐标转换方法的流程图。
图3是本申请优选实施例提供的机械臂系统的结构示意图。
图4是本申请优选实施例提供的机械臂系统的参考坐标系和关节坐标系的示意图。
图5是本申请优选实施例提供的机械臂系统双臂工作时从用户坐标系的示意图。
图6是本申请优选实施例的并联平台的主从映射方法的示意图。
具体实施方式
以下将对本申请提供的并联平台的主从映射方法、机械臂系统和存储介质作进一步说明。
本实施例提供了一种并联平台的主从映射方法。该并联平台的主从映射方法应用于包括并联平台和主操作手的机械臂系统，该并联平台包括静平台、动平台和多个设置在静平台和动平台之间的伸缩杆。
图1是本申请实施例的并联平台的主从映射方法的流程图，如图1所示，该流程包括如下步骤。
步骤S101：在静平台建立并联平台的计算坐标系，在静平台建立从用户坐标系以及在主操作手建立主用户坐标系，其中，计算坐标系与从用户坐标系的原点重合，且从用户坐标系和主用户坐标系的Z轴均与参考坐标系的Z轴平行。
步骤S102：获取从用户坐标系与计算坐标系的第一转换关系。
步骤S103：将主操作手的末端在主用户坐标系内的位移量按照设定比例系数映射到动平台的末端在从用户坐标系内，得到动平台的末端在从用户坐标系内的第一目标位置。
步骤S104：根据第一转换关系和第一目标位置，确定动平台的末端在计算坐标系内的第二目标位置。
步骤S105：根据第二目标位置，通过逆运动学算法解得并联平台的各伸缩杆的运动量，并根据各伸缩杆的运动量控制并联平台的运动。
本实施例的并联平台可以实现多个自由度的运动，以具有六自由度的Stewart并联平台为例，Stewart并联平台包括静平台、动平台和多个设置在静平台与动平台之间的伸缩组件，可以实现空间上六个自由度的运动，分别为沿X轴位移、沿Y轴位移、沿Z轴位移、绕X轴转动、绕Y轴转动和绕Z轴转动。Stewart并联平台由6根伸缩组件支撑，与采用串联的悬臂梁结构的被动臂相比刚度大，结构稳定，并且由于刚度大，并联结构较串联结构在相同的自重或体积下，有较高的承载能力。采用串联的悬臂梁结构的被动臂末端的误差是各个关节误差的积累和放大，因而误差大、精度低，而并联平台则没有那样的误差积累和放大关系， 微动精度高，更适宜执行高精度的手术操作。此外，在位置求解上，并联平台的逆解非常容易，容易根据坐标位置求得并联平台各伸缩组件的运动姿态。
正是基于并联平台逆解非常容易的特点，在上述步骤中通过建立主用户坐标系和从用户坐标系，将主操作手在主用户坐标系内的控制量通过位移量的形式映射到从用户坐标系内，再通过从用户坐标系与计算坐标系的转换从而得到第二目标位置在计算坐标系内的位置信息，根据该位置信息通过逆解就能够很容易地得到并联平台各伸缩组件的运动姿态，相对于相关技术中通过正运动学求解并联平台末端的位置信息，上述方式大大降低了运算复杂度，提高了控制效率，节约了运算资源。
上述的参考坐标系又称为全局坐标系，该坐标系可以任意选取。但为了计算更方便，在本申请实施例中选取在机械臂系统的基座底部中心建立的基座坐标系为参考坐标系。
需要说明的是，在上述实施例中的主用户坐标系和从用户坐标系可以是相同的坐标系，也可以是不同的坐标系。在他们是相同坐标系时，也就是说主用户坐标系和从用户坐标系的原点、各坐标轴均完全重合，即主用户坐标系的坐标原点也与静平台上的计算坐标系重合。在他们是不同的坐标系时，主用户坐标系的坐标原点例如可以设置在主操作手的末端，且各坐标轴与从用户坐标系的各坐标轴分别平行，以便计算简便。
在其中一些实施例中，从用户坐标系与计算坐标系的第一转换关系可以通过下列的方式获取：获取参考坐标系与从用户坐标系的第二转换关系，以及获取参考坐标系与计算坐标系的第三转换关系；根据第二转换关系和第三转换关系，确定第一转换关系。
在其中一些实施例中，参考坐标系为机械臂系统的基座坐标系；机械臂系统还包括串联机械臂，并联平台搭载于串联机械臂的末端，图2是本申请实施例的坐标转换方法的流程图，如图2所示，获取参考坐标系与计算坐标系的第三转换关系包括如下步骤。
步骤S201：建立串联机械臂中各关节的关节坐标系。
串联机械臂的控制通常基于DH参数或改进的DH参数进行坐标系的转换。相连接的两个关节为相邻关节。相邻两个关节的关节坐标系的变换通常采用DH参数或改进的DH参数来表示。以DH参数为例，相邻两个关节坐标系通过绕Z轴旋转θ、平移d后，再绕X轴旋转α、平移a，就能够相互重合，上述的θ、d、α和a即为DH参数。由此可知，如果DH参数越简洁，则相邻两个关节坐标系的转换越简单。
为了简化DH参数，在本实施例中，旋转关节的关节坐标系的Z轴沿旋转轴设置，移动关节的关节坐标系的Z轴沿移动方向设置，参考坐标系与各关节的关节坐标系同为左手系或右手系，且当旋转关节之前的关节为移动关节时，旋转关节的关节坐标系的原点与该移动关节的关节坐标系的原点重合。
在串联机械臂中，在大多数情况下旋转关节在接收到转角为0或2π的指令时，可能不需要区分二者，而是根据预先的设定保持不旋转或者以设定方向旋转2π。但在一些情况下，需要对这两个转角进行区分。在需要对0或2π转角进行区分的情形下，旋转关节的DH参数中Z轴的旋转角度不为0或2π，以避免混淆0或2π的旋转角度。
步骤S202：获取串联机械臂中首个关节的关节坐标系与参考坐标系的DH参数，确定参考坐标系与首个关节的关节坐标系的转换关系
Figure PCTCN2020141274-appb-000006
其中，首个关节是与基座直接连接的关节，DH参数为传统的DH参数或改进的DH参数。
步骤S203：获取串联机械臂中第i个关节的关节坐标系与第i-1个关节的关节坐标系的DH参数，确定第i-1个关节的关节坐标系与第i个关节的关节坐标系的转换关系
Figure PCTCN2020141274-appb-000007
其中，i＝2,3,4,…,N；N为串联机械臂的关节的总数量。
步骤S204：根据转换关系
Figure PCTCN2020141274-appb-000008
和转换关系
Figure PCTCN2020141274-appb-000009
确定参考坐标系与第N个关节的关节坐标系的转换关系
Figure PCTCN2020141274-appb-000010
即为第三转换关系，其中，第N个关节的关节坐标系与计算坐标系完全重合。
在建立各关节的关节坐标系之后，就可以依次获得相邻关节之间的DH参数，并根据DH参数，确定机械臂系统的参考坐标系到串联机械臂的计算坐标系之间的转换关系。
其中，根据DH法则，第i-1关节的坐标到第i关节的坐标的齐次变换被构造为具有两个旋转和两个变换的序列，采用矩阵可表示如下：
Figure PCTCN2020141274-appb-000011
其中，i＝2,3,4,…,N；N为串联机械臂的旋转关节和移动关节的总数量。串联机械臂的第1个关节的DH参数是表示的该第一个关节与参考坐标系之间的坐标系的转换，记为
Figure PCTCN2020141274-appb-000012
则参考坐标系与第1个关节的关节坐标系的转换关系：
Figure PCTCN2020141274-appb-000013
可见，该变换关系与第i-1关节的坐标到第i关节的坐标的齐次变换形式完全相同。
在得到
Figure PCTCN2020141274-appb-000014
与
Figure PCTCN2020141274-appb-000015
之后，从第0个坐标系(参考坐标系)到第N关节的关节坐标系的转换矩阵可表示为：
Figure PCTCN2020141274-appb-000016
其中，第N个关节为末端关节。
上述步骤S204中确定的
Figure PCTCN2020141274-appb-000017
表示的就是参考坐标系与计算坐标系之间的坐标转换关系，根据该转换关系就能够实现参考坐标系与计算坐标系之间的坐标转换。
下面通过优选实施例对本申请实施例进行描述和说明。
图3是本申请优选实施例提供的机械臂系统的结构示意图，如图3所示的机械臂系统包括串联机械臂，该串联机械臂依次包括移动关节1、旋转关节2、移动关节3、旋转关节4、旋转关节5、移动关节6、旋转关节7、移动关节8、旋转关节9和移动关节10，此外，该机械臂系统还包括与移动关节1固连的基座11。图4是本申请优选实施例提供的机械臂系统的参考坐标系和关节坐标系的示意图。参考图4，该优选实施例的并联平台的主从映射方法包括如下步骤。
步骤1：依照世界坐标系的规则在串联机械臂的基座处建立参考坐标系，以及各关节的关节坐标系。
参考坐标系F 0-X 0Y 0Z 0坐标系原点F 0固连于机械臂基座处，Z 0轴由F 0指向移动关节1，Y 0轴由基座F 0点指向串联机械臂，X 0轴指向符合右手坐标系。
移动关节1的关节坐标系L 1-X 1Y 1Z 1的原点L 1固连在移动关节 1上，各坐标轴的指向和参考坐标系的对应轴指向相同。
旋转关节2的关节坐标系R 2-X 2Y 2Z 2的原点R 2固连在旋转关节2上且与L 1重合，Z 2指向和Z 1轴指向相同，X 2轴和Y 2轴的指向分别与X 1轴和Y 1轴指向相反。
移动关节3的关节坐标系L 3-X 3Y 3Z 3原点L 3固连在移动关节3上，Z 3轴由L 1点指向L 3点，X 3轴和Y 3轴分别与X 2轴和Z 2轴指向相同。
旋转关节4的关节坐标系R 4-X 4Y 4Z 4原点R 4固连在旋转关节4上且与L 3点重合(图4中为清晰标明移动关节3的关节坐标系和旋转关节4的关节坐标系将L 3和R 4分开标出，下同)，Z 4轴指向和Y 3轴指向相反，初始时，X 4轴和Y 4轴指向分别与X 3轴和Z 3轴指向相反。
旋转关节5的关节坐标系R 5-X 5Y 5Z 5原点R 5固连在旋转关节5上，Z 5轴方向和Z 4轴方向相同，初始时，X 5轴和Y 5轴指向分别与X 4轴和Y 4轴指向相反。
移动关节6的关节坐标系L 6-X 6Y 6Z 6原点L 6固连在移动关节6上，Z 6轴由R 5点指向L 6点，X 6轴和Y 6轴指向分别与X 5轴和Z 5轴指向相同。
旋转关节7的关节坐标系R 7-X 7Y 7Z 7原点R 7固连在旋转关节7上且和L 6点重合，初始时，Z 7轴和Y 7轴的指向分别与Y 6轴和X 6轴的指向相反，X 7轴和Z 6轴的指向相同。
移动关节8的关节坐标系L 8-X 8Y 8Z 8的原点L 8固连在移动关节8上，Z 8轴由L 8点指向R 7点，X 8和Y 8轴的指向分别与X 7和Y 7轴的指向相同。
旋转关节9的关节坐标系R 9-X 9Y 9Z 9的原点R 9点固连在旋转关节9上且和L 8点重合，Z 9轴的方向与Y 8轴的方向相反，初始时，X 9轴的方向与Z 8轴的方向相反，Y 9轴的方向与X8轴的方向相同。
移动关节10的关节坐标系L 10-X 10Y 10Z 10的原点L 10固连在移动关节10上，Z 10轴由R 9点指向L 10点，X 10轴和Y 10轴的指向分别与X 9轴和Z 9轴的指向相同。
F 0R 2的长度为l 1，R 2R 4的长度为l 2，R 4R 5的长度为l 3，R 5R 7的长度为l 4，R 7R 9的长度为l 5，R 9L 10的长度为l 6，点L 1、R 2、L 3、R 4、R 5、L 6和R 7位于同一水平面上。
步骤2：获取DH参数，并计算参考坐标系到串联机械臂的末端关节的转换关系。
DH参数如表1所示。在表1中，为了避免混淆旋转关节的旋转角度0和2π，DH参数中，Z轴的旋转角度避开了0和2π两个位置。
表1图4所示的串联机械臂的DH参数表
Figure PCTCN2020141274-appb-000018
解算Stewart计算坐标系到参考坐标系的转换矩阵，即移动关节坐标系L 10-X 10Y 10Z 10到参考坐标系F 0-X 0Y 0Z 0的转换矩阵与逆矩阵。
根据机器人正运动学可知两相邻关节之间的转换矩阵为：
Figure PCTCN2020141274-appb-000019
从第m关节(包含m关节的自由度)到第n关节的转换矩阵可表示为：
Figure PCTCN2020141274-appb-000020
可解算得单条串联机械臂从基座到Stewart平台静平台的转换矩阵
Figure PCTCN2020141274-appb-000021
即参考坐标系到Stewart计算坐标系的转换矩阵，命名为T trans_mach_st，而Stewart计算坐标系到参考坐标系的转换矩阵则为逆矩阵
Figure PCTCN2020141274-appb-000022
步骤3：根据转换矩阵和转换矩阵的逆矩阵进行参考坐标系与Stewart计算坐标系的坐标转换。
本申请实施例通过建立用户坐标系，以简化主从控制的运动映射。在机械臂系统为单臂工作的情况下，本优选实施例的并联平台的主从映射方法还包括如下步骤。
步骤S205：建立从用户坐标系，其中，从用户坐标系的XY坐标平面平行于参考坐标系的XY平面，且从用户坐标系的原点与计算坐标系的原点重合。
步骤S206：获取用户输入的视角值，并根据视角值和参考坐标系与计算坐标系之间的转换关系，确定从用户坐标系与参考坐标系之间的转换关系。
在步骤S205建立的从用户坐标系的XY坐标平面绕Z轴旋转角度为视角值。单臂工作时，视角值由用户根据视角自行输入，命名为θ theta_mach_user，根据用户坐标的定义方式，可得到从用户坐标系相对于参考坐标系的转换矩阵：
Figure PCTCN2020141274-appb-000023
其中，
Figure PCTCN2020141274-appb-000024
表示上述
Figure PCTCN2020141274-appb-000025
中第1行第4列的数据。
图5是本申请优选实施例提供的机械臂系统双臂工作时从用户坐标系的示意图，如图5所示，参考坐标系为O 0-X 0Y 0Z 0，Stewart计算坐标系为O S-X SY SZ S，从用户坐标系为O P-X PY PZ P。
在机械臂系统为双臂工作的情况下，本优选实施例的并联平台的主从映射方法还包括如下步骤。
步骤S207：建立第一串联机械臂的第一从用户坐标系和第二串联机械臂的第二从用户坐标系，其中，第一从用户坐标系的X轴方向与第二从用户坐标系的X轴方向相同且共线，且第一从用户坐标系的原点与第一串联机械臂的计算坐标系的原点重合，第二从用户坐标系的原点与第二串联机械臂的计算坐标系的原点重合。
以参考坐标系为基准面向被操作对象为串联机械臂向前方向，左手侧为左串联机械臂，右手侧为右串联机械臂。根据单臂转换矩阵设定方法分别输入左右臂的DH参数，可得到左右臂各自的转换矩阵T trans_mach_st_left和T trans_mach_st_right，两只串联机械臂静平台原点在参考坐标系下的坐标为：
C coord_mach_st_left＝[T trans_mach_st_left(1，4) T trans_mach_st_left(2，4) T trans_mach_st_left(3，4) 1] T；
C coord_mach_st_right＝[T trans_mach_st_right(1，4) T trans_mach_st_right(2，4) T trans_mach_st_right(3，4) 1] T。
此时规定，两只串联机械臂各自从用户坐标系的X轴的方向相同且共线，正方向为C coord_mach_st_left指向C coord_mach_st_right点。
步骤S208：确定第一从用户坐标系的X轴方向与参考坐标系的X轴方向的夹角，并根据该夹角和参考坐标系与每条串联机械臂的计算坐标系的转换关系，确定参考坐标系分别与第一从用户坐标系以及第二从用户坐标系的第二转换关系。
X轴和参考坐标系下的夹角θ theta_mach_user可由下式计算得到：
Figure PCTCN2020141274-appb-000026
其中，θ＝atan2(y,x)，为MATLAB或C语言库中的内置函数。从而左右串联机械臂对应的从用户坐标系的转换矩阵可由单臂转换矩阵相似的方法得出：
Figure PCTCN2020141274-appb-000027
Figure PCTCN2020141274-appb-000028
获得从用户坐标系相对于参考坐标系的转换矩阵T trans_mach_user，即可得到参考坐标系相对于从用户坐标系的转换矩阵
Figure PCTCN2020141274-appb-000029
在已获得参考坐标系到从用户坐标系和参考坐标系到Stewart计算坐标系的情况下，从用户坐标系到Stewart计算坐标系的转换矩阵T trans_user_st可通过以下公式计算得到：
T trans_user_st＝T trans_mach_user -1·T trans_mach_st。
从Stewart计算坐标系到从用户坐标系的转换矩阵则为逆矩阵
Figure PCTCN2020141274-appb-000030
在上述实施例中，机械臂系统单臂工作时，通过用户输入的视角值来确定从用户坐标系与参考坐标系之间的转换关系；机械臂系统双臂工作时，由于每条单臂都建立了从用户坐标系，因此，在将两个从用户坐标系的X轴方向设置为相同且共线之后，可以将从用户坐标系的X轴方向与参考坐标系的X轴方向的夹角作为视角值，进而确定每条单臂的从用户坐标系与参考坐标系之间的转换关系。
在获得从用户坐标系与参考坐标系之间的转换关系之后，即可根据参考坐标系与计算坐标系之间的转换关系，以及从用户坐标系与参考坐标系之间的转换关系，确定从用户坐标系到串联机械臂的计算坐标系之间的转换关系。
图6是本申请优选实施例的并联平台的主从映射方法的示意图，如图6所示，左图为被动臂，右图为主操作手。参考图6，具体而言，本优选实施例提供的并联平台的主从映射方法可以包括如下步骤。
步骤1：操作者握持主操作手时刻起，至操作者的手离开主操作手为止，视为一个工作周期T。操作者握持主操作手开始操作时刻即T(0)时刻，将该时刻的主操作手的位置坐标设为原点M0(0，0，0)；该时刻动平台上安装的操作器械末端点在从用户坐标系的位置坐标为S0(X0，Y0，Z0)，系统计算并保存S0(X0，Y0，Z0)作为已知值，记为C coord_now_user。
步骤2：在工作周期内的任一时刻t，设主手末端点的位置坐标为M t(X mt，Y mt，Z mt)，记为C coord_offset_mas：
Figure PCTCN2020141274-appb-000031
此时器械末端点在从用户坐标系中运动目标点位置坐标S t(X t，Y t，Z t)可通过M t(X mt，Y mt，Z mt)经位移比例缩放系数K 0获得：
Xt＝X 0+K 0*X mt；
Yt＝Y 0+K 0*Y mt；
Zt＝Z 0+K 0*Z mt。
基于T(0)时刻器械末端点在从用户坐标系的位置坐标为S 0(X 0，Y 0，Z 0)，在每一个运动执行周期，主手会发送当下的坐标M t(X mt，Y mt，Z mt)来解算该时刻器械末端点在从用户坐标系下的坐标S t(X t，Y t，Z t)，记做C coord_new_user：
C coord_new_user＝C coord_now_user+K 0×C coord_offset_mas。
步骤3：将器械末端点在从用户坐标系下的坐标S t(X t，Y t，Z t)通过从用户坐标系到Stewart计算坐标系的转换矩阵转换到Stewart计算坐标系下，记做C coord_new_st：
C coord_new_st＝T trans_st_user·C coord_new_user。
其中，T trans_st_user为从用户坐标系到Stewart计算坐标系的转换矩阵。
步骤4：已知器械末端点在Stewart计算坐标系下的坐标，即可通过Stewart平台的逆运动学解算出平台各个关节的运动量，完成主从运动的映射。
在其中的一些实施例中，预设位移比例系数K 0可调节，该值可以为大于1的数值，也可以为小于1的数值；其中，在，预设位移比例系数K 0为小于1的数值时，可以实现对被动臂的高精度控制，并消除操作过程中操作者手部的抖动可提高操作可靠性。
在上述的主从映射方法中采用了相对零位的运动映射控制，避免了误差的累积，也提高了控制精度和操作安全性。
本实施例还提供了一种机械臂系统，包括并联平台、主操作手、存储器和控制器，并联平台包括静平台、动平台和多个设置在静平台和动平台之间的伸缩杆，存储器中存储有计算机程序，控制器被设置为运行计算机程序以执行上述实施例中的任意一种并联平台的主从映射方法。
另外，结合上述实施例中的方法，本申请实施例还提供一种计算机可读存储介质来实 现。该计算机可读存储介质上存储有计算机程序指令；该计算机程序指令被处理器执行时实现上述实施例中的任意一种并联平台的主从映射方法。
需要说明的是，本实施例中的具体示例可以参考上述实施例及可选实施方式中所描述的示例，本实施例在此不再赘述。
以上所述实施例的各技术特征可以进行任意的组合，为使描述简洁，未对上述实施例中的各个技术特征所有可能的组合都进行描述，然而，只要这些技术特征的组合不存在矛盾，都应当认为是本说明书记载的范围。
以上所述实施例仅表达了本申请的几种实施方式，其描述较为具体和详细，但并不能因此而理解为对申请专利范围的限制。应当指出的是，对于本领域的普通技术人员来说，在不脱离本申请构思的前提下，还可以做出若干变形和改进，这些都属于本申请的保护范围。因此，本申请专利的保护范围应以所附权利要求为准。

Claims (11)

  1. 一种并联平台的主从映射方法，应用于机械臂系统，所述机械臂系统包括并联平台和主操作手，所述并联平台包括静平台、动平台和多个设置在所述静平台和所述动平台之间的伸缩杆，其特征在于，所述并联平台的主从映射方法包括：
    在所述静平台建立并联平台的计算坐标系，在所述静平台建立从用户坐标系以及在所述主操作手建立主用户坐标系，其中，所述计算坐标系与所述从用户坐标系的原点重合，且所述从用户坐标系和所述主用户坐标系的Z轴均与参考坐标系的Z轴平行；
    获取所述从用户坐标系与所述计算坐标系的第一转换关系；
    将所述主操作手的末端在所述主用户坐标系内的位移量按照设定比例系数映射到所述动平台的末端在所述从用户坐标系内，得到所述动平台的末端在所述从用户坐标系内的第一目标位置；
    根据所述第一转换关系和所述第一目标位置，确定所述动平台的末端在所述计算坐标系内的第二目标位置；
    根据所述第二目标位置，通过逆运动学算法解得所述并联平台的各伸缩杆的运动量，并根据各所述伸缩杆的运动量控制所述并联平台的运动。
  2. 根据权利要求1所述的并联平台的主从映射方法，其特征在于，所述获取所述从用户坐标系与所述计算坐标系的第一转换关系包括：
    获取所述参考坐标系与所述从用户坐标系的第二转换关系，以及获取所述参考坐标系与所述计算坐标系的第三转换关系；
    根据所述第二转换关系和所述第三转换关系，确定所述第一转换关系。
  3. 根据权利要求2所述的并联平台的主从映射方法，其特征在于，所述参考坐标系为所述机械臂系统的基座坐标系；所述机械臂系统还包括串联机械臂，所述并联平台搭载于所述串联机械臂的末端；其中，所述获取所述参考坐标系与所述计算坐标系的第三转换关系包括：
    建立所述串联机械臂中各关节的关节坐标系；
    获取所述串联机械臂中首个关节的关节坐标系与所述参考坐标系的DH参数，确定所述参考坐标系与所述首个关节的关节坐标系的转换关系
    Figure PCTCN2020141274-appb-100001
    其中，所述首个关节是与基座直接连接的关节，所述DH参数为传统的DH参数或改进的DH参数；
    获取所述串联机械臂中第i个关节的关节坐标系与第i-1个关节的关节坐标系的DH参数，确定第i-1个关节的关节坐标系与第i个关节的关节坐标系的转换关系
    Figure PCTCN2020141274-appb-100002
    其中，i＝2,3,4,…,N；N为所述串联机械臂的关节的总数量；
    根据转换关系
    Figure PCTCN2020141274-appb-100003
    和转换关系
    Figure PCTCN2020141274-appb-100004
    确定所述参考坐标系与第N个关节的关节坐标系的转换关系
    Figure PCTCN2020141274-appb-100005
    即为所述第三转换关系，其中，第N个关节的关节坐标系与所述计算坐标系完全重合。
  4. 根据权利要求3所述的并联平台的主从映射方法，其特征在于，所述串联机械臂包括旋转关节和移动关节；其中，所述旋转关节的关节坐标系的Z轴沿旋转轴设置，所述移动关节的关节坐标系的Z轴沿移动方向设置，所述参考坐标系与各关节的关节坐标系同为左手系或右手系，且当旋转关节之前的关节为移动关节时，所述旋转关节的关节坐标系的原点与该移动关节的关节坐标系的原点重合。
  5. 根据权利要求4所述的并联平台的主从映射方法，其特征在于，所述串联机械臂中旋转关节的DH参数中Z轴的旋转角度不为0或2π。
  6. 根据权利要求2所述的并联平台的主从映射方法，其特征在于，所述获取所述参考坐标系与所述从用户坐标系的第二转换关系包括：
    获取用户相对于所述机械臂系统的视角值；
    根据所述视角值和所述第三转换关系，确定所述参考坐标系与所述从用户坐标系的第二转换关系。
  7. 根据权利要求6所述的并联平台的主从映射方法，其特征在于，在所述机械臂系统单臂工作的情况下，所述视角值基于用户输入的配置信息确定。
  8. 根据权利要求2所述的并联平台的主从映射方法，其特征在于，在所述机械臂系统中第一串联机械臂和第二串联机械臂同时工作的情况下，所述获取所述参考坐标系与所述从用户坐标系的第二转换关系包括：
    建立所述第一串联机械臂的第一从用户坐标系和所述第二串联机械臂的第二从用户坐标系，其中，所述第一从用户坐标系的X轴方向与所述第二从用户坐标系的X轴方向相同且共线，且所述第一从用户坐标系的原点与所述第一串联机械臂的计算坐标系的原点重合，所述第二从用户坐标系的原点与所述第二串联机械臂的计算坐标系的原点重合；
    确定所述第一从用户坐标系的X轴方向与所述参考坐标系的X轴方向的夹角，并根据该夹角和所述参考坐标系与每条串联机械臂的计算坐标系的转换关系，确定所述参考坐标系分别与所述第一从用户坐标系以及所述第二从用户坐标系的第二转换关系。
  9. 一种机械臂系统，包括并联平台、主操作手、存储器和控制器，所述并联平台包括静平台、动平台和多个设置在所述静平台和所述动平台之间的伸缩杆，其特征在于，所述存储器中存储有计算机程序，所述控制器被设置为运行所述计算机程序以执行权利要求1至8中 任一项所述的并联平台的主从映射方法。
  10. 根据权利要求9所述的机械臂系统，其特征在于，所述机械臂系统还包括串联机械臂，所述并联平台搭载于所述串联机械臂的末端。
  11. 一种存储介质，其特征在于，所述存储介质中存储有计算机程序，其中，所述计算机程序被设置为运行时执行权利要求1至8中任一项所述的并联平台的主从映射方法。
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