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CN114055467A - Space pose online simulation system based on five-degree-of-freedom robot - Google Patents

Space pose online simulation system based on five-degree-of-freedom robot Download PDF

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CN114055467A
CN114055467A CN202111275418.XA CN202111275418A CN114055467A CN 114055467 A CN114055467 A CN 114055467A CN 202111275418 A CN202111275418 A CN 202111275418A CN 114055467 A CN114055467 A CN 114055467A
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end effector
robot
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CN114055467B (en
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丁飞
张海涛
庄衡衡
章华涛
马海蓉
张美楠
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Nanjing University of Posts and Telecommunications
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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
    • B25J9/1602—Programme controls characterised by the control system, structure, architecture
    • B25J9/161—Hardware, e.g. neural networks, fuzzy logic, interfaces, processor
    • 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
    • B25J9/1612—Programme controls characterised by the hand, wrist, grip control
    • B—PERFORMING OPERATIONS; TRANSPORTING
    • B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
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    • 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
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Abstract

本发明公开了一种基于五自由度机器人的空间位姿在线仿真系统，包括以下步骤：S1，执行机器人位姿初始化调整业务流程；S2，设置机器人末端执行器的目标位姿；S3，调用逆向运动学算法，计算机器人的多电机驱动单元的目标调整量；S4，驱动末端执行器向目标位姿调整；S5，调用正向运动学算法确定末端执行器调整后的位姿；S6，比较末端执行器调整后的位姿与目标位姿之间的相对误差是否超过预设的误差范围，若超过，则返回步骤S2，直至末端执行器调整后的位姿与目标位姿之间的相对误差在预设的误差范围内。本发明基于机器人控制的运动学方法，简化了正向运动学的推导求解方法，使得对机器人运动学建模时，可灵活规定各关节轴的轴向定义。

Figure 202111275418

The invention discloses an on-line simulation system for spatial pose and attitude based on a five-degree-of-freedom robot, comprising the following steps: S1, executing the robot pose initialization adjustment business process; S2, setting the target pose of the robot end effector; S3, calling the reverse direction Kinematics algorithm, calculates the target adjustment amount of the multi-motor drive unit of the robot; S4, drives the end effector to adjust to the target pose; S5, calls forward kinematics algorithm to determine the adjusted pose of the end effector; S6, compares the end effector Whether the relative error between the adjusted pose of the actuator and the target pose exceeds the preset error range, if so, return to step S2 until the relative error between the adjusted pose of the end effector and the target pose within the preset error range. Based on the kinematics method of robot control, the invention simplifies the derivation and solution method of forward kinematics, so that when modeling the kinematics of the robot, the axial definition of each joint axis can be flexibly specified.

Figure 202111275418

Description

Space pose online simulation system based on five-degree-of-freedom robot
Technical Field
The invention belongs to the technical field of robot control, and particularly relates to a five-degree-of-freedom robot-based space pose online simulation system.
Background
With the development of advanced manufacturing technology in China, the multi-degree-of-freedom robot has the advantages of automation, high efficiency and intelligence, and can be widely applied to the fields of high-end manufacturing, space teleoperation, intelligent autonomous systems and the like. The motion control of the multi-degree-of-freedom robot can influence the in-place attitude to reach the working space and the target pointing accuracy, and the effective cooperation between the two can determine the working performance of the multi-degree-of-freedom robot. The common robot control methods mainly include two types: the first is a kinematic method for performing negative feedback control according to the deviation of an actual track and an expected track, the control rule of the method is simple and easy to implement, but good dynamic quality is difficult to guarantee, and larger control energy is needed; the second is a dynamics method for designing a nonlinear control law according to a dynamics model, which can realize good dynamic quality, but needs real-time dynamics calculation and is difficult to control in real time.
In the kinematics method of robot control, the main steps of the derivation solution include: the method mainly comprises a DH coordinate system method, the robot needs to be subjected to kinematic modeling to obtain DH parameters, and the DH parameters are substituted into corresponding formulas to obtain the result. The solution method of inverse kinematics is mainly divided into two categories: closed-form solutions and numerical solutions. The method is suitable for the robot with the structure meeting Pieper criterion, namely, three adjacent joint axes of the robot are intersected in one point or three axes to be parallel, the solution is simple and fast, and the accurate solution of each joint of the robot can be solved. However, for robots with structures that do not meet the Pieper criterion, it is difficult to find a closed solution. By applying a numerical solution, a unique solution can be solved for a serial robot with any structure, the problem of singular form and position cannot be solved in the solving process, but the solving speed is slower than that of a closed solution, for example, when the solution is solved by adopting a Jacobi matrix iteration method, the solution generally needs to be iterated for many times to solve an accurate solution.
The simulation of the spatial pose of the robot can be realized by robot simulation software and the like, for example: a robot Toolbox is installed and used in Matlab, kinematic modeling is carried out on the robot, corresponding DH parameters are set, and a robot space pose simulation graph under different joint variables can be obtained.
In the existing kinematics method for robot control, a DH coordinate system method is generally adopted for solving forward kinematics, but the method is divided into a standard type and an improved type, the standard type and the improved type are greatly different, certain theoretical basis discrimination is required, and axial definitions of joint axes cannot be flexibly specified; when the inverse kinematics is solved by a Jacobian matrix iteration method in a numerical method, a Jacobian matrix J (q) can be used for linking differential movement delta v and differential rotation delta omega of the end effector when the end effector moves from a current pose to a target pose with a joint differential motion vector delta q, but the representation methods of the differential motion are various, such as a rotation matrix, an Euler angle, a quaternion and the like, and different representation methods have certain influence on the solving efficiency. In addition, motion control and spatial pose simulation of the robot are generally used as independent functional modules to respectively execute functions of coordinating motion motors of the robot, driving the robot to move and analyzing the motion pose of the robot in the motion process.
Chinese patent publication No. CN110549334A discloses a control method for a four-degree-of-freedom robot arm, which is implemented based on a control system, and the control system is implemented by using a three-level control system and based on a control architecture of an upper computer, a motion controller and a bottom controller. After the upper computer sends pose information and a motion mode command to the motion controller, the motion controller automatically completes path planning and kinematics calculation of the mechanical arm to obtain a planning result, and the planning result is sent to the bottom controller to control the servo motor to move. The command state, the motor state, the driver state, the position, the speed and other information can be fed back in real time. And the system has control universality and can be suitable for mechanical arm configurations with different configurations. The speed look-ahead function, the fault-tolerant/protection mechanism and the hardware protection function are provided, so that the operation process of the mechanical arm is more stable, smooth and safe. The forward kinematics model of the robot is solved by the improved DH coordinate system method, the axial definitions of all joint axes cannot be flexibly specified, and the solving efficiency of the inverse kinematics is low.
Disclosure of Invention
The invention aims to solve the problems in the prior art, provides a five-degree-of-freedom robot-based space pose online simulation system, simplifies the solving method of forward kinematics on the premise of ensuring the solving accuracy of the forward kinematics and the reverse kinematics, enables the kinematics modeling to flexibly stipulate the axial definition of each joint axis, compares the representation methods of various differential movements, improves the efficiency of solving the reverse kinematics by using a Jacobian matrix, designs and realizes a five-degree-of-freedom robot motion control and space pose collaborative simulation system based on a kinematics calibration method, and realizes the integration of multifunctional modules.
In order to achieve the purpose, the invention adopts the technical scheme that:
a space pose online simulation system based on a five-degree-of-freedom robot comprises a control side and a simulation side, wherein the control side is connected with a multi-motor driving unit of the robot, and the simulation side is synchronously connected with the control side;
the control side includes:
the initialization module is used for carrying out initialization adjustment on the pose of the robot end effector;
the target pose setting module is used for setting the target pose of the robot end effector;
the data processing module is used for calling a reverse kinematics algorithm to calculate the target adjustment amount of each motor driving unit when the robot end effector is adjusted to the target pose, and calling a forward kinematics algorithm to calculate the pose of the robot end effector after adjustment;
the motor cooperative control module is used for controlling each motor driving unit to adjust the pose of the robot end effector according to the calculated target adjustment amount;
the initialization module, the target pose setting module and the motor cooperative control module are respectively connected with the data processing module;
triggering pose feedback when the relative error between the adjusted pose and the target pose exceeds a preset error magnitude, and calling a reverse kinematics algorithm again by the data processing module according to the current pose and the target pose of the adjusted robot end effector to calculate the target adjustment amount of each motor driving unit when the robot end effector is adjusted to the target pose until the relative error between the adjusted pose and the target pose does not exceed the preset error magnitude;
the simulation side is used for carrying out data synchronization on the business process of the control side, carrying out online simulation on the stage pose in the robot pose adjustment process, and finally carrying out error check and evaluation on the target pose of the robot end effector.
Specifically, the simulation method of the simulation system includes the following steps:
s1, performing initialization adjustment on the current pose of the robot end effector, and simultaneously performing online synchronous simulation on the current pose of the robot end effector on a simulation side;
s2, setting a target pose of the robot end effector;
s3, calling a reverse kinematics algorithm according to the current pose and the target pose of the robot end effector, and calculating the target adjustment amount of each motor driving unit of the robot;
s4, driving the robot end effector to adjust to a target pose according to the target adjustment amount, and simultaneously carrying out online simulation on the staged pose in the pose adjustment process of the robot end effector at the simulation side;
s5, calling a forward kinematics algorithm according to the current pose and the target adjustment quantity of the robot end effector, and determining the adjusted pose of the end effector; simultaneously, error checking and evaluation are carried out on the target pose of the robot end effector at the simulation side;
and S6, comparing whether the relative error between the pose adjusted by the end effector and the target pose exceeds a preset error magnitude, if so, executing pose feedback, returning to the step S3, substituting the adjusted current pose into the step S3 to obtain a new target adjustment amount, and adjusting the pose of the end effector of the robot according to the new target adjustment amount until the relative error between the pose adjusted by the end effector of the robot and the target pose does not exceed the preset error magnitude.
Specifically, the robot comprises a three-degree-of-freedom moving mechanism, a two-degree-of-freedom rotating mechanism and an end effector;
the three degrees of freedom of the moving mechanism are defined as movement along the X-axis, Y-axis and Z-axis, O, respectively1、O2And O3Joint nodes on the X-axis, Y-axis and Z-axis, Ox、OyAnd OzAre each O1、O2And O3A starting point of movement on the respective axis;
the two degrees of freedom of the rotating mechanism are defined as rotation about the X-axis and the Y-axis, O, respectively4And O5Joint nodes on the two rotating shafts respectively; c. C2、a4And b5Are each O1And O2，O3And O4，O4And O5Structural offset between adjacent joints; the end effector is arranged at a joint node O of the robot5And the end effector points to node P.
Further, a basic coordinate system XYZ and a terminal coordinate system X ' Y ' Z ' after five-degree-of-freedom transformation are defined in the structural model of the robot, the positive direction of each coordinate axis of the terminal coordinate system is defined as the direction of the positive direction of each coordinate axis of the basic coordinate system after five-degree-of-freedom movement and rotation transformation, and when the end effector is in the initial pose, the positive directions of each coordinate axis of the terminal coordinate system and the basic coordinate system are kept consistent; node O1、O2、O3、O4、O5The positions of P and P are expressed by adopting a basic coordinate system; defining the pointing direction of the end effector as the positive direction along the Z ' axis in the X ' Y ' Z ' of the end coordinate system, with the node P on the Z ' axis and the pointing direction of the end effector as the positive direction along the O axis5Point to point P direction.
Specifically, in step S3, the target position of the end effector is setIs arranged as
Figure BDA0003329276620000041
The formula of the inverse kinematics algorithm is as follows:
Figure BDA0003329276620000042
wherein, J (q)-1A pseudo-inverse matrix that is a Jacobian matrix of the robot; the delta v and the delta omega are respectively differential movement and differential rotation of the end effector when the end effector moves from the current pose to the target pose; q. q.s1、q2And q is3The displacement of the robot on the X axis, the Y axis and the Z axis of the moving joint axis, q4And q is5The rotation amounts of the robot on the X axis and the Y axis of the rotating joint axis are respectively;
Figure BDA0003329276620000043
and theta0Respectively representing the corresponding angles of the X axis and the Y axis of the rotating shaft when the ZYZ type Euler angle represents the current pose of the end effector;
Figure BDA0003329276620000044
and theta1Respectively representing the corresponding angles of the X axis and the Y axis of the rotating shaft when the ZYZ type Euler angle represents that the end effector is in the target pose;
targeting the end effector position
Figure BDA0003329276620000045
And substituting the formula to calculate a joint differential motion vector delta q, and multiplying the joint differential motion vector delta q by the scanning time interval of the motor to obtain the target adjustment quantity of the multi-motor driving unit of the robot.
Further, in step S5, the method for determining the adjusted pose of the end effector by invoking the forward kinematics algorithm includes:
after the robot is transformed by five degrees of freedom, the homogeneous transformation matrix between adjacent joint points
Figure BDA0003329276620000046
Comprises the following steps:
Figure BDA0003329276620000047
Figure BDA0003329276620000048
Figure BDA0003329276620000049
Figure BDA0003329276620000051
Figure BDA0003329276620000052
multiplying the matrixes in sequence to obtain an equivalent homogeneous transformation matrix of the end effector relative to a base coordinate system XYZ:
Figure BDA0003329276620000053
after the robot is subjected to five-degree-of-freedom movement and rotation transformation, the coordinates of the end effector are as follows:
O5＝(q1+a4,q2-b5 cos q5,c2+q3-b5 sin q4)
according to O5Point coordinates and O5And the position and posture of the end effector relative to the basic coordinate system can be determined by the pointing direction from the point to the point P.
Compared with the prior art, the invention has the beneficial effects that: (1) the kinematics method based on robot control simplifies the derivation solving method of forward kinematics, so that the axial definition of each joint axis can be flexibly specified when the kinematics of the robot is modeled; (2) the inverse kinematics solving method based on the Jacobian matrix iteration method can improve the solving efficiency of the inverse kinematics, and can optimize the pointing deviation of a motor in the initial adjustment stage by applying verification to the cooperative adjustment algorithm on the motion control side of the five-degree-of-freedom robot, so that the target pointing accuracy and the empirical work efficiency of the system are improved.
Drawings
Fig. 1 is a schematic flow diagram of a five-degree-of-freedom robot-based space pose online simulation system according to an embodiment of the present invention.
Fig. 2 is a schematic structural model diagram of a five-degree-of-freedom robot according to an embodiment of the present invention.
Fig. 3 is a schematic view of the angular velocity vector plane when euler angular rotation definition of the ZYZ type is used in the embodiment of the present invention.
Fig. 4 is a schematic vector plane diagram of angular velocities in a practical use scenario according to an embodiment of the present invention.
Fig. 5 is a diagram illustrating the effect of the collaborative simulation of the motion control and the spatial pose of the robot according to the embodiment of the present invention.
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the embodiment provides an online simulation system for a space pose based on a five-degree-of-freedom robot, which includes a control side and a simulation side, wherein the control side is connected with multiple motor driving units of the robot, and the simulation side is synchronously connected with the control side;
the control side includes:
the initialization module is used for carrying out initialization adjustment on the pose of the robot end effector;
the target pose setting module is used for setting the target pose of the robot end effector;
the data processing module is used for calling a reverse kinematics algorithm to calculate the target adjustment amount of each motor driving unit when the robot end effector is adjusted to the target pose, and calling a forward kinematics algorithm to calculate the pose of the robot end effector after adjustment;
the motor cooperative control module is used for controlling each motor driving unit to adjust the pose of the robot end effector according to the calculated target adjustment amount;
the initialization module, the target pose setting module and the motor cooperative control module are respectively connected with the data processing module;
triggering pose feedback when the relative error between the adjusted pose and the target pose exceeds a preset error magnitude, and calling a reverse kinematics algorithm again by the data processing module according to the current pose and the target pose of the adjusted robot end effector to calculate the target adjustment amount of each motor driving unit when the robot end effector is adjusted to the target pose until the relative error between the adjusted pose and the target pose does not exceed the preset error magnitude;
the simulation side is used for carrying out data synchronization on the business process of the control side, carrying out online simulation on the stage pose in the robot pose adjustment process, and finally carrying out error check and evaluation on the target pose of the robot end effector.
Specifically, the simulation method of the simulation system includes the following steps:
s1, performing initialization adjustment on the current pose of the robot end effector, and simultaneously performing online synchronous simulation on the current pose of the robot end effector on a simulation side;
s2, setting a target pose of the robot end effector;
s3, calling a reverse kinematics algorithm according to the current pose and the target pose of the robot end effector, and calculating the target adjustment amount of each motor driving unit of the robot;
s4, driving the robot end effector to adjust to a target pose according to the target adjustment amount, and simultaneously carrying out online simulation on the staged pose in the pose adjustment process of the robot end effector at the simulation side;
s5, calling a forward kinematics algorithm according to the current pose and the target adjustment quantity of the robot end effector, and determining the adjusted pose of the end effector; simultaneously, error checking and evaluation are carried out on the target pose of the robot end effector at the simulation side;
and S6, comparing whether the relative error between the pose adjusted by the end effector and the target pose exceeds a preset error magnitude, if so, executing pose feedback, returning to the step S3, substituting the adjusted current pose into the step S3 to obtain a new target adjustment amount, and adjusting the pose of the end effector of the robot according to the new target adjustment amount until the relative error between the pose adjusted by the end effector of the robot and the target pose does not exceed the preset error magnitude.
Further, initializing the robot end effector in step S1 includes the steps of:
s11, calling a driving interface of each motor driving unit, and establishing communication connection between 5 motors and the controller;
s12, reading the code value of the motor, and executing the return-to-original point operation on the hardware definition for the robot;
s13, calling a forward kinematics algorithm to calculate the current pose of the end effector;
and S14, calling an inverse kinematics algorithm to control the end effector to move to the initial working pose.
Specifically, the robot comprises a three-degree-of-freedom moving mechanism, a two-degree-of-freedom rotating mechanism and an end effector;
the three degrees of freedom of the moving mechanism are defined as movement along the X-axis, Y-axis and Z-axis, O, respectively1、O2And O3Joint nodes on the X-axis, Y-axis and Z-axis, Ox、OyAnd OzAre each O1、O2And O3A starting point of movement on the respective axis;
the two degrees of freedom of the rotating mechanism are defined as rotation about the X-axis and the Y-axis, O, respectively4And O5Respectively two rotating shaftsAn upper joint node; c. C2、a4And b5Are each O1And O2，O3And O4，O4And O5Structural offset between adjacent joints; the end effector is arranged at a joint node O of the robot5And the end effector points to node P, the starting angles of the two revolute joint axes are shown in fig. 2 (a).
Furthermore, for convenience of describing the direction of the end effector after five-degree-of-freedom movement and rotation transformation, a basic coordinate system XYZ and an end coordinate system X ' Y ' Z ' after five-degree-of-freedom transformation are defined in the structural model of the robot, the positive direction of each coordinate axis of the end coordinate system is defined as the direction of each coordinate axis of the basic coordinate system after five-degree-of-freedom movement and rotation transformation, and when the end effector is in an initial pose, the positive directions of the coordinate axes of the end coordinate system and the basic coordinate system are kept consistent; node O1、O2、O3、O4、O5The positions of P and P are expressed by adopting a basic coordinate system; defining the pointing direction of the end effector as the positive direction along the Z ' axis in the X ' Y ' Z ' of the end coordinate system, with the node P on the Z ' axis and the pointing direction of the end effector as the positive direction along the O axis5Point to point P direction. The structure adjustment of the five-degree-of-freedom robot is respectively driven by high-precision servo motors on respective motion axes, and the five-degree-of-freedom robot can move along positive and negative directions on the respective motion axes, and the positive direction of the motion is shown in figure 2 (a); the pose of the mechanical arm on the five degrees of freedom is adjusted through high-precision cooperative control of the 5 servo motors, so that the pose control and the precise alignment of the robot end effector are realized.
Specifically, in step S3, the inverse kinematics calculation is a process of solving the amount of relative motion between adjacent nodes by using the current pose and the target pose of the end effector.
The known speed can be regarded as differential motion in unit time, inverse kinematics is solved by utilizing a Jacobian matrix J (q), differential movement delta v and differential rotation delta omega of the end effector when the end effector moves from a current pose to a target pose are connected with a joint differential motion vector delta q, namely the Jacobian matrix is used as a conversion matrix of differential motion mapping of joint space to differential motion of the end effector space, and finally the joint differential motion vector delta q is multiplied by the scanning time interval of a motor to be used as the adjustment quantity of each joint.
When the target posture of the end effector is fixed, the direction vector of the target direction is constantly zero vector, the direction vector adjusted from the current direction to the target direction is the azimuth angle error between the target direction and the current direction, and the position of the target end effector is assumed to be
Figure BDA0003329276620000081
The differential shift per unit time is then:
Figure BDA0003329276620000082
given that angular velocities are described relative to the same coordinate system, they can be accumulated as free vectors, and thus by representing the differential rotation of each joint on the base coordinate system, the total amount of differential rotation of the end effector relative to the base coordinate system is determined by accumulation. In combination with the five-degree-of-freedom robot kinematics model of the present embodiment, in the case of using the rotation axis definition of the yz-type euler angle and not considering the Z-axis rotation of the last rotation axis, the total differential rotation amount of the end effector with respect to the base coordinate system is:
Figure BDA0003329276620000083
the transformation matrix B represents a transformation method when the attitude transformation of the end effector corresponds to the representation of a basic coordinate system, wherein the 1 st column and the 2 nd column respectively represent unit direction vectors of a Y axis and a Z axis corresponding to the rotation transformation;
Figure BDA0003329276620000084
Δθ＝θ1-θ0in the formula
Figure BDA0003329276620000085
And theta0Respectively showing the corresponding angles of the rotating shaft Z and the Y axis when the ZYZ type Euler angle is used for showing the pose of the current end effector,
Figure BDA0003329276620000086
and theta1The respective angles corresponding to the rotation axis Z and the Y axis when the position and attitude of the target end effector are expressed by the Euler angles of the ZYZ type.
For a five-degree-of-freedom robot, the jacobian matrix is a 6 × 5 matrix, where the first 3 rows represent the transfer ratio of the linear velocity of the end effector and the last 3 rows represent the transfer ratio of the angular velocity of the end effector, i.e.:
for the movement axis i, Z is generated on the end effectoriThe same linear velocity v, but an angular velocity of 0; namely:
Figure BDA0003329276620000087
in the formula: ziIs a representation of the unit vector of the mobile joint axis i relative to the base coordinate system.
For a rotational joint axis i, the linear velocity v produced at the end effector is the vector product, i.e.:
Figure BDA0003329276620000088
in the formula: o is5-OiRepresenting the origin of coordinates of the end effector relative to the revolute joint node OiIs represented in the base coordinate system.
For the rotational joint axis i, Z is generated on the end effectoriThe same angular velocity ω, i.e.:
Figure BDA0003329276620000091
for the kinematic model of the five-degree-of-freedom robot described in this embodiment, eachThe joint axes are respectively: x1、Y2、Z3、X4、Y5. Wherein, the first three are mobile joint shafts, the second two are rotary joint shafts, and then the Jacobian matrix of the five-degree-of-freedom robot is:
Figure BDA0003329276620000092
in summary, the expression is obtained:
Figure BDA0003329276620000093
in the formula, the joint differential motion vector Δ q ═ q1 q2 q3 q4 q5]TThe derived inverse kinematics formula is:
Figure BDA0003329276620000094
wherein, J (q)-1A pseudo-inverse matrix that is a Jacobian matrix of the robot; the delta v and the delta omega are respectively differential movement and differential rotation of the end effector when the end effector moves from the current pose to the target pose; q. q.s1、q2And q is3The displacement of the robot on the X axis, the Y axis and the Z axis of the moving joint axis, q4And q is5The rotation amounts of the robot on the X axis and the Y axis of the rotating joint axis are respectively;
Figure BDA0003329276620000095
and theta0Respectively representing the corresponding angles of the X axis and the Y axis of the rotating shaft when the ZYZ type Euler angle represents the current pose of the end effector;
Figure BDA0003329276620000096
and theta1Respectively showing the corresponding angles of the X axis and the Y axis of the rotating shaft when the end effector is in the target pose by using the ZYZ type Euler angle.
Hold the end onTarget position of vehicle
Figure BDA0003329276620000097
And substituting the formula to calculate a joint differential motion vector delta q, and multiplying the joint differential motion vector delta q by the scanning time interval of the motor to obtain the target adjustment quantity of the multi-motor driving unit of the robot.
Further, in step S5, the method for determining the adjusted pose of the end effector by invoking the forward kinematics algorithm includes:
the forward kinematics algorithm is a process of solving the pose of the end effector by combining the relative motion amount between adjacent joint points on the premise of knowing the initial position of each joint point, the structural offset between the adjacent joint points and other parameters; adjusting q on the X, Y and Z axes of the mobile joint respectively1，q2And q is3Respectively adjusting q on the X-axis and Y-axis of the rotary joint4And q is5The state model after the adjustment of the rotation amount and the five-degree-of-freedom transformation is shown in FIG. 2(b), and the homogeneous transformation matrix between the adjacent joint points
Figure BDA0003329276620000101
Comprises the following steps:
Figure BDA0003329276620000102
Figure BDA0003329276620000103
Figure BDA0003329276620000104
Figure BDA0003329276620000105
Figure BDA0003329276620000106
multiplying the matrixes in sequence to obtain an equivalent homogeneous transformation matrix of the end effector relative to a base coordinate system XYZ:
Figure BDA0003329276620000107
after the robot is subjected to five-degree-of-freedom movement and rotation transformation, the coordinates of the end effector are as follows:
O5＝(q1+a4,q2-b5 cos q5,c2+q3-b5 sin q4)
according to O5Point coordinates and O5And the position and posture of the end effector relative to the basic coordinate system can be determined by the pointing direction from the point to the point P.
The five-degree-of-freedom robot only has Rotx-RotyTwo rotational degrees of freedom, and in inverse kinematics solution, the rotation axis using Euler angles of the ZYZ type defines Rotz-Roty-RotzThree rotational degrees of freedom, without taking into account the last RotzIn the case of autorotation, z at which the angular velocity vector of the first two rotational degrees of freedom lies2y2The plane is shown as the dashed area in fig. 3, and in the actual usage scenario of the robot, the x of the angular velocity vector of the two rotational degrees of freedom is2y2The plane is shown in the dashed area in fig. 4. Due to the inconsistency of the two spatial angular velocity planes, the solution of the inverse kinematics is actually to move the Euler angular spatial angular velocity vector to x in the actual usage scene2y2The plane is projected to obtain the achievable approximate spatial angular velocity, which generally cannot move in place in one step, but the ideal direction can be obtained after multiple approximation, so that the result is not influenced under the condition of time and velocity allowance. In order to calculate the accurate direction adjustment amount at one time, the invention defines the direction of the rotating shaft by user, and the invention will calculate the accurate direction adjustment amount at one time
Figure BDA0003329276620000111
As a directional definition, it is consistent with the actual rotation axis.
In forward kinematics solution, the pointing angle definition of the end effector needs to be changed: the azimuth angle of the target pointing in the horizon coordinate is as follows:
Figure BDA0003329276620000112
the X axis is positive along the counterclockwise direction; the zenith distance of the target pointing in the horizon coordinate is as follows:
θ＝atan2(sin q5,cos q5)
the Y-axis is positive clockwise and is not calculated here with the acos () function because rotation through pi/2 produces a jump that is not easily handled.
In inverse kinematics solution, the method of calculating the differential rotation sum Δ ω of the end-effector relative to the base coordinate system is varied by rotation along the X-axis
Figure BDA0003329276620000113
Angle and rotation matrix of θ degrees along the Y axis:
Figure BDA0003329276620000114
the resulting equivalent rotation matrix is:
Figure BDA0003329276620000115
thus, the transformation matrix B in the formula is modified to:
Figure BDA0003329276620000116
in this embodiment, the simulation process of the spatial pose of the five-degree-of-freedom robot is as follows:
(1) the control program reads in the target pose of the end effector, calls a reverse velocity kinematics algorithm and calculates respective adjustment values of the motors on the five degrees of freedom.
(2) And transmitting control signals to the 5 servo motors through a standardized control interface.
(3) After the motor finishes moving, pose calibration is carried out, the program reads the code value on the wheel of the motor, a forward kinematics algorithm is called, and the pose of the end effector after adjustment is determined.
In the executing process, if the relative error between the adjusted pose and the target pose exceeds the preset error magnitude, pose feedback is triggered at the moment, and the operation is repeated until the pose of the end effector after adjustment meets the preset value.
The motion control and the collaborative simulation of the space pose are carried out on the five-degree-of-freedom robot, the end effector is adjusted to reach a preset initial working point through a motion control program, the parameters of the initial pose and the target pose of the end effector are shown in a table 1, a motion control and space pose collaborative simulation effect graph of the five-degree-of-freedom robot is shown in a figure 5, the positions of each joint node and each pointing node under three static poses of the robot are shown in the graph, wherein numbers 0, 1 and 2 on the pointing node P respectively represent the times of pose adjustment, the 0 th time represents the initial structure pose of the robot, and then the end effector calls a kinematics algorithm from the initial pose to the target pose and adjusts for 2 times. And calculating corresponding position errors and pointing errors after the 2 nd adjustment, wherein the error results are both 0, and the results show that the robot motion control and space pose simulation system is accurate and effective.
TABLE 1 parameters for end effector Start and target poses
Figure BDA0003329276620000121
By adopting the collaborative simulation method of the embodiment, the pointing deviation phenomenon of the five-degree-of-freedom motor in the initial adjustment stage is optimized, and the target pointing accuracy and the empirical work efficiency of the system are improved. The multi-motor multi-target robot system can be used for the reachable working space analysis and the structure optimization of a multi-degree-of-freedom robot.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that changes, modifications, substitutions and alterations can be made in these embodiments without departing from the principles and spirit of the invention, the scope of which is defined in the appended claims and their equivalents.

Claims (6)

1. The space pose online simulation system based on the five-degree-of-freedom robot is characterized by comprising a control side and a simulation side, wherein the control side is connected with a multi-motor driving unit of the robot, and the simulation side is synchronously connected with the control side;
the control side includes:
the initialization module is used for carrying out initialization adjustment on the pose of the robot end effector;
the target pose setting module is used for setting the target pose of the robot end effector;
the data processing module is used for calling a reverse kinematics algorithm to calculate the target adjustment amount of each motor driving unit when the robot end effector is adjusted to the target pose, and calling a forward kinematics algorithm to calculate the pose of the robot end effector after adjustment;
the motor cooperative control module is used for controlling each motor driving unit to adjust the pose of the robot end effector according to the calculated target adjustment amount;
the initialization module, the target pose setting module and the motor cooperative control module are respectively connected with the data processing module;
triggering pose feedback when the relative error between the adjusted pose and the target pose exceeds a preset error magnitude, and calling a reverse kinematics algorithm again by the data processing module according to the current pose and the target pose of the adjusted robot end effector to calculate the target adjustment amount of each motor driving unit when the robot end effector is adjusted to the target pose until the relative error between the adjusted pose and the target pose does not exceed the preset error magnitude;
the simulation side is used for carrying out data synchronization on the business process of the control side, carrying out online simulation on the stage pose in the robot pose adjustment process, and finally carrying out error check and evaluation on the target pose of the robot end effector.
2. The five-degree-of-freedom robot-based space pose online simulation system according to claim 1, wherein the simulation method of the simulation system comprises the following steps:
s1, performing initialization adjustment on the current pose of the robot end effector, and simultaneously performing online synchronous simulation on the current pose of the robot end effector on a simulation side;
s2, setting a target pose of the robot end effector;
s3, calling a reverse kinematics algorithm according to the current pose and the target pose of the robot end effector, and calculating the target adjustment amount of each motor driving unit of the robot;
s4, driving the robot end effector to adjust to a target pose according to the target adjustment amount, and simultaneously carrying out online simulation on the staged pose in the pose adjustment process of the robot end effector at the simulation side;
s5, calling a forward kinematics algorithm according to the current pose and the target adjustment quantity of the robot end effector, and determining the adjusted pose of the end effector; simultaneously, error checking and evaluation are carried out on the target pose of the robot end effector at the simulation side;
and S6, comparing whether the relative error between the pose adjusted by the end effector and the target pose exceeds a preset error magnitude, if so, executing pose feedback, returning to the step S3, substituting the adjusted current pose into the step S3 to obtain a new target adjustment amount, and adjusting the pose of the end effector of the robot according to the new target adjustment amount until the relative error between the pose adjusted by the end effector of the robot and the target pose does not exceed the preset error magnitude.
3. The five-degree-of-freedom robot-based space pose online simulation system according to claim 2, wherein the robot comprises a three-degree-of-freedom moving mechanism, a two-degree-of-freedom rotating mechanism and an end effector;
the three degrees of freedom of the moving mechanism are defined as movement along the X-axis, Y-axis and Z-axis, O, respectively1、O2And O3Joint nodes on the X-axis, Y-axis and Z-axis, Ox、OyAnd OzAre each O1、O2And O3A starting point of movement on the respective axis;
the two degrees of freedom of the rotating mechanism are defined as rotation about the X-axis and the Y-axis, O, respectively4And O5Joint nodes on the two rotating shafts respectively; c. C2、a4And b5Are each O1And O2，O3And O4，O4And O5Structural offset between adjacent joints; the end effector is arranged at a joint node O of the robot5And the end effector points to node P.
4. The five-degree-of-freedom robot-based space pose online simulation system according to claim 3, wherein a basic coordinate system XYZ and a terminal coordinate system X ' Y ' Z ' after five-degree-of-freedom transformation are defined in the structural model of the robot, the positive direction of each coordinate axis of the terminal coordinate system is defined as the direction of each coordinate axis of the basic coordinate system after five-degree-of-freedom movement and rotation transformation, and when the end effector is in the initial pose, the positive directions of each coordinate axis of the terminal coordinate system and the basic coordinate system are kept consistent; node O1、O2、O3、O4、O5The positions of P and P are expressed by adopting a basic coordinate system; defining the pointing direction of the end effector as the positive direction along the Z ' axis in the X ' Y ' Z ' of the end coordinate system, with the node P on the Z ' axis and the pointing direction of the end effector as the positive direction along the O axis5Point to point P direction.
5. The five-degree-of-freedom robot-based space position according to claim 4The attitude online simulation system is characterized in that, in step S3, the target position of the end effector is set to
Figure FDA0003329276610000021
The formula of the inverse kinematics algorithm is as follows:
Figure FDA0003329276610000022
wherein, J (q)-1A pseudo-inverse matrix that is a Jacobian matrix of the robot; the delta v and the delta omega are respectively differential movement and differential rotation of the end effector when the end effector moves from the current pose to the target pose; q. q.s1、q2And q is3The displacement of the robot on the X axis, the Y axis and the Z axis of the moving joint axis, q4And q is5The rotation amounts of the robot on the X axis and the Y axis of the rotating joint axis are respectively;
Figure FDA0003329276610000031
and theta0Respectively representing the corresponding angles of the X axis and the Y axis of the rotating shaft when the ZYZ type Euler angle represents the current pose of the end effector;
Figure FDA0003329276610000032
and theta1Respectively representing the corresponding angles of the X axis and the Y axis of the rotating shaft when the ZYZ type Euler angle represents that the end effector is in the target pose;
targeting the end effector position
Figure FDA0003329276610000033
And substituting the formula to calculate a joint differential motion vector delta q, and multiplying the joint differential motion vector delta q by the scanning time interval of the motor to obtain the target adjustment quantity of the multi-motor driving unit of the robot.
6. The five-degree-of-freedom robot-based on-line spatial pose simulation system according to claim 4, wherein in step S5, the method for determining the adjusted pose of the end effector by calling the forward kinematics algorithm comprises the following steps:
after the robot is transformed by five degrees of freedom, the homogeneous transformation matrix between adjacent joint points
Figure FDA0003329276610000034
Comprises the following steps:
Figure FDA0003329276610000035
Figure FDA0003329276610000036
multiplying the matrixes in sequence to obtain an equivalent homogeneous transformation matrix of the end effector relative to a base coordinate system XYZ:
Figure FDA0003329276610000037
after the robot is subjected to five-degree-of-freedom movement and rotation transformation, the coordinates of the end effector are as follows:
O5＝(q1+a4,q2-b5cosq5,c2+q3-b5sinq4)
according to O5Point coordinates and O5And the position and posture of the end effector relative to the basic coordinate system can be determined by the pointing direction from the point to the point P.
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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116494250A (en) * 2023-06-26 2023-07-28 极限人工智能(北京)有限公司 Mechanical arm control method, controller, medium and system based on speed compensation
CN116652968A (en) * 2023-07-24 2023-08-29 贵州翰凯斯智能技术有限公司 Multi-mechanical arm collaborative online simulation method and device, electronic equipment and storage medium
CN118386240A (en) * 2024-05-13 2024-07-26 顺德职业技术学院 A robot precision control method and related device

Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4999553A (en) * 1989-12-28 1991-03-12 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Method and apparatus for configuration control of redundant robots
CN106406277A (en) * 2016-09-23 2017-02-15 贵州珞石三盛科技有限公司 Robot Kinematics Parameter Error Optimization Compensation Method and Device
CN110549334A (en) * 2019-08-15 2019-12-10 大连大华中天科技有限公司 Control method of four-degree-of-freedom mechanical arm
CN111409077A (en) * 2020-05-09 2020-07-14 南京工程学院 Robot terminal multi-target pose approximation method based on joint angle compensation
CN111538949A (en) * 2020-07-10 2020-08-14 深圳市优必选科技股份有限公司 Redundant robot inverse kinematics solution method, device and redundant robot
CN111761586A (en) * 2020-07-22 2020-10-13 西安文理学院 A remote control robot based on big data
CN112084576A (en) * 2020-08-17 2020-12-15 盐城工学院 Vehicle-mounted mechanical arm kinematics modeling method
CN112659124A (en) * 2020-12-14 2021-04-16 南昌大学 Virtual simulation and control system based on Android system
CN113288429A (en) * 2021-05-07 2021-08-24 山东商业职业技术学院 Space registration and real-time navigation method of breast minimally invasive interventional operation robot

Patent Citations (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4999553A (en) * 1989-12-28 1991-03-12 The United States Of America As Represented By The Administrator Of The National Aeronautics And Space Administration Method and apparatus for configuration control of redundant robots
CN106406277A (en) * 2016-09-23 2017-02-15 贵州珞石三盛科技有限公司 Robot Kinematics Parameter Error Optimization Compensation Method and Device
CN110549334A (en) * 2019-08-15 2019-12-10 大连大华中天科技有限公司 Control method of four-degree-of-freedom mechanical arm
CN111409077A (en) * 2020-05-09 2020-07-14 南京工程学院 Robot terminal multi-target pose approximation method based on joint angle compensation
CN111538949A (en) * 2020-07-10 2020-08-14 深圳市优必选科技股份有限公司 Redundant robot inverse kinematics solution method, device and redundant robot
CN111761586A (en) * 2020-07-22 2020-10-13 西安文理学院 A remote control robot based on big data
CN112084576A (en) * 2020-08-17 2020-12-15 盐城工学院 Vehicle-mounted mechanical arm kinematics modeling method
CN112659124A (en) * 2020-12-14 2021-04-16 南昌大学 Virtual simulation and control system based on Android system
CN113288429A (en) * 2021-05-07 2021-08-24 山东商业职业技术学院 Space registration and real-time navigation method of breast minimally invasive interventional operation robot

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
李万莉;李宁;: "一种五自由度机械臂的运动学分析与逆运动学求解", 机电一体化, no. 11 *

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116494250A (en) * 2023-06-26 2023-07-28 极限人工智能(北京)有限公司 Mechanical arm control method, controller, medium and system based on speed compensation
CN116494250B (en) * 2023-06-26 2023-11-03 极限人工智能(北京)有限公司 Mechanical arm control method, controller, medium and system based on speed compensation
CN116652968A (en) * 2023-07-24 2023-08-29 贵州翰凯斯智能技术有限公司 Multi-mechanical arm collaborative online simulation method and device, electronic equipment and storage medium
CN118386240A (en) * 2024-05-13 2024-07-26 顺德职业技术学院 A robot precision control method and related device

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