Kinematics and performance analysis method of three-degree-of-freedom temporary support robot for coal mine tunnel

Abstract

The invention discloses a kinematics and performance analysis method for a three-degree-of-freedom temporary support robot for a coal mine tunnel, and belongs to the technical field of image processing, and the method comprises the steps: determining the framework composition of the robot, and calculating and verifying the degree of freedom of the robot based on a spiral theory and a corrected Grubler-Kutzbach formula; establishing an inverse kinematics equation based on a closed loop method, establishing a Jacobian matrix and performing singularity analysis, judging whether the structure of the robot has a singularity type, and analyzing the feasibility of the robot mechanism based on the singularity type; establishing a simulation model, and verifying the degree of freedom of the robot and the correctness of an inverse kinematics equation; the structure constraint condition and the structure parameter of the robot are obtained, the working space volume of the robot is obtained based on the structure constraint condition, and the structure parameter is adjusted based on the working space volume, so that the working space volume of the robot reaches the target threshold value. According to the invention, the reliability and accuracy of the temporary support of the coal mine tunnel are improved.

Description

Technical Field

[0001] The invention belongs to the technical field of control devices, and in particular relates to a kinematics and performance analysis method of a three-degree-of-freedom temporary support robot for a coal mine tunnel. Background Art

[0002] The intelligent development of tunneling work is slow. In the production process, contradictions such as "imbalance between mining and excavation" and "imbalance between excavation and support" are prominent, which are the main problems restricting the efficient and safe production of coal mines. Due to the small working space of coal mine tunnels, numerous equipment, complex geological conditions and other factors, the tunneling machine needs to advance and retreat frequently during permanent support operations, which seriously affects the work efficiency. Moreover, the environment of the tunnel is complex and changeable, and the height and angle of the roof often change. The existing temporary support equipment is difficult to adapt to the changing conditions of the roof.

[0003] For example, the Chinese patent application with publication number CN115788525A proposes a parallel gantry rolling walking temporary support robot, including a robot body, a roof support mechanism, and a support posture adjustment mechanism; the robot body includes a gantry frame mechanism, a crawler walking mechanism, a PU connection pair, a URR connection pair, a left ultrasonic distance sensor and a right ultrasonic distance sensor; the roof support mechanism includes a support frame, a crawler mechanism, a roller mechanism, and an ultrasonic distance sensor, and the support frame is connected to the gantry frame mechanism through a PU connection pair and a URR connection pair; the support posture adjustment mechanism includes an electric cylinder, a linear displacement sensor, and a pressure sensor, which are respectively connected to the gantry frame mechanism and the roof support mechanism through a universal joint.

[0004] The temporary support robot in the above-mentioned prior art can realize continuous, timely and stable support for the roof under complex geological conditions. However, under rapidly changing geological conditions, the response speed of the above-mentioned robot may not be sufficient to provide timely support, and the analysis and construction process of the robot mechanism is not described in detail. Therefore, the present invention proposes a temporary support robot that can adjust the position and posture of the moving platform in real time according to the changes in the height and angle of the roof to improve work efficiency. Summary of the invention

[0005] In order to solve the above problems, the present invention provides a kinematics and performance analysis method for a three-degree-of-freedom temporary support robot in a coal mine tunnel to solve the problems in the prior art.

[0006] In order to achieve the above-mentioned invention object, the present invention proposes a kinematics and performance analysis method of a three-degree-of-freedom temporary support robot for coal mine tunnels, comprising:

[0007] S1: Determine the framework components of the robot, the framework components include a gantry frame, a dynamic platform, a static platform, a driving branch and a constraint branch, establish a dynamic coordinate system and a static coordinate system on the dynamic platform and the static platform respectively, and calculate and verify the degree of freedom of the robot based on the screw theory and the modified Grubler-Kutzbach formula;

[0008] S2: establishing the inverse kinematics equation of the robot based on a closed loop method, establishing a Jacobian matrix, performing a singularity analysis on the Jacobian matrix, and determining whether the structure of the robot has a singular type. If not, the robot is a feasible mechanism;

[0009] S3: establishing a simulation model of the robot, and verifying the correctness of the degrees of freedom of the robot and the inverse kinematics equation based on the simulation model;

[0010] S4: Obtain structural constraints and structural parameters of the robot, obtain the workspace volume of the robot based on the structural constraints, and adjust the structural parameters based on the workspace volume so that the workspace volume of the robot reaches a target threshold.

[0011] Further, calculating and verifying the degrees of freedom of the robot comprises the following steps:

[0012] Determine all branches in the robot structure, represent each branch information in a motion spiral system to obtain first data information, perform an inverse operation on the motion spiral system to obtain second data information of the branch in an anti-spiral system, obtain third data information of the robot system in the anti-spiral system based on the second data information of all branches in the anti-spiral system, invert the third data information to obtain fourth data information of the robot system in the motion spiral system, and obtain the number of degrees of freedom of the robot based on the fourth data information, which is defined as the first number of degrees of freedom;

[0013] The second degree of freedom of the robot is calculated based on a first formula, wherein the first formula is: Where d is the order of the robot, n is the total number of all individual components in the robot, g is the total number of kinematic pairs of the robot, and f is the total number of kinematic pairs of the robot. i is the number of degrees of freedom of the i-th kinematic pair, v is the redundant constraint added to the robot, γ is the local degree of freedom of the robot, and if the first number of degrees of freedom is the same as the second number of degrees of freedom, the first number of degrees of freedom of the robot is verified successfully.

[0014] Furthermore, establishing the inverse kinematics equation of the robot comprises the following steps:

[0015] Obtain the first position information A of the bottom plate of the robot in the static coordinate system i (i=1, 2, 3, 4), and the second position information B' of the top plate in the moving coordinate system i (i=1, 2, 3, 4), based on the second formula, the second position information is converted into the third position information B in the static coordinate system i (i=1,2,3,4), the second formula is: B i =RB' i +P, R is the rotation Euler angle of the moving coordinate system relative to the static coordinate system, R= Wherein, α is the angle of rotation of the moving platform around the x-axis, β is the angle of rotation of the moving platform around the y-axis, and P is the position information of the coordinate origin of the moving platform of the robot in the static coordinate system. The coordinate representation of the robot rod is obtained based on the third formula, and the third formula is: i =P+Rb i -a i , where l i represents the direction vector of each rod in the robot, O is the origin of the coordinate system in the static coordinate system, a i represents the unit normal vector of the i-th revolute pair of the static platform, b i represents the unit normal vector of the ith rotation pair of the moving platform, and the inverse kinematics equation of the robot is obtained based on the fourth formula, which is: 1i 2 = l i 2 .

[0016] Furthermore, establishing the Jacobian matrix includes the following steps:

[0017] The mapping relationship between the input speed of the driving joint of the robot and the output speed of the moving platform is determined based on the inverse kinematics equation, and the mapping relationship is: in, is the input velocity of the driven joint, is the output speed of the moving platform, J q and J Q are the forward and inverse Jacobian matrices of the robot, Among them, J Lij (i=1, 2, 3, 4; j=1, 2, 3) is the partial derivative of the i-th output velocity of the moving platform and the j-th input velocity of the driving joint. The Jacobian matrix of the robot is obtained based on the fifth formula: J=J q -1 ·J Q .

[0018] Further, the singularity analysis of the Jacobian matrix includes the following steps:

[0019] Obtain the determinants of the forward and inverse Jacobian matrices, which are |J q | and |J Q |. If |J q | = 0 and |J Q | ≠ 0, then the mechanism of the robot is in a forward singular configuration, the driving joints of the robot are fixed, and the moving platform still has degrees of freedom. If |J q | ≠ 0 and |J Q | = 0, then the mechanism of the robot is in a reverse singular configuration, and there is an instantaneous motion of the moving platform. If |J q | = 0 and |J Q | = 0, then the mechanism of the robot is in a hybrid singular configuration, and there is an instantaneous motion of both the driving joints and the moving platform.

[0020] Further, verifying the degrees of freedom of the robot based on the simulation model includes the following steps:

[0021] Set the simulation parameters of the simulation model. The simulation parameters include simulation time, simulation steps, and driving functions. Run the simulation model based on the simulation parameters to obtain a first simulation result. The first simulation result includes the displacement and velocity curves of the robot. Obtain the degrees of freedom of the robot in the simulation model based on the first simulation result, which is defined as the third number of degrees of freedom. Compare whether the first number of degrees of freedom is the same as the third number of degrees of freedom. If so, it indicates that the calculation of the degrees of freedom of the robot is correct.

[0022] Further, verifying the correctness of the inverse kinematics model includes the following steps:

[0023] Define the theoretical motion law of the configuration parameters of the robot changing with time based on the sixth formula. The sixth formula is: where α1 and β1 are the angular displacements of the moving platform about the x-axis and y-axis, Z is the linear displacement of the moving platform along the z-axis, time is time, and d1 is a preset constant. Obtain the theoretical result based on the theoretical motion law. The theoretical result includes the position, velocity, and acceleration of the moving platform. Perform a simulation of the position and attitude of the moving platform based on the simulation model and output a second simulation result. Compare the theoretical result with the second simulation result and determine whether the changes in the position, velocity, and acceleration of the moving platform in the second simulation result conform to the theoretical motion law. If so, it indicates that the inverse kinematics model is correct.

[0024] Further, obtaining the working space volume of the robot includes the following steps:

[0025] A random function is set, and multiple random values ​​are generated based on the random function. The random values ​​are substituted into the inverse kinematics equation to obtain the configuration parameters of the robot. Constraints are set to determine whether the configuration parameters can satisfy the constraints. If so, the corresponding random numbers are retained, otherwise they are discarded. A workspace image of the robot is obtained based on the retained random values, and the workspace volume of the robot is obtained based on the workspace image.

[0026] Furthermore, setting the constraint conditions includes the following steps:

[0027] The constraint conditions include the travel limit of the robot's moving pair, the joint angle limit and the non-interference limit between the rods, wherein the travel limit of the moving pair is: L min ≤L i ≤L max , L i represents the length of the i-th rod, L min and L max are the minimum and maximum lengths of the rod, respectively, and the joint rotation angle is limited to: Among them, θ i and δ i l i with a i , b i The first angle and the second angle, and θ min ≤θ i ≤θ max , δ min ≤δ i ≤δ max ,θ min and θ max are the minimum and maximum values ​​of the first angle, δ min and δ max are the minimum and maximum values ​​of the second angle respectively. The restriction condition that no interference occurs between the rods is: D≤D i , where D is the diameter of the rod, D i is the shortest distance between the i-th rod and the i+1-th rod.

[0028] Further, adjusting the structural parameters based on the workspace volume comprises the following steps:

[0029] The structural parameters include the length range of the rod, the rotational secondary angular range of the moving platform and the size of the moving platform. The change in the working space volume of the robot is obtained based on different length ranges and different rotational secondary angular ranges, and a target threshold of the working space volume of the robot is set. The length range of the rod and the rotational secondary angular range of the moving platform are adjusted based on the target threshold.

[0030] Compared with the prior art, the beneficial effects of the present invention are at least as follows:

[0031] The present invention uses the screw theory and the modified GK formula to analyze the robot's degrees of freedom, accurately calculates the robot's degrees of freedom, lays the foundation for the robot's kinematic modeling, and ensures the accuracy and reliability of the model; uses the closed loop method to establish the robot's inverse kinematics model, establishes the Jacobian matrix of the velocity mapping relationship between the robot's rods and the moving platform, and analyzes the singularity of the mechanism. Through the singularity analysis, the motion restriction or loss of control problems that may occur in the robot under a specific configuration can be identified and avoided, thereby improving the robot's operational safety and reliability; uses ADAMS and MATLAB to perform simulation analysis, verifies the robot's degrees of freedom and the correctness of the established model, and through simulation, can discover potential design problems before actually manufacturing the robot, thereby saving time and cost; and helps designers optimize the robot's structure by analyzing the influence of the robot's structural parameters on the volume of the workspace, so that it can better adapt to specific application scenarios and improve the robot's application range and efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart of the steps of a kinematics and performance analysis method of a three-degree-of-freedom temporary support robot for a coal mine tunnel according to the present invention;

[0033] Figure 2 The figure is an outline diagram of the temporary support robot of the present invention;

[0034] Figure 3 is a structural diagram of the temporary support robot of the present invention;

[0035] Figure 4 is a structural diagram of the C1c1 branch of the present invention;

[0036] Figure 5 It is the structural diagram of the D1d1 branch of the present invention;

[0037] Figure 6 It is a structural diagram of the driving branch chain of the present invention;

[0038] Figure 7 This is a diagram showing the top plate of the present invention changing along the x-axis and z-axis directions;

[0039] Figure 8 This is a diagram showing the top plate of the present invention changing along the y-axis direction;

[0040] Fig. 9 is the displacement curve of the center motion of the moving platform of the present invention;

[0041] Fig.10 is the motion speed curve of the moving platform of the present invention;

[0042] Fig.11 It is the displacement variation curve of the four rods of the present invention;

[0043] Fig.12 is a curve showing the change of the speed of the rod member with time according to the present invention;

[0044] Fig.13 is a curve of acceleration of the rod member of the present invention varying with time;

[0045] Fig.14 is a workspace analysis flow chart of the present invention;

[0046] Fig.15 A workspace point cloud diagram of the reference point of the moving platform of the present invention;

[0047] Fig.16 A diagram showing the relationship between the rod range and the working space volume of the present invention;

[0048] Fig.17 A diagram showing the relationship between the rotation angle range of the rotation pair and the volume of the working space of the present invention;

[0049] Fig.18 Graph showing the relationship between the size of the moving platform and the volume of the working space of the present invention. DETAILED DESCRIPTION

[0050] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0051] It is understood that the terms "first", "second", etc. used in this application may be used herein to describe various elements, but unless otherwise specified, these elements are not limited by these terms. These terms are only used to distinguish a first element from another element. For example, without departing from the scope of this application, a first xx script may be referred to as a second xx script, and similarly, a second xx script may be referred to as a first xx script.

[0052] like Figure 1 As shown, a kinematics and performance analysis method of a three-degree-of-freedom temporary support robot for a coal mine tunnel includes:

[0053] S1: Determine the components of the robot frame, which include the gantry frame, dynamic platform, static platform, drive branch and constraint branch. Establish the dynamic coordinate system and static coordinate system on the dynamic platform and static platform respectively. Calculate and verify the robot's degrees of freedom based on the screw theory and the modified Grubler-Kutzbach formula.

[0054] Specifically, the present invention proposes a gantry frame type temporary support robot, such as Figure 2 As shown in FIG. 1 , it is the appearance diagram of the temporary support robot, where 1 is the moving platform, 2 is the constraint branch, 3 is the driving branch, 4 is the gantry frame, and 5 is the static platform. Figure 3 As shown in the figure, it is a structural diagram of the temporary support robot, wherein the driving branch 3 includes 4 branches, namely, 11 , l 22 , l 33 and l 44 The intersection points of the driving branch 3 connected to the static platform 5 are A1, A2, A3 and A4 respectively, and the intersection points connected to the moving platform 1 are B1, B2, B3 and B4. The constraint branch 2 includes the constraint branch c1c1 and the constraint branch d1D1. The constraint branch c1c1 intersects with the gantry frame and the moving platform 1 at points c1 and C1 respectively, and the constraint branch d1D1 intersects with the gantry frame and the moving platform 1 at points d1 and D1 respectively.

[0055] A moving coordinate system P_XYZ is defined on the moving platform 1, where point P is the center of the moving platform 1, the X-axis is parallel to B1B4 (B2B3), the Y-axis is parallel to B1B2 (B3B4), and the Z-axis is perpendicular to the static platform 5, which conforms to the right-hand screw rule. A static coordinate system o_xyz is defined on the static platform 5, where point o is the center of the static platform 5, the x-axis is parallel to A1A4 (A2A3), the y-axis is parallel to A1A2 (A3A4), and the z-axis is perpendicular to the static platform 5, which conforms to the right-hand screw rule.

[0056] Each branch chain is analyzed through the spiral theory. The spiral theory provides a method for comprehensively analyzing the robot motion, which not only considers the motion of the joints, but also includes the transmission of forces and torques. This method allows a more comprehensive analysis of the dynamic performance of the robot and verifies the degrees of freedom with the help of the modified Grubler-Kutzbach formula. The Grubler-Kutzbach formula provides a method for quickly calculating the degrees of freedom of the mechanism. By considering the order (d), the number of links (n), the number of kinematic pairs (g) and the number of degrees of freedom (fi) of each kinematic pair, the degrees of freedom of the mechanism can be calculated more accurately, thereby improving the accuracy and efficiency of the design. The specific calculation and verification methods will be explained later.

[0057] S2: Based on the closed-loop method, the inverse kinematics equation of the robot is established, and the Jacobian matrix is ​​established. The Jacobian matrix represents the mapping relationship between the driving branch of the robot and the moving platform. The Jacobian matrix is ​​subjected to singularity analysis to determine whether the structure of the robot has a singular type. If not, the robot is a feasible mechanism.

[0058] Specifically, in order to subsequently solve the length of each rod of the robot according to the changes in the position and posture of the end effector (moving platform 1), it is necessary to establish an inverse kinematics model. The inverse kinematics model is implemented by the inverse kinematics equation. In complex environments such as coal mine tunnels, the changes in the roof are unpredictable. The inverse kinematics model allows the robot to dynamically adjust the length of each rod according to the roof change information obtained by the sensor to adapt to different working environments.

[0059] The Jacobian matrix describes the relationship between the input velocity of the driving joint and the output velocity of the moving platform 1. This relationship is the core of kinematic analysis. Through the Jacobian matrix, small changes in the driving joint (input) can be linked to small changes in the end effector (output), thereby understanding the kinematic characteristics of the robot.

[0060] A singular configuration refers to a point where a mechanism cannot move or its instantaneous motion cannot be determined. It is an inherent property of a mechanism. A singular configuration will cause changes in the degree of freedom and degradation of stiffness of the mechanism. Therefore, a feasible mechanism should theoretically avoid or stay away from singular configurations. Therefore, a singularity analysis should be performed on the temporary support robot in the present invention to determine whether the robot has a singular type. The singular type will be explained later. If no singular type exists, it indicates that the robot's mechanism is a feasible mechanism.

[0061] S3: Establish a simulation model of the robot and verify the correctness of the robot's degrees of freedom and inverse kinematics equations based on the simulation model.

[0062] Specifically, first, the robot mechanism is analyzed theoretically, a mathematical model is established, and a virtual prototype model of the robot is created using 3D modeling software such as SolidWorks according to the design parameters of the mathematical model. The simplified virtual prototype model is exported to a format that can be recognized by ADAMS, and these model files are imported into ADAMS to establish a simulation model. According to the actual connection method of the robot, corresponding constraints are added to each component in ADAMS, such as hinges, sliding, and fixing, etc., and drives are added to the joints of the robot. These drives can be speed drives, position drives, or force drives to simulate actual control inputs. Run the simulation model to observe whether the robot's degrees of freedom and the inverse kinematics equations are consistent with the theoretical analysis to verify the correctness.

[0063] S4: Obtain structural constraints and structural parameters of the robot, obtain the workspace volume of the robot based on the structural constraints, and adjust the structural parameters based on the workspace volume so that the workspace volume of the robot reaches a target threshold.

[0064] Specifically, the shape and size of the mechanism's working space affect the quality of the mechanism's motion performance. Usually, the parallel mechanism's working space is irregular and small in shape, which greatly limits its application. The temporary support robot requires a large and regular working space to ensure that its lower equipment and personnel have a safe and reliable working area. Therefore, the working space of the temporary support robot in the present invention is analyzed, and the working space of the parallel temporary support robot's moving platform 1 is calculated and analyzed using the Monte Carlo method. When the structural parameters of the robot mechanism change, the robot's working space will also change accordingly. The structural parameters include the range of rods, the rotation angle range of the moving platform 1, and the size of the moving platform 1. By analyzing the influence of relevant structural parameters on the volume of the working space, a theoretical basis is provided for the structural design and optimization of the temporary support robot.

[0065] The present invention uses the screw theory and the modified GK formula to analyze the robot's degrees of freedom, accurately calculates the robot's degrees of freedom, lays the foundation for the robot's kinematic modeling, and ensures the accuracy and reliability of the model; uses the closed loop method to establish the robot's inverse kinematics model, establishes the Jacobian matrix of the velocity mapping relationship between the robot's rods and the moving platform, and analyzes the singularity of the mechanism. Through the singularity analysis, the motion restriction or loss of control problems that may occur in the robot under a specific configuration can be identified and avoided, thereby improving the robot's operational safety and reliability; uses ADAMS and MATLAB to perform simulation analysis, verifies the robot's degrees of freedom and the correctness of the established model, and through simulation, can discover potential design problems before actually manufacturing the robot, thereby saving time and cost; and helps designers optimize the robot's structure by analyzing the influence of the robot's structural parameters on the volume of the workspace, so that it can better adapt to specific application scenarios and improve the robot's application range and efficiency.

[0066] As a preferred technical solution of the present invention, calculating and verifying the robot's degrees of freedom includes the following steps:

[0067] Determine all branches in the robot structure, represent each branch information in a motion spiral system, obtain first data information, perform inverse operation on the motion spiral system, obtain second data information of the branches in the anti-spiral system, based on the second data information of all branches in the anti-spiral system, obtain third data information of the robot system in the anti-spiral system, invert the third data information to obtain fourth data information of the robot system in the motion spiral system, and obtain the number of degrees of freedom of the robot based on the fourth data information, which is defined as the first degree of freedom.

[0068] The second degree of freedom of the robot is calculated based on the first formula, which is: Where d is the order of the robot, n is the total number of individual components in the robot, g is the total number of kinematic pairs of the robot, and f is the total number of individual components in the robot. i is the number of degrees of freedom of the i-th kinematic joint, v is the redundant constraint added to the robot, γ is the local degree of freedom of the robot, if the first degree of freedom is the same as the second degree of freedom, the first degree of freedom of the robot is verified successfully.

[0069] Specifically, the branches in the robot structure include branches of constraint branch 2 and branches of drive branch 3. The branches of constraint branch 2 include C1c1 branch and D1d1 branch analysis, and the branches of drive branch 3 include A1B1 branch, A2B2 branch, A3B3 branch and A4B4 branch. Figure 4 As shown in the figure, it is the structural diagram of the C1c1 branch chain. The C1c1 branch chain can be expressed as follows under the moving spiral system: The expression in the anti-helical system is:

[0070] like Figure 5 As shown in the figure, it is the structural diagram of the D1d1 branch chain. The D1d1 branch chain can be expressed as follows under the moving spiral system:

[0071] The expression in the anti-helical system is:

[0072] like Figure 6 As shown, it is the drive branch 3 branch A i B i (i=1,2,3,4) structure diagram, driving branch 3 branch A i B i (i=1,2,3,4) can be expressed as: The expression in the anti-helical system is: According to the information representation of all branches of the above robot structure in the motion spiral system and anti-spiral system, the anti-spiral system of the robot system is obtained as follows: By inverting the anti-spiral system, we can get the representation of the robot system in the motion spiral system: where e i , f i , g i , E and F are parameters that describe the motion of the robot branch chain. They are used to define the translation and rotation motion of the branch chain in the motion spiral system.

[0073] The representation of the robot system in the motion spiral system proves that the first degree of freedom is 3, indicating that the robot system has three degrees of freedom, one degree of freedom of movement in the z-axis direction, one degree of freedom of rotation around the x-axis of the coordinate system, and one degree of freedom of rotation around the y-axis of the coordinate system. The degrees of freedom are calculated and verified by the modified Grubler-Kutzbach formula. In the present invention, the order of the robot mechanism is d=5, the number of components including the frame is n=13, the total number of kinematic pairs is g=17, and the number of degrees of freedom of the ith kinematic pair is f i =27, the redundant constraint v added to the robot mechanism is 1, the local degree of freedom γ is 0, and the above parameters are substituted into the first formula to obtain the second degree of freedom M=3, so the robot has 3 degrees of freedom.

[0074] Establishing the inverse kinematics equations of the robot includes the following steps:

[0075] Get the first position information A of the robot's base in the static coordinate system i (i=1,2,3,4), and the second position information B' of the top plate in the moving coordinate system i (i=1,2,3,4), based on the second formula, the second position information is converted into the third position information B in the static coordinate system i (i=1,2,3,4), the second formula is: B i =RB' i +P, R is the Euler angle of rotation of the moving coordinate system relative to the static coordinate system, Among them, α is the angle of rotation of the moving platform around the x-axis, β is the angle of rotation of the moving platform around the y-axis, and P is the position information of the coordinate origin of the robot moving platform in the static coordinate system. The coordinate representation of the robot rod is obtained based on the third formula. The third formula is: i =P+Rb i -a i , where l i represents the direction vector of each rod in the robot, O is the origin of the static coordinate system, a i represents the unit normal vector of the ith rotation pair of the static platform, b i represents the unit normal vector of the i-th rotation pair of the moving platform. Based on the fourth formula, the inverse kinematics equation of the robot is obtained. The fourth formula is: 1i 2 = l i 2 .

[0076] Specifically, the temporary support robot obtains the change information of the roof through relevant sensors, such as Figure 7 As shown in the figure, it is the change diagram of the top plate along the x-axis and z-axis directions. Figure 8As shown in the figure, the top plate changes along the y-axis direction. In order to work, the robot needs to adapt to the change of the top plate. In the static coordinate system o-xyz, A i The coordinates of the point (i=1,2,3,4) can be expressed as: Where c and d are the length and width of the static platform 5 respectively. In the moving coordinate system P-XYZ, B' i The coordinates of the point (i=1,2,3,4) can be expressed as: Where, e and f are the length and width of the moving platform 1 respectively, and the position information of the coordinate origin of the robot moving platform in the static coordinate system is P = [XY Z] T , substitute the Euler angle R of the coordinate system P-XYZ relative to the coordinate system o-xyz and the coordinates of point P into the second formula to obtain the third position information B of the top plate in the static coordinate system i (i=1,2,3,4), where

[0078] Define vectors in the static coordinate system in, Vector of moving coordinate system in,

[0079]

[0081] Substituting the above content into the third formula l i =P+Rb i -a i Get the rod representation of the robot, l1 = A1B1 = [c + fsinαsinβ -ecosβfcosα - dz + esinβ + fcosβsinα] T , l2=A2B2=[-c+ecosβ+fsinαsinβ-d+fcosαz+fcosβsinα-esinβ] T , l3=A3B3=[c-fsinαsinβ-ecosβ-d+fcosαz-fcosβsinα+esinβ] T , l4=A4B4=[-c-fsinαsinβ+ecosβd-fcosαz-fcosβsinα-esinβ] T .

[0082] Finally, the inverse kinematics equation of the robot is as follows: 11 2 =(c+fsinαsinβ-ecosβ) 2 +(fcosα-d)2 +(z+esinβ+fcosβsinα) 2 , l 12 2 =(-c+fsinαsinβ+ecosβ) 2 +(fcosα-d) 2 +

[0083] z-esinβ+fcosβsinα) 2 , l 13 2 =(c-fsinαsinβ-ecosβ) 2 +(-fcosα+d) 2 +(z+

[0084] esinβ-fcosβsinα) 2 , l 14 2 =(-c-fsinαsinβ+ecosβ) 2 +(-fcosα+d) 2 +(z-esinβ-fcosβsinα) 2 .

[0085] Building the Jacobian matrix involves the following steps:

[0086] Based on the inverse kinematics equation, the mapping relationship between the input velocity of the robot's driving joint and the output velocity of the moving platform is determined as follows: in, is the input velocity of the driving joint, is the output speed of the moving platform, J q and J Q are the forward and inverse Jacobian matrices of the robot, Among them, J Lij (i=1,2,3,4;j=1,2,3) is the partial derivative of the ith output velocity of the moving platform and the jth input velocity of the driving joint. The Jacobian matrix of the robot is obtained based on the fifth formula: J=J q -1 ·J Q .

[0087] Specifically, the partial derivatives of the i-th output velocity of the moving platform 1 and the j-th input velocity of the driving joint are: Substitute the above partial derivatives into the fifth formula to calculate the Jacobian matrix.

[0089] Singularity analysis of the Jacobian matrix consists of the following steps:

[0090] Obtain the determinants of the forward and inverse Jacobian matrices, which are |J q | and |J Q |. If |J q | = 0 and |J Q | ≠ 0, then the mechanism of the robot is in a forward singular configuration, the driving joints of the robot are fixed, and the moving platform still has degrees of freedom. If |J q | ≠ 0 and |J Q | = 0, then the mechanism of the robot is in a reverse singular configuration, and the moving platform has an instantaneous motion. If |J q | = 0 and J Q | = 0, then the mechanism of the robot is in a hybrid singular configuration, and both the driving joints and the moving platform have instantaneous motions.

[0091] Specifically, if the mechanism of the robot is in a forward singular configuration, at this time the driving part is fixed, but the moving platform 1 still has degrees of freedom. The moving platform 1 is difficult to bear one or more forces or couples, and at this time the moving platform 1 is in an unstable state. For the robot mechanism of the present invention, the occurrence condition is that any one of the four elements on the diagonal of the matrix J q is zero, that is, l1l2l3l4 = 0. It can be seen that this type of singularity will not occur.

[0092] If the mechanism of the robot is in a reverse singular configuration, at this time the input driving joints of the fixed parallel mechanism are fixed, and the end effector still has an instantaneous motion, indicating that the mechanism obtains at least one instantaneous degree of freedom. At this time, the parallel mechanism loses stiffness and cannot bear any load.

[0093] If the mechanism of the robot is in a hybrid singular configuration, at this time there are instantaneous non-zero inputs and outputs that do not affect each other between the driving joints and the end effector of the mechanism, and the corresponding pose is the third type of singularity. The third singularity is different from the previous two. The third singularity not only depends on the pose, but also is related to the structural parameters. When in this type of singularity, the mechanism of the robot will lose degrees of freedom, and this type of singular configuration is called a configuration singularity, which should be avoided in the mechanism design stage.

[0094] Verifying the degrees of freedom of the robot based on the simulation model includes the following steps:

[0095] Set the simulation parameters of the simulation model. The simulation parameters include the simulation time, the number of simulation steps, and the driving function. Run the simulation model based on the simulation parameters to obtain the first simulation result. The first simulation result includes the displacement and velocity curves of the robot. Obtain the degrees of freedom of the robot in the simulation model based on the first simulation result, which is defined as the third degrees of freedom. Compare whether the first degrees of freedom and the third degrees of freedom are the same. If so, it means that the degrees of freedom calculation of the robot is correct.

[0096] Specifically, set the simulation time to 5s, the number of simulation steps to 500, and the three driving functions:: m1 = 10*sin(5*time), m2 = 5*sin(15*time), m3 = 20*sin(10*time), such as Fig. 9 As shown in the figure, it is the displacement curve of the center motion of the moving platform 1. Through this curve, it can be observed that the moving platform 1 swings. Modify the value of the drive pair and re-simulate the robot. The simulation time is 5s, the number of simulation steps is steps = 500, and the three drive functions are: m1 = m2 = m3 = 20*sin(10*time). It can be observed that the moving platform 1 swings. The moving platform motion speed curve is as follows Fig.10 As shown by Fig. 9 It can be obtained that the robot rotates around the X-axis and Y-axis, but not around the Z-axis. Fig.10 It can be obtained that the robot moves up and down in the Z direction and has no movement in the X and Y directions; the correctness of the analysis of the robot's degrees of freedom is verified through Adams simulation, that is, the robot has three degrees of freedom, namely, movement in the Z-axis direction and rotation around the X-axis and Y-axis.

[0097] Verifying the correctness of the inverse kinematics model includes the following steps:

[0098] The sixth formula is used to define the theoretical motion law of the robot's configuration parameters changing with time. The sixth formula is: Among them, α1 and β1 are the angular displacements of the moving platform around the x-axis and y-axis, Z is the linear displacement of the moving platform along the z-axis, time is time, d1 is a preset constant, and the theoretical results are obtained based on the theoretical laws of motion. The theoretical results include the position, velocity and acceleration of the moving platform. The position and posture of the moving platform are simulated based on the simulation model, and the second simulation result is output. The theoretical result is compared with the second simulation result to determine whether the changes in the position, velocity and acceleration of the moving platform in the second simulation result conform to the theoretical laws of motion. If so, it means that the inverse kinematics model is correct.

[0099] Specifically, a drive is added to the center point P of the moving platform 1, and its motion law is given as follows: α1 = 3d*sin(10*time), β = 2d*sin(5*time), Z = -928+5*time. The theoretical results are obtained based on the theoretical motion law, and the sixth formula is calculated using Matlab. The theoretical results obtained by Matlab are compared and analyzed with the results obtained by Adams simulation. The displacement change curves of the four rods are as follows: Fig.11 As shown in the figure, the velocity and acceleration of the rod change with time. Fig.12 and 13 As shown by Fig.11It can be seen that the Matlab theoretical calculation results are basically the same as the Adams simulation results, with the maximum error being only 0.4%. Fig.12 , 13 It can be seen that the moving platform 1 performs periodic motion, the speed and acceleration of the rod also change periodically, and the motion laws of rods 1, 2 and rods 3, 4 are the same, only the directions are different; this proves the correctness of the kinematic equation of the constructed robot.

[0100] Obtaining the robot's workspace volume includes the following steps:

[0101] A random function is set, and multiple random values ​​are generated based on the random function. The random values ​​are substituted into the inverse kinematics equation to obtain the configuration parameters of the robot. Constraints are set to determine whether the configuration parameters can meet the constraints. If so, the corresponding random numbers are retained, otherwise they are discarded. The workspace image of the robot is obtained based on the retained random values, and the workspace volume of the robot is obtained based on the workspace image.

[0102] Specifically, Fig.14 As shown in the figure, it is a workspace analysis flow chart. First, a random function is used to generate N random values ​​between 0 and 1. The random value is used as the pseudo-random value of the robot's end reference point position variable. Then it is substituted into the inverse kinematics model to obtain the robot's configuration parameters, including the electric cylinder stroke, the rotation angle, the shortest distance between two adjacent branches, etc. It is analyzed whether these configuration parameters can meet the constraint requirements. If they can, they are retained. If not, they are discarded. The retained random values ​​are plotted to obtain the robot's workspace image. The Monte Carlo method is used to calculate and analyze the workspace of the parallel temporary support robot's dynamic platform. The random value N = 300000 is taken, as shown in Fig.15 As shown, the workspace point cloud map of the reference point of the moving platform 1 can be obtained. The figure shows the three-dimensional space of the workspace and the point cloud map in each two-dimensional space.

[0103] Setting up constraints involves the following steps:

[0104] The constraints include the robot's travel limit, joint angle limit, and non-interference limit between rods. The travel limit of the moving pair is: L min ≤L i ≤L max , L i represents the length of the i-th rod, L min and L max are the minimum and maximum lengths of the rod, respectively, and the joint rotation limit is: Among them, θ i and δ i l i with a i , b iThe first angle and the second angle, and θ min ≤θ i ≤θ max , δ min ≤δ i ≤δ max ,θ min and θ max are the minimum and maximum values ​​of the first angle, δ min and δ max are the minimum and maximum values ​​of the second angle respectively. The restriction condition that no interference occurs between the rods is: D≤D i , where D is the diameter of the rod, D i is the shortest distance between the i-th rod and the i+1-th rod.

[0105] Adjusting the structural parameters based on the workspace volume includes the following steps:

[0106] The structural parameters include the length range of the rod, the rotational secondary angular range of the moving platform and the size of the moving platform. The change of the robot's workspace volume is obtained based on different length ranges and different rotational secondary angular ranges, and the target threshold of the robot's workspace volume is set. The length range of the rod and the rotational secondary angular range of the moving platform are adjusted based on the target threshold.

[0107] Specifically, the following is an analysis of the parameters such as the connecting rod length range, the size of the moving platform 1, and the rotation angle range of the rotating pair. Fig.16 As shown in the figure, it is a relationship diagram between the range of the rod and the volume of the workspace. It can be seen from the figure that both the upper and lower limits of the rod will affect the volume of the robot's workspace, but the lower limit of the connecting rod Lmin has a more obvious effect on the volume of the workspace. When Lmin=240mm, Lmax changes from 600mm to 800mm, and the volume of the workspace changes from 3.3*10 6 mm 3 becomes 3.5*10 6 mm 3 ; When Lmax = 600mm, Lmin changes from 200mm to 400mm, and the working space volume changes from 3.5*10 6 mm 3 becomes 4.9*10 6 mm 3 When Lmin is less than 280 mm, the change in the working space volume is relatively small. When Lmin is greater than 280 mm, the working space volume decreases significantly with the increase of the lower limit value of the rod. This structure can be used as the main basis for rod design.

[0108] like Fig.17 As shown in the figure, it is the relationship between the rotation angle range of the rotation pair and the volume of the workspace. minAs the workspace volume increases, θ gradually decreases. max As the working space volume increases, it gradually becomes larger. Therefore, a larger working space can be obtained by increasing the range of the secondary rotation angle of the movable platform 1.

[0109] like Fig.18 As shown in the figure, it is a relationship diagram between the size of the moving platform 1 and the volume of the workspace. In the length direction of the robot moving platform (along the Y axis), with the increase of the two rotation pair distances (B1B2, B3B4), the volume of the workspace gradually decreases, and the descending speed becomes faster after 430mm; in the width direction of the robot moving platform (along the X axis), the two rotation pair distances (B1B4, B2B3) are between 400mm-430mm, and the change of the rotation pair distance has little effect on the workspace volume. After 430mm, with the increase of the rotation pair distance, the volume of the workspace gradually increases. This result can be used as the main basis for the size design of the moving platform 1.

[0110] By analyzing the influence of structural parameters on the volume of the workspace, it is found that the lower limit value Lmin of the rod has a more obvious influence on the volume of the workspace than its upper limit value Lmax. The influence of the rotation angle range on the volume of the workspace is also obvious. By increasing the distance of the revolving pair in the width direction of the moving platform (along the X-axis), the volume of the workspace can be significantly increased.

[0111] It should be understood that, although each step in the flow chart of each embodiment of the present invention is shown in sequence according to the indication of the arrow, these steps are not necessarily performed in sequence according to the order indicated by the arrow. Unless there is a clear explanation in this article, the execution of these steps does not have a strict order restriction, and these steps can be performed in other orders. Moreover, at least a portion of the steps in each embodiment may include a plurality of sub-steps or a plurality of stages, and these sub-steps or stages are not necessarily performed at the same time, but can be performed at different times, and the execution order of these sub-steps or stages is not necessarily performed in sequence, but can be performed in turn or alternately with at least a portion of other steps or sub-steps or stages of other steps.

[0112] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program. The above-mentioned program can be stored in a non-volatile computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory may include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory may include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0113] The technical features of the above-mentioned embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above-mentioned embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0114] The above embodiments only express several implementation methods of the present invention, and the description is relatively specific and detailed, but it cannot be understood as limiting the scope of the present invention. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

[0115] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A kinematics and performance analysis method for a three-degree-of-freedom temporary support robot for coal mine tunnels, characterized in that: The method comprises the following steps: S1: Determine the framework components of the robot, the framework components include a gantry frame, a dynamic platform, a static platform, a driving branch and a constraint branch, establish a dynamic coordinate system and a static coordinate system on the dynamic platform and the static platform respectively, and calculate and verify the degree of freedom of the robot based on the screw theory and the modified Grubler-Kutzbach formula; S2: establishing the inverse kinematics equation of the robot based on a closed loop method, establishing a Jacobian matrix, performing a singularity analysis on the Jacobian matrix, and determining whether the structure of the robot has a singular type. If not, the robot is a feasible mechanism; S3: establishing a simulation model of the robot, and verifying the correctness of the degrees of freedom of the robot and the inverse kinematics equation based on the simulation model; S4: Obtain structural constraints and structural parameters of the robot, obtain the workspace volume of the robot based on the structural constraints, and adjust the structural parameters based on the workspace volume so that the workspace volume of the robot reaches a target threshold.

2. The method according to claim 1, characterized in that: Calculating and verifying the robot's degrees of freedom comprises the following steps: Determine all branches in the robot structure, represent each branch information in a motion spiral system to obtain first data information, perform an inverse operation on the motion spiral system to obtain second data information of the branch in an anti-spiral system, obtain third data information of the robot system in the anti-spiral system based on the second data information of all branches in the anti-spiral system, invert the third data information to obtain fourth data information of the robot system in the motion spiral system, and obtain the number of degrees of freedom of the robot based on the fourth data information, which is defined as the first number of degrees of freedom; The second degree of freedom of the robot is calculated based on a first formula, wherein the first formula is: Where d is the order of the robot, n is the total number of all individual components in the robot, g is the total number of kinematic pairs of the robot, and f is i is the number of degrees of freedom of the i-th kinematic pair, v is the redundant constraint added to the robot, γ is the local degree of freedom of the robot, and if the first number of degrees of freedom is the same as the second number of degrees of freedom, the first number of degrees of freedom of the robot is verified successfully.

3. The method according to claim 1, characterized in that Establishing the inverse kinematics equation of the robot comprises the following steps: Obtain the first position information A of the bottom plate of the robot in the static coordinate system i (i=1, 2, 3, 4), and the second position information B' of the top plate in the moving coordinate system i (i=1, 2, 3, 4), based on the second formula, the second position information is converted into the third position information B in the static coordinate system i (i=1,2,3,4), the second formula is: B i =RB' i +P, R is the Euler angle of rotation of the moving coordinate system relative to the static coordinate system, Wherein, α is the angle of rotation of the moving platform around the x-axis, β is the angle of rotation of the moving platform around the y-axis, and P is the position information of the coordinate origin of the moving platform of the robot in the static coordinate system. The coordinate representation of the robot rod is obtained based on the third formula, and the third formula is: i =P+Rb i -a i , where li 表 represents the direction vector of each rod in the robot, O is the origin of the coordinate system in the static coordinate system, a i represents the unit normal vector of the ith rotational pair of the static platform, bi represents the unit normal vector of the ith rotational pair of the dynamic platform, and the inverse kinematics equation of the robot is obtained based on the fourth formula, which is: 1i 2 = l i 2 .

4. The method according to claim 3, characterized in that Building the Jacobian matrix involves the following steps: The mapping relationship between the input speed of the driving joint of the robot and the output speed of the moving platform is determined based on the inverse kinematics equation, and the mapping relationship is: in, is the input velocity of the driven joint, is the output speed of the moving platform, J q and J Q are the forward and inverse Jacobian matrices of the robot, Among them, J Lij (i=1, 2, 3, 4; j=1, 2, 3) is the partial derivative of the i-th output velocity of the moving platform and the j-th input velocity of the driving joint. The Jacobian matrix of the robot is obtained based on the fifth formula: J=J q -1 ·J Q .

5. The method according to claim 4, characterized in that Performing singularity analysis on the Jacobian matrix comprises the following steps: Obtain the determinants of the forward and inverse Jacobian matrices, which are |J q | and |J Q | respectively. If |J q | = 0 and |J Q | ≠ 0, then the mechanism of the robot is in a forward singular configuration, the driving joints of the robot are fixed, and the moving platform still has degrees of freedom. If |J q | ≠ 0 and |J Q | = 0, then the mechanism of the robot is in a reverse singular configuration, and the moving platform has an instantaneous motion. If |J q | = 0 and |J Q | = 0, then the mechanism of the robot is in a hybrid singular configuration, and both the driving joints and the moving platform have the instantaneous motion.

6. The method according to claim 2, characterized in that Verifying the degrees of freedom of the robot based on the simulation model comprises the following steps: Simulation parameters of the simulation model are set, wherein the simulation parameters include simulation time, simulation steps and driving function; the simulation model is run based on the simulation parameters to obtain a first simulation result, wherein the first simulation result includes a displacement and a velocity curve of the robot; the degrees of freedom of the robot in the simulation model are obtained based on the first simulation result, which is defined as a third degree of freedom; and the first degree of freedom and the third degree of freedom are compared to see whether they are the same. If yes, it indicates that the degrees of freedom of the robot are calculated correctly.

7. The method according to claim 5, characterized in that Verifying the correctness of the inverse kinematics model includes the following steps: The theoretical motion law of the robot's configuration parameters changing with time is defined based on the sixth formula, and the sixth formula is: Among them, α1 and β1 are the angular displacements of the moving platform around the x-axis and y-axis, Z is the linear displacement of the moving platform along the z-axis, time is time, d1 is a preset constant, and a theoretical result is obtained based on the theoretical motion law. The theoretical result includes the position, velocity and acceleration of the moving platform. The position and posture of the moving platform are simulated based on the simulation model, and a second simulation result is output. The theoretical result is compared with the second simulation result to determine whether the changes in the position, velocity and acceleration of the moving platform in the second simulation result conform to the theoretical motion law. If yes, it means that the inverse kinematics model is correct.

8. The method according to claim 1, characterized in that: Obtaining the working space volume of the robot comprises the following steps: A random function is set, and multiple random values ​​are generated based on the random function. The random values ​​are substituted into the inverse kinematics equation to obtain the configuration parameters of the robot. Constraints are set to determine whether the configuration parameters can satisfy the constraints. If so, the corresponding random numbers are retained, otherwise they are discarded. A workspace image of the robot is obtained based on the retained random values, and the workspace volume of the robot is obtained based on the workspace image.

9. The method according to claim 8, characterized in that Setting up constraints involves the following steps: The constraint conditions include the travel limit of the robot's moving pair, the joint angle limit and the non-interference limit between the rods, wherein the travel limit of the moving pair is: L min ≤L i ≤L max , L i represents the length of the i-th rod, L min and L max are the minimum and maximum lengths of the rod, respectively, and the joint rotation angle is limited to: Among them, θ i and δ i l i with a i , b i The first angle and the second angle, and θ min ≤θ i ≤θ max , δ min ≤δ i ≤δ max ,θ min and θ max are the minimum and maximum values ​​of the first angle, δ min and δ max are the minimum and maximum values ​​of the second angle respectively. The restriction condition that no interference occurs between the rods is: D≤D i , where D is the diameter of the rod, D i is the shortest distance between the i-th rod and the i+1-th rod.

10. The method according to claim 9, characterized in that Adjusting the structural parameters based on the workspace volume comprises the following steps: The structural parameters include the length range of the rod, the rotational secondary angular range of the moving platform and the size of the moving platform. The change in the working space volume of the robot is obtained based on different length ranges and different rotational secondary angular ranges, and a target threshold of the working space volume of the robot is set. The length range of the rod and the rotational secondary angular range of the moving platform are adjusted based on the target threshold.

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