A method and system for workspace analysis of a hybrid flexible robot

Abstract

The application discloses a kind of hybrid flexible robot workspace analysis method and system, the method comprises the following steps: considering minimizing rope length error, constructing the forward kinematics model of hybrid flexible robot, obtaining the end pose of hybrid flexible robot;The inverse kinematics model of hybrid flexible robot is constructed, and the generalized joint angle control quantity of hybrid flexible robot is obtained;The statics analysis model of hybrid flexible robot is constructed, and the static force balance condition of robot is obtained;The end pose of hybrid flexible robot, the generalized joint angle control quantity and static force balance condition are combined, and the workspace of hybrid flexible robot is constructed, and the working state of hybrid flexible robot is controlled according to workspace.It can quickly and accurately complete the task that needs large space movement and local fine operation simultaneously.The application can be widely applied to the technical field of hybrid flexible robot as a kind of hybrid flexible robot workspace analysis method and system.

Description

Technical Field

[0001] This invention relates to the field of hybrid flexible robot technology, and in particular to a method and system for analyzing the workspace of a hybrid flexible robot. Background Technology

[0002] Rope-driven parallel robots, characterized by high load-bearing capacity, large workspace, wide mobility, and simple installation and configuration, can solve problems in various fields requiring rapid response and expansive space. They are widely used in search and rescue, astronomical telescopes, and high-speed industrial operations. However, they suffer from drawbacks such as insufficient end effector flexibility and rope tension exceeding limits at the edges of the workspace. Flexible robots offer advantages such as lower interaction forces with the environment and flexible arm designs, but their workspace is limited by a fixed robot base. In disaster relief and other scenarios, there are often processes involving searching vast areas and performing precise operations in localized locations. Performing these processes manually is time-consuming, labor-intensive, and inefficient. Therefore, there is an urgent need for a robot that can replace human labor, move rapidly in space, and operate flexibly in localized areas to solve this problem. Summary of the Invention

[0003] To address the aforementioned technical problems, the present invention aims to provide a workspace analysis method and system for hybrid flexible robots, which can quickly and accurately complete tasks requiring both large-scale spatial movement and precise local operations.

[0004] The first technical solution adopted in this invention is: a workspace analysis method for a hybrid flexible robot, comprising the following steps:

[0005] To minimize the rope length error, a forward kinematics model of the hybrid flexible robot is constructed to obtain the end-effector pose of the hybrid flexible robot, which includes a flexible robotic arm and a rope-driven parallel robot.

[0006] Based on the end-effector pose of the hybrid flexible robot, an inverse kinematics model of the hybrid flexible robot is constructed to obtain the generalized joint angle control quantities of the hybrid flexible robot.

[0007] Construct a static analysis model of the hybrid flexible robot and obtain the static equilibrium conditions of the hybrid flexible robot;

[0008] By combining the end-effector pose, generalized joint angle control parameters, and static equilibrium conditions of the hybrid flexible robot, a workspace for the hybrid flexible robot is constructed, and the working state of the hybrid flexible robot is controlled according to the workspace.

[0009] Furthermore, the step of considering minimizing the rope length error, constructing a positive kinematics model of the hybrid flexible robot, and obtaining the end-effector pose of the hybrid flexible robot specifically includes:

[0010] Based on the DH parameters of the flexible manipulator with n joint degrees of freedom, construct the DH coordinate system of the flexible manipulator with n joints;

[0011] Transform the DH coordinate system of the flexible manipulator with n joints to construct a homogeneous transformation matrix of the DH coordinate system of the flexible manipulator with n adjacent joints.

[0012] Based on the chain rule, the forward kinematics model of the flexible manipulator is constructed using the homogeneous transformation matrix of the DH coordinate system of the flexible manipulator with n adjacent joints.

[0013] Considering the problem of minimizing rope length error, and solving the problem of minimizing rope length error using the Levenberg-Marquardt optimization method, a forward kinematics model of the rope-driven parallel robot is constructed.

[0014] By calculating the homogeneous transformation matrix from the end-effector coordinate system to the world coordinate system of the flexible manipulator, the forward kinematics model of the flexible manipulator is combined with the forward kinematics model of the rope-driven parallel robot to construct the forward kinematics model of the hybrid flexible robot and obtain the end-effector pose of the hybrid flexible robot.

[0015] The formula for calculating the end-effector pose of the hybrid flexible robot is as follows:

[0016] X ee =HFK(l1,l2,…,l m ,θ1,θ2,…,θ n , pf H b ) = HFK(Q2, pf H b )

[0017] In the above formula, l1, l2, ..., l m Representing the lengths of each rope, θ1, θ2, ..., θ n This indicates the angles of each joint in the flexible robotic arm. pf H b Let HFK(·) represent the homogeneous transformation matrix of the flexible robotic arm base relative to the coordinate system of the moving platform, and let X represent the forward kinematics function of the hybrid flexible robot. ee This indicates the end-effector pose of the hybrid flexible robot.

[0018] Furthermore, the specific expression for minimizing the rope length error problem is as follows:

[0019]

[0020] subject to L i =PIK(p i ,r i,X pf )

[0021] In the above formula, PIK(·) represents the inverse kinematics function of the rope-driven parallel robot, l i X represents the observed rope length. pf Represents the positive kinematics model of a rope-driven parallel robot, ||L i ‖2 represents the magnitude of the rope vector obtained from the inverse kinematics solution, p i r represents the position vector of the fixed anchor point relative to the world coordinate system. i The vector represents the position of the moving anchor point relative to the coordinate system of the moving platform, m represents the number of ropes, and i represents the counting variable, i = 1, 2, ..., m.

[0022] Furthermore, the expression for the forward kinematics model of the hybrid flexible robot is as follows:

[0023] X ee =HFK(l i ,θ1,θ2,…,θ n , pf H b ) = HFK(Q1, pf H b )

[0024] In the above formula, X ee Let HFK(·) represent the end-effector pose of the hybrid flexible robot, and let θ1, θ2, ..., θ3 represent the inverse kinematics function of the hybrid flexible robot. n Indicates the angles of each joint of a flexible robot, l i The observed rope length is represented by Q1, which represents the generalized pose of the hybrid flexible robot. pf H b This represents the homogeneous transformation matrix of the flexible robotic arm base relative to the coordinate system of the moving platform.

[0025] Furthermore, the step of constructing an inverse kinematics model of the hybrid flexible robot based on its end-effector pose and obtaining the generalized joint angle control quantities of the hybrid flexible robot specifically includes:

[0026] Based on the end-effector pose of the hybrid flexible robot, obtain the complete solution set between the base pose of the flexible manipulator and the joint angles of the flexible manipulator.

[0027] Based on the preset selection rules, a subset of the complete solution set is selected to determine the optimal base pose and the optimal joint angle of the flexible robotic arm.

[0028] Based on the base pose and joint angle of the optimal flexible manipulator, an inverse kinematics model of the hybrid flexible robot is constructed to obtain the generalized joint angle control quantity of the hybrid flexible robot.

[0029] The specific expression of the inverse kinematics model of the hybrid flexible robot is shown below;

[0030] (Q1,Q2)=(L i ,X pf ,θ)=HIK(p i ,r i ,X ee , pf H b )

[0031] In the above formula, Q2 represents the generalized joint control quantity of the hybrid flexible robot, HIK(·) represents the inverse kinematics function of the hybrid flexible robot, θ represents the joint angle of the flexible robotic arm, and L i This represents the rope vector.

[0032] The expression for the generalized joint angle control quantity of the hybrid flexible robot is:

[0033]

[0034]

[0035] In the above formula, Q1 represents the generalized pose of the hybrid flexible robot, Q2 represents the generalized joint control quantity of the hybrid flexible robot, and X... pf =[x pf ,y pf ,z pf ,α pf ,β pf ,γ pf ] T The moving platform is represented relative to the world coordinate system ∑ w The pose is given by m, where m represents the number of ropes and n represents the number of joints of the flexible robot.

[0036] Furthermore, the expression for the preset selection rule is as follows:

[0037]

[0038] X b =[x b ,y b ,z b ,α b ,β b ,γ b ] T ∈U inv

[0039] θ = [θ1, θ2, ..., θ n ] T ∈Q inv

[0040] In the above formula, f base (·) indicates the selection of a rule function, (U inv Q inv X represents the complete solution set of the relationship between the base pose of the flexible robotic arm and the joint angles of the flexible robotic arm. b θ represents the pose of the flexible robotic arm base relative to the world coordinate system. i x represents the joint angle of the flexible robotic arm. b y b z b α b β b γ b They represent X respectively b The amount.

[0041] Furthermore, the step of constructing a static analysis model of the hybrid flexible robot and obtaining the static equilibrium conditions of the hybrid flexible robot specifically includes:

[0042] Construct the force balance equations for the i-th joint of the flexible robotic arm;

[0043] The reaction force and reaction torque applied by the (i+1)th joint to the ith joint of the flexible robotic arm are obtained according to the force balance equation.

[0044] A static model of the flexible robotic arm is constructed based on its reaction force and reaction torque.

[0045] Calculate the coupling force between the flexible manipulator and the moving platform based on the static model of the flexible manipulator;

[0046] By setting the center of mass of the moving platform as the equivalent force point, the force balance equation of the rope-driven parallel robot is constructed.

[0047] A static model of the rope-driven parallel robot is constructed based on the force balance equation of the rope-driven parallel robot.

[0048] The coupling force of the flexible robotic arm on the moving platform is input into the static model of the rope-driven parallel robot to construct the static analysis model of the hybrid flexible robot.

[0049] The specific expression of the static analysis model of the hybrid flexible robot is shown below;

[0050]

[0051] s.bA·T c +G pf +W ex =O

[0052] T min ≤Tci ≤T max i = 1, 2, ..., m

[0053] In the above formula, T min T represents the lower limit of rope force. nax T represents the upper limit of rope force, A represents the rope structure matrix, and T represents the upper limit of rope force. c G represents the vector of tension in the rope. pf W represents the force of gravity acting on the moving platform. ex Let f represent the external force acting on the moving platform, and let f represent the optimization objective function that minimizes the rope force.

[0054] The static equilibrium conditions of the robot are obtained based on the static analysis model of the hybrid flexible robot.

[0055] Furthermore, the step of constructing the workspace of the hybrid flexible robot by combining its end-effector pose, generalized joint angle control parameters, and static equilibrium conditions, and controlling the working state of the hybrid flexible robot based on the workspace, specifically includes:

[0056] S801. Given the end-effector pose and generalized joint angle control values ​​of the hybrid flexible robot, generate a random generalized pose of the hybrid flexible robot using the Monte Carlo method.

[0057] S802. Based on the static model of the flexible robot, calculate the coupling force of the flexible robot on the moving platform, and establish the static equilibrium equation with the center of mass of the moving platform as the equivalent force point.

[0058] S803. Given the upper and lower limits of the rope force, establish an optimization problem with the goal of minimizing the rope force according to the static equilibrium equation and solve it using the quadratic programming method. Perform a static equilibrium judgment on the solution results. If the numerical solution is successful, static equilibrium is satisfied and proceed to S804. If the optimization problem has no solution, static equilibrium is not satisfied and proceed to S801.

[0059] S804. Based on the forward kinematics of the hybrid flexible robot, calculate the position of its end effector relative to the world coordinate system, and determine whether the calculation result is inside the bounding box formed by the fixed anchor point. If so, add the random generalized pose point of the hybrid flexible robot obtained in S801 to the workspace set. If not, go to S801.

[0060] Repeat steps S801 to S804 until a sufficient number of random generalized pose points of the hybrid flexible robot are obtained. All the generalized pose points of the hybrid flexible robot generated in S901 form a set of workspace points.

[0061] Furthermore, it also includes a method for solving the flexibility space of hybrid flexible robots, which specifically includes:

[0062] S901. Generate the joint angles of the flexible robot according to the Monte Carlo method and calculate the pose of the end effector relative to the base. Repeat this step several times to obtain the predefined arm shape space of the flexible robot.

[0063] S902. Given the cross-sectional equation, sampling range and sampling interval, uniformly sample position points according to the cross-sectional equation, maximum sampling range and sampling interval, and use them as the position points of the moving platform.

[0064] S903. For each moving platform position point, combine it with all joint angles in the predefined arm space of the flexible robot to form a generalized pose.

[0065] S904. Based on the static model of the hybrid flexible robot, determine the static equilibrium for each generalized pose obtained in S903, and calculate the number of combinations that satisfy the static equilibrium.

[0066] S905. Based on the number of combinations that satisfy static equilibrium, calculate the flexibility of the hybrid flexible robot at the position point of the moving platform obtained in S902.

[0067] Repeat steps S902 to S905 until the position points of the S902 section equation are uniformly sampled. All the moving platform position points obtained from S902 and the hybrid flexible robot flexibility obtained from S905 constitute the flexibility space, which is used in practical applications to determine the size of the flexible robot's operating space when the moving platform is in different positions, and to guide the deployment of the hybrid flexible robot so that the flexible robot's operating space covers the target object.

[0068] The second technical solution adopted in this invention is: a workspace analysis system for a hybrid flexible robot, comprising:

[0069] The positive kinematics model construction module is used to construct the positive kinematics model of the hybrid flexible robot by considering minimizing the rope length error, and to obtain the end pose of the hybrid flexible robot, which includes a flexible manipulator and a rope-driven parallel robot.

[0070] The inverse kinematics model construction module constructs an inverse kinematics model of the hybrid flexible robot based on the end-effector pose, and obtains the generalized joint angle control quantities of the hybrid flexible robot.

[0071] The static analysis model construction module is used to build a static analysis model of the hybrid flexible robot and obtain the static equilibrium conditions of the robot.

[0072] The control module is used to construct the workspace of the hybrid flexible robot by combining the end-effector pose, generalized joint angle control quantity and static balance condition, and to control the working state of the hybrid flexible robot according to the workspace.

[0073] The beneficial effects of the method and system of this invention are as follows: This invention achieves large-space motion of the moving platform and fine local operation of the flexible robot by combining a flexible robotic arm and a rope-driven parallel robot, thereby improving the working range of the flexible robot. The structure is accurately modeled using a hybrid flexible robot modeling method, the end-effector pose is accurately obtained using forward kinematics analysis, the generalized joint control quantities of the hybrid flexible robot are efficiently obtained using inverse kinematics analysis, and the static equilibrium conditions of the robot are accurately determined using static analysis. Furthermore, a workspace analysis method for hybrid flexible robots is provided to determine the reachable range of motion, thus providing a reference for the deployment of hybrid flexible robots in application scenarios. Attached Figure Description

[0074] Figure 1 This is a flowchart of the steps of a workspace analysis method for a hybrid flexible robot according to the present invention;

[0075] Figure 2 This is a structural block diagram of a workspace analysis system for a hybrid flexible robot according to the present invention;

[0076] Figure 3 This is a schematic diagram of a hybrid flexible robot structure according to the present invention;

[0077] Figure 4 This is a schematic diagram of hybrid flexible robot modeling parameters according to the present invention;

[0078] Figure 5 This is a schematic diagram of the static analysis of the dynamic platform of the hybrid flexible robot according to a specific embodiment of the present invention;

[0079] Figure 6 This is a flowchart of the workspace analysis of a hybrid flexible robot according to a specific embodiment of the present invention. Detailed Implementation

[0080] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are only for ease of explanation and do not limit the order of the steps. The execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.

[0081] The following table explains the symbols used in the embodiments of this invention:

[0082]

[0083] Furthermore, refer to Figure 3 The hybrid flexible robot structure described in this embodiment specifically includes:

[0084] The peripheral station of the rope-driven parallel robot is used to arrange fixed anchor points and connect the rope to the rope controller through the fixed anchor points;

[0085] The moving platform is used to support the load-bearing flexible robotic arm and to connect the rope to the moving platform via a moving anchor point.

[0086] Flexible robotic arms are used to perform fine operations in local spaces and expand the workspace of hybrid robots, enabling movement over a wider area and reducing cable tension at the edges.

[0087] Reference Figure 1 and Figure 4 This invention provides a workspace analysis method for a hybrid flexible robot, the method comprising the following steps:

[0088] S1. Considering minimizing the rope length error, construct a positive kinematics model of the hybrid flexible robot and obtain the end-effector pose of the hybrid flexible robot, which includes a flexible robotic arm and a rope-driven parallel robot.

[0089] S11. Based on the DH parameters of the flexible robot, establish the forward kinematics model of the flexible robot;

[0090] Specifically, based on the DH parameters of the flexible robot with n joint degrees of freedom, its DH coordinate system is established, and the homogeneous transformation matrix of adjacent joint coordinate systems is calculated using the following formula:

[0091]

[0092] In the above formula, cθ i =cosθ i sθ i =sinθ i ,cα i =cosα i sα i =sinα i , (θ i ,a i ,α i ,d i ) represents the DH parameters of joint i in the flexible robot.

[0093] According to the chain rule, the forward kinematics model of the flexible robot is established as follows:

[0094] 0 H n = 0 H1· 1 H2… n-1 H n =SFK(θ1,θ2,…,θ) n )

[0095] In the above formula, SFK(·) represents the positive kinematics function of the flexible robot, θ1,θ2,…,θ n This indicates the angles of each joint of the flexible robot.

[0096] S12. Establish the positive kinematics model of the rope-driven parallel robot;

[0097] Specifically, an optimization model is created by minimizing the rope length error as the optimization objective, using the following formula:

[0098]

[0099] subject to L i =PIK(p i ,r i ,X pf )

[0100] In the above formula, PIK(·) represents the inverse kinematics function of the rope-driven parallel robot. This formula indicates that, during the iterative process of the moving platform's pose, the observed rope length l is gradually decreased. i And the ||L obtained through the inverse kinematics of the rope-driven parallel robot i The difference between ||2, l i X represents the observed rope length. pf Represents the positive kinematics model of a rope-driven parallel robot, ||L i ‖2 represents the magnitude of the rope vector obtained from the inverse kinematics solution, p i r represents the position vector of the fixed anchor point relative to the world coordinate system. i The vector represents the position of the moving anchor point relative to the coordinate system of the moving platform, m represents the number of ropes, and i represents the counting variable, i = 1, 2, ..., m.

[0101] Then, the Levenberg-Marquardt optimization method is used to solve the optimization problem expressed in the above equation. In this invention, the initial dynamic platform pose is iterated. Always select the center point of all fixed anchor points with no rotational orientation, specifically:

[0102]

[0103] Based on the steps described herein, the forward kinematics model of the rope-driven parallel robot can be expressed as:

[0104] X pf =PFK(p i ,r i ,l i )

[0105] In the above formula, PFK(·) is the positive kinematics function of the rope-driven parallel robot.

[0106] S13. Combining the forward kinematics models of flexible robots and rope-driven parallel robots, establish a forward kinematics model for a hybrid flexible robot.

[0107] Specifically, the pose X of the moving platform is obtained according to step S12. pf And based on this, the homogeneous transformation matrix is ​​obtained. w H pf :

[0108] Calculate the coordinate system ∑ of the flexible robot base using the following formula. b To the world coordinate system ∑ w The homogeneous transformation matrix is:

[0109] w H b = w H pf · pf H b

[0110] Then, calculate the coordinate system ∑ of the flexible robot's end effector according to the following formula. ee Relative to the flexible robot base coordinate system ∑ b The homogeneous transformation matrix is ​​as follows:

[0111] b H ee = 0 H b =SFK(θ1,θ2,…,θ) n )

[0112] Combining the above two equations, the coordinate system of the flexible robot's end effector is ∑ ee To the world coordinate system ∑ w The homogeneous transformation matrix can be expressed as:

[0113] w H ee = w H b · b H ee

[0114] The end-effector pose X is calculated using the following formula. ee :

[0115]

[0116] In the above formula, w H ee (2,1) is the element in the second row and first column of the matrix, and so on.

[0117] Furthermore, the forward kinematics model of the hybrid flexible robot can be expressed as:

[0118] X ee =HFK(l i ,θ1,θ2,…,θ n , pf H b ) = HFK(Q1, pf H b )

[0119] In the above formula, X ee Let HFK(·) represent the end-effector pose of the hybrid flexible robot, and let θ1, θ2, ..., θ3 represent the inverse kinematics function of the hybrid flexible robot. n Indicates the angles of each joint of a flexible robot, l i The observed rope length is represented by Q1, which represents the generalized pose of the hybrid flexible robot. pf H b The homogeneous transformation matrix represents the base of the flexible robotic arm relative to the coordinate system of the moving platform;

[0120] The formula for calculating the end-effector pose of the hybrid flexible robot is specifically expressed as follows:

[0121] X ee =HFK(l1,l2,…,l m ,θ1,θ2,…,θ n , pf H b ) = HFK(Q2, pf H b )

[0122] In the above formula, l1, l2, ..., l m Representing the lengths of each rope, θ1, θ2, ..., θ n This indicates the angles of each joint in the flexible robotic arm. pf H b Let HFK(·) represent the homogeneous transformation matrix of the flexible robotic arm base relative to the coordinate system of the moving platform, and let X represent the forward kinematics function of the hybrid flexible robot. ee This indicates the end-effector pose of the hybrid flexible robot.

[0123] S2. Based on the end-effector pose of the hybrid flexible robot, construct the inverse kinematics model of the hybrid flexible robot and obtain the generalized joint angle control quantities of the hybrid flexible robot.

[0124] S21. Given the pose X of the end effector of the hybrid flexible robot relative to the world coordinate system. ee Next, find a possible solution for the base pose and the joint angle of the flexible robot;

[0125] S211. Generating joint angles θ1, θ2, ..., θ of a flexible robot using the Monte Carlo random method. n ;

[0126] S212. Calculate the ∑ of the flexible robot's end effector according to the following formula. ee Compared to the flexible robot base ∑ b homogeneous transformation matrix b H ee :

[0127] b H ee = 0 H b =SFK(θ1,θ2,…,θ) n )

[0128] S213. Calculate the flexible robot base ∑ according to the following formula. b Relative to the world coordinate system ∑ w The homogeneous transformation matrix is ​​obtained, and the relative pose is derived from it.

[0129] w H b = w H ee ·( b H ee ) -1

[0130] S214. Calculate the joint angles θ1, θ2, ..., θ1 obtained in step S211. n The relative pose calculated in step S213 Subsets (U) of the complete solution set of joint angles and base poses of the flexible robot are respectively included. inv Q inv )middle.

[0131] S22. Repeat step S0 N times to obtain a subset (U) containing the complete solution set of N elements of the flexible robot joint angles and base poses. inv Q inv );

[0132] S23. According to the selection rules, the (U) obtained in step S22... inv Q inv ) Select elements to obtain the optimal base pose and joint angles;

[0133] Specifically, the selection rules are as follows:

[0134]

[0135] X b =[x b,y b ,z b ,α b ,β b ,γ b ] T ∈U inv

[0136] θ = [θ1, θ2, ..., θ n ] T ∈Q inv

[0137] In the above formula, f base (·) indicates the selection of a rule function, (U inv Q inv X represents the complete solution set of the relationship between the base pose of the flexible robotic arm and the joint angles of the flexible robotic arm. b θ represents the pose of the flexible robotic arm base relative to the world coordinate system. i x represents the joint angle of the flexible robotic arm. b y b z b α b β b γ b They represent X respectively b The amount;

[0138] Furthermore, the formula for uniquely determining the optimal base pose and joint angles is as follows:

[0139] ( b H ee ,θ)=f base (U inv Q inv )

[0140] S24. Obtain the position of the moving platform relative to the world coordinate system and the rope vector to obtain the inverse kinematics model of the hybrid flexible robot;

[0141] Specifically, the moving coordinate system ∑ is obtained according to the following formula. pf Relative to the world coordinate system ∑ w The homogeneous transformation matrix is ​​obtained, and the relative pose X is derived from it. pf :

[0142]

[0143] Furthermore, the rope vector is obtained using the following formula:

[0144] L i =p i -( w R pf ·r i +w T pf )

[0145] Furthermore, the calculation formula for the inverse kinematics model of the hybrid flexible robot is as follows:

[0146] (Q1,Q2)=(L i ,X pf ,θ)=HIK(p i ,r i ,X ee , pf H b )

[0147] In the above formula, Q2 represents the generalized joint control quantity of the hybrid flexible robot, HIK(·) represents the inverse kinematics function of the hybrid flexible robot, θ represents the joint angle of the flexible robotic arm, and L i Represents the rope vector;

[0148] The expression for the generalized joint angle control quantity of the hybrid flexible robot is:

[0149]

[0150]

[0151] In the above formula, Q1 represents the generalized pose of the hybrid flexible robot, Q2 represents the generalized joint control quantity of the hybrid flexible robot, and X... pf =[x pf ,y pf ,z pf ,α pf ,β pf ,γ pf ] T The moving platform is represented relative to the world coordinate system ∑ w The pose is given by m, where m represents the number of ropes and n represents the number of joints of the flexible robot.

[0152] S3. Construct a static analysis model of the hybrid flexible robot and obtain the static equilibrium conditions of the robot;

[0153] S31. Specifically, taking the i-th joint of a flexible robot as an example, the force balance equation is established using the following formula:

[0154]

[0155] In the above formula, i f i and i τ i The force applied to link i by link i-1 relative to link i is ∑ i The forces and torques acting on each other, i fi+1 and i τ i+1 The force applied to link i by link i+1 relative to link i is ∑ i The reaction force and reaction torque, i G i The force of gravity acting on link i. i p i+1 For ∑ i+1 Relative to ∑ i The position vector, which is also the reaction force. i f i+1 lever arm, i r i It is the lever arm of gravity.

[0156] Furthermore, the calculation expression for the gravitational lever arm is as follows:

[0157]

[0158] Furthermore, the following formula is used to calculate the ∑ applied by link i+1 to link i relative to the joint coordinate system of the flexible robot i. i The reaction force and reaction torque are as follows:

[0159]

[0160] In the above formula, i R i+1 Let ∑ be the coordinate system of joint i+1 of the flexible robot. i+1 To the i-joint coordinate system ∑ i The rotation transformation matrix, i+1 f i+1 and i+1 τ i+1 The ∑ applied to link i by link i+1 relative to the joint coordinate system i+1 are respectively i+1 The forces and torques acting on them.

[0161] Furthermore, the static model expression of the flexible robot is as follows:

[0162] ( 0 f1, 0 τ1)=SST( 1 G1, 2 G2,…, n G n , 1 p2, 2 p3,…, n-1 p n , 1 R2, 2 R3,…, n-1 R n )

[0163]

[0164] In the above formula, 0 f1 and 0 τ1 represents the force applied by link 1 to the base relative to ∑ b The forces and torques, SST(·) is the statics function of the flexible robot.

[0165] S32. Establish a static model of the rope-driven parallel robot;

[0166] Specifically, such as Figure 5 As shown, taking the center of mass of the moving platform as the equivalent force point, the force balance equation is established using the following formula:

[0167]

[0168] In the above formula, F ci Let T be the vector of the rope tension. ci G represents the tension in the rope. pf Let g be the force of gravity acting on the moving platform, and g be the acceleration due to gravity. For the external forces acting on the moving platform, M i Let M be the torque exerted by rope i on the moving platform. ex The external torque acting on the moving platform.

[0169] Furthermore, the static model expression of the rope-driven parallel robot is as follows:

[0170] A·T c +G pf +W ex =O

[0171] In the above formula, T represents the rope structure matrix. c =[T c1 T c2 …T cm ] T This represents the vector of tension in the rope. External forces acting on the moving platform.

[0172] S33. Based on the static model of the flexible robot, calculate the coupling force of the flexible robot on the moving platform, and based on the static model of the rope-driven parallel robot, establish the static model of the hybrid flexible robot, and determine the static equilibrium condition through the solution results of the model.

[0173] Specifically, the coupling force between the flexible robot and the moving platform is calculated using the following formula:

[0174] F ex =F a =- pf Rb · 0 f1

[0175] M ex =M a = pf R b · 0 τ1- pf T b × 0 f1

[0176]

[0177] In the above formula, F a and M a Applying ∑ to the coordinate system of the moving platform relative to the flexible robot's base to the flexible robot b Force and torque, W a For use as a wrench, pf R b and pf T b These represent the coordinates of the flexible robot's base coordinate system ∑b relative to the moving platform coordinate system ∑b. pf The rotation matrix and position vector.

[0178] Furthermore, the static equilibrium equation of the dynamic platform under the load of the flexible robot is calculated using the following formula:

[0179]

[0180] Furthermore, the static model expression of the hybrid flexible robot is as follows:

[0181]

[0182] sb A·T c +G pf +W ex =O

[0183] T min ≤T ci ≤T max i = 1, 2, ..., m

[0184] In the above formula, T min T represents the lower limit of rope force. max T represents the upper limit of rope force, A represents the rope structure matrix, and T represents the upper limit of rope force. c G represents the vector of tension in the rope. pf W represents the force of gravity acting on the moving platform. ex Let f represent the external force acting on the moving platform, and let f represent the optimization objective function that minimizes the rope force.

[0185] Furthermore, the determination of the static equilibrium condition includes: performing a quadratic programming solution on the above equation; if a numerical solution of the rope force can be obtained, then the hybrid flexible robot satisfies the force closure condition under the generalized pose.

[0186] S4. Combining the end-effector pose, generalized joint angle control parameters, and static balance conditions of the hybrid flexible robot, construct the workspace of the hybrid flexible robot, and control the working state of the hybrid flexible robot according to the workspace.

[0187] S41. Reference Figure 6 Given the pose range of the moving platform and the joint angle range of the flexible robot, a random generalized pose of the hybrid flexible robot is generated according to the Monte Carlo method.

[0188] Specifically, the given platform pose range and flexible robot joint angle range include:

[0189]

[0190] In the above formula, γ and Let be the upper and lower limits of the rotational attitude of the moving platform relative to the z-axis of the world coordinate system, respectively.

[0191] Furthermore, taking the k-th S0 step as an example, the generalized pose is calculated using the following formula:

[0192]

[0193]

[0194] In the above formula, rand(·) is the Monte Carlo method function.

[0195] S42. Based on the static model of the flexible robot, calculate the coupling force of the flexible robot on the moving platform, and establish the static equilibrium equation with the center of mass of the moving platform as the equivalent force point.

[0196] S43. Given the upper and lower limits of the rope force, establish an optimization problem with the goal of minimizing the rope force according to the static equilibrium equation and solve it using the quadratic programming method. Perform a static equilibrium judgment on the solution results. If the numerical solution is successful, static equilibrium is satisfied, and proceed to step S44. If the optimization problem has no solution, static equilibrium is not satisfied, and proceed to step S41.

[0197] S44. Based on the forward kinematics of the hybrid flexible robot, calculate the position of its end relative to the world coordinate system, and determine whether the calculation result is inside the bounding box formed by the fixed anchor point. If yes, the desired random generalized pose point of the hybrid flexible robot is added to the workspace set. If no, proceed to step S41.

[0198] S45. Repeat steps S41, S42, S43, and S44 until a sufficient number of random generalized pose points of the hybrid flexible robot are obtained. All the generalized pose points of the hybrid flexible robot generated in step S41 form a set of workspaces, which are used to deploy the hybrid flexible robot according to the actual application task, so that the workspace covers the target as much as possible, and to determine whether the hybrid flexible robot will exceed the workspace when performing actual work, thus failing to meet static balance.

[0199] Furthermore, the workspace set expression is as follows:

[0200]

[0201]

[0202] In the above formula, U hybri This represents the set of workspaces within a hybrid flexible machine.

[0203] This invention also provides a method for solving the hybrid flexible degree space, comprising the following steps:

[0204] S101. Generate the joint angles of the flexible robot according to the Monte Carlo method, and calculate the pose of the end effector relative to the base. Repeat this step several times to obtain the predefined arm shape space of the flexible robot, and calculate the size of the predefined arm shape space of the flexible robot.

[0205] Specifically, taking the k-th step S101 as an example, the flexible robot joint angles generated according to the Monte Carlo method using the following formula include:

[0206]

[0207]

[0208] In the above formula, random(·) is the Monte Carlo method function.

[0209] Furthermore, the predefined arm shape space of the flexible robot is as follows:

[0210]

[0211] In the above formula, U arm This represents the predefined arm shape space of a flexible robot.

[0212] Furthermore, the predefined arm-shaped space size for the computationally flexible robot is as follows:

[0213] C = len(U arm )

[0214] In the above formula, len(·) represents the function for calculating the number of elements in the set, and C represents the number of elements in the predefined arm-shaped space of the flexible robot.

[0215] S201. Given the cross-sectional equation, sampling range and sampling interval, uniformly sample position points according to the cross-sectional equation, maximum sampling range and sampling interval, and use them as the position points of the moving platform.

[0216] Specifically, the given cross-sectional equation includes:

[0217] f section (x pf ,y pf )

[0218] In the above formula, f section (·) represents the cross-sectional equation function, x pf and y pf Indicates the pose of the moving platform X pf The amount.

[0219] Furthermore, the maximum sampling range includes:

[0220] x min ≤x pf ≤x max ,y min <y pf <y max ,

[0221] α pf =0,β pf =0,γ pf =0

[0222] In the above formula, x min and x max x represents pf The lower and upper limits of sampling, y min and y max Indicates y pf The lower and upper limits of sampling, α pf ,β pf and γ pf Indicates the pose of the moving platform X pf The amount.

[0223] Furthermore, the sampling interval is k x k y .

[0224] Furthermore, the uniform sampling location points include:

[0225]

[0226]

[0227] In the above formula, v represents the cross-sectional uniform sampling count variable described in step S201 for the vth time.

[0228] S301. For each moving platform position point, combine it with all joint angles in the predefined arm space of the flexible robot to form a generalized pose.

[0229] Specifically, the position points of the moving platform are combined with all joint angles in the predefined arm-shaped space of the flexible robot to form a generalized pose, including:

[0230]

[0231]

[0232] S401. Based on the static model of the hybrid flexible robot, determine the static equilibrium for each generalized pose obtained in step S301, and calculate the number of combinations that satisfy the static equilibrium.

[0233] Specifically, the k-th generalized pose in the v-th uniform sampling For example, the static equilibrium determination for each generalized pose includes the following steps:

[0234] S4011. Initialize the number of combinations to zero. Based on the static model of the flexible robot, calculate the coupling force of the flexible robot on the moving platform, and establish the static equilibrium equation with the center of mass of the moving platform as the equivalent force point.

[0235] Specifically, the initial combination number being zero is:

[0236] count = 0

[0237] S4012. Given the upper and lower limits of the rope force, establish an optimization problem with the objective of minimizing the rope force based on the static equilibrium equation and solve it using the quadratic programming method. Perform a static equilibrium judgment on the solution results. If the numerical solution is successful, static equilibrium is satisfied, the combination number is incremented by one, the count variable k is incremented by one, and the process proceeds to step S4011. If the optimization problem has no solution, the count variable k is incremented by one, and the process proceeds to step S4011.

[0238] Specifically, the number of combinations plus one is:

[0239] count = count + 1

[0240] S501. Based on the number of combinations that satisfy static equilibrium, calculate the flexibility of the hybrid flexible robot at the position point of the moving platform obtained in step S401.

[0241] Specifically, the dexterity of the hybrid flexible robot at the position point of the moving platform obtained in calculation step S401 is as follows:

[0242]

[0243] In the above formula, R represents the position point of the moving platform. The flexibility of the hybrid flexible robot.

[0244] Repeat steps S201 to S501 until the position points of the cross-sectional equation in step S201 are uniformly sampled. All the position points of the moving platform obtained in step S201 and the flexibility of the hybrid flexible robot obtained in step S501 constitute the flexibility space. In practical applications, this space is used to determine the size of the flexible robot's operating space when the moving platform is in different positions, and to guide the deployment of the hybrid flexible robot so that the flexible robot's operating space covers the target object as much as possible.

[0245] Reference Figure 2 A workspace analysis system for a hybrid flexible robot, comprising:

[0246] The positive kinematics model construction module is used to construct the positive kinematics model of the hybrid flexible robot by considering minimizing the rope length error, and to obtain the end pose of the hybrid flexible robot, which includes a flexible manipulator and a rope-driven parallel robot.

[0247] The inverse kinematics model construction module constructs an inverse kinematics model of the hybrid flexible robot based on the end-effector pose, and obtains the generalized joint angle control quantities of the hybrid flexible robot.

[0248] The static analysis model construction module is used to build a static analysis model of the hybrid flexible robot and obtain the static equilibrium conditions of the robot.

[0249] The control module is used to construct the workspace of the hybrid flexible robot by combining the end-effector pose, generalized joint angle control quantity and static balance condition, and to control the working state of the hybrid flexible robot according to the workspace.

[0250] The content of the above method embodiments is applicable to this system embodiment. The specific functions implemented in this system embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0251] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A hybrid flexible robot workspace analysis method, characterized by, Includes the following steps: To minimize the rope length error, a forward kinematics model of the hybrid flexible robot is constructed to obtain the end-effector pose of the hybrid flexible robot, which includes a flexible robotic arm and a rope-driven parallel robot. Based on the end-effector pose of the hybrid flexible robot, an inverse kinematics model of the hybrid flexible robot is constructed to obtain the generalized joint angle control parameters of the hybrid flexible robot. Construct a static analysis model of the hybrid flexible robot and obtain the static equilibrium conditions of the hybrid flexible robot; By combining the end-effector pose, generalized joint angle control parameters, and static equilibrium conditions of the hybrid flexible robot, a workspace for the hybrid flexible robot is constructed, and the working state of the hybrid flexible robot is controlled according to the workspace. The step of constructing a positive kinematics model of the hybrid flexible robot to minimize the rope length error and obtain the end-effector pose of the hybrid flexible robot specifically includes: According to D-H parameters of a flexible manipulator with one joint degree of freedom, a D-H coordinate system of a flexible manipulator with one joint is constructed D-H parameters of a flexible manipulator with one joint degree of freedom, a D-H coordinate system of a flexible manipulator with one joint is constructed right The flexible robotic arm with each joint is transformed into the DH coordinate system to construct... Homogeneous transformation matrix of the DH coordinate system of a flexible robotic arm with adjacent joints; According to the chain rule, the forward kinematics model of the flexible manipulator is constructed based on the homogeneous transformation matrix of the D-H coordinate system of the adjacent joints. According to the chain rule, the forward kinematics model of the flexible manipulator is constructed based on the homogeneous transformation matrix of the D-H coordinate system of the adjacent joints. Considering the problem of minimizing rope length error, and solving the problem of minimizing rope length error using the Levenberg-Marquardt optimization method, a forward kinematics model of the rope-driven parallel robot is constructed. By calculating the homogeneous transformation matrix from the end-effector coordinate system to the world coordinate system of the flexible manipulator, the forward kinematics model of the flexible manipulator is combined with the forward kinematics model of the rope-driven parallel robot to construct the forward kinematics model of the hybrid flexible robot and obtain the end-effector pose of the hybrid flexible robot. The formula for calculating the end-effector pose of the hybrid flexible robot is as follows: In the above formula, denotes the length of each rope, denotes the angle of each joint of the flexible manipulator, denotes the homogeneous transformation matrix of the base of the flexible manipulator relative to the moving platform coordinate system, denotes the forward kinematics function of the hybrid flexible robot, denotes the end pose of the hybrid flexible robot; denotes the generalized joint control quantity of the hybrid flexible robot; The specific expression for minimizing the rope length error problem is as follows: In the above formula, denotes the inverse kinematics function of the rope-driven parallel robot, denotes the rope length observation, denotes the forward kinematics model of the rope-driven parallel robot, denotes the rope vector length obtained by inverse kinematics solving, denotes the position vector of the fixed anchor base relative to the world coordinate system, denotes the position vector of the moving anchor base relative to the moving platform coordinate system, denotes the number of ropes, denotes the count variable, .

2. The workspace analysis method of a hybrid flexible robot according to claim 1, wherein The specific expression for the forward kinematics model of the hybrid flexible robot is as follows: In the above formula, denotes the end pose of the hybrid flexible robot, denotes the hybrid flexible robot inverse kinematics function, denotes the angle of each joint of the flexible robot, denotes the rope length observation value, denotes the generalized pose of the hybrid flexible robot, denotes the homogeneous transformation matrix of the flexible robot base relative to the moving platform coordinate system. 3.The workspace analysis method of a hybrid flexible robot according to claim 2, wherein, The step of constructing an inverse kinematics model of the hybrid flexible robot based on its end-effector pose and obtaining the generalized joint angle control quantities of the hybrid flexible robot specifically includes: Based on the end-effector pose of the hybrid flexible robot, obtain the complete solution set between the base pose of the flexible manipulator and the joint angles of the flexible manipulator. Based on the preset selection rules, a subset of the complete solution set is selected to determine the optimal base pose and the optimal joint angle of the flexible robotic arm. Based on the base pose and joint angle of the optimal flexible manipulator, an inverse kinematics model of the hybrid flexible robot is constructed to obtain the generalized joint angle control quantity of the hybrid flexible robot. The specific expression of the inverse kinematics model of the hybrid flexible robot is shown below; In the above formula, denotes a hybrid flexible robot generalized joint control variable, denotes a hybrid flexible robot inverse kinematics function, denotes a flexible manipulator joint angle, denotes a cable vector; The expression for the generalized joint angle control quantity of the hybrid flexible robot is: In the above formula, denotes the generalized pose of the hybrid flexible robot, denotes the generalized joint control variable of the hybrid flexible robot, denotes the pose of the moving platform with respect to the world coordinate system , denotes the number of ropes, denotes the number of flexible robot joints.

4. The workspace analysis method of a hybrid flexible robot according to claim 3, wherein, The expression for the preset selection rule is as follows: In the above formula, This indicates the selection of a rule function. This represents the complete solution set relating the base pose of the flexible robotic arm to the joint angles of the flexible robotic arm. This indicates the pose of the flexible robotic arm base relative to the world coordinate system. Indicates the joint angle of the flexible robotic arm. , , , , , They represent The amount. 5.The workspace analysis method of a hybrid flexible robot according to claim 4, wherein, The step of constructing a static analysis model of the hybrid flexible robot and obtaining the static equilibrium conditions of the hybrid flexible robot specifically includes: Constructing force balance equation of flexible manipulator joint ​ According to the force balance equation, the reaction force and reaction torque applied to the first joint of the flexible robot arm by the second joint are obtained ​​ A static model of the flexible robotic arm is constructed based on its reaction force and reaction torque. Calculate the coupling force between the flexible manipulator and the moving platform based on the static model of the flexible manipulator; By setting the center of mass of the moving platform as the equivalent force point, the force balance equation of the rope-driven parallel robot is constructed. A static model of the rope-driven parallel robot is constructed based on the force balance equation of the rope-driven parallel robot. The coupling force of the flexible manipulator on the moving platform is input to a statics model of the cable-driven parallel robot, and a statics analysis model of the hybrid flexible robot is constructed; The expression of the statics analysis model of the hybrid flexible robot is specifically as follows: In the above formula, represents the lower limit of the rope force, represents the upper limit of the rope force, represents the rope structure matrix, is the rope tension vector; represents the rope tension size, represents the gravity suffered by the moving platform, represents the external force suffered by the moving platform, represents the optimization objective function for minimizing the rope force; The statics balance condition of the hybrid flexible robot is obtained based on the statics analysis model of the hybrid flexible robot. 6.The workspace analysis method of a hybrid flexible robot according to claim 5, wherein, The workspace of the hybrid flexible robot is constructed by combining the end pose of the hybrid flexible robot, the generalized joint angle control quantity, and the statics balance condition, and the working state of the hybrid flexible robot is controlled according to the workspace, and the step specifically includes: S801, the end pose and the generalized joint angle control quantity of the hybrid flexible robot are given, and a random generalized pose of the hybrid flexible robot is generated according to the Monte Carlo method; S802, the coupling force of the flexible robot on the moving platform is calculated according to the statics model of the flexible robot, and a statics balance equation is established with the mass center of the moving platform as an equivalent force point; S803, the upper and lower limits of the cable force are given, the statics balance equation is used to establish an optimization problem with the minimum cable force as the target, and a quadratic programming method is used to solve the optimization problem, and the statics balance is judged for the solution, if the numerical solution is successful, the statics balance is satisfied, and S804 is entered, if the optimization problem has no solution, the statics balance is not satisfied, and S801 is entered; S804, the position of the end of the hybrid flexible robot relative to the world coordinate system is calculated according to the forward kinematics of the hybrid flexible robot, and it is judged whether the calculation result is inside the bounding box formed by the fixed anchor point, if yes, the random generalized pose point of the hybrid flexible robot obtained in S801 is added to the workspace set, if not, S801 is entered; The above S801 to S804 are repeated until a sufficient number of random generalized pose points of the hybrid flexible robot are obtained, and all the generalized pose points of the hybrid flexible robot generated in S901 form a workspace set. 7.The workspace analysis method of a hybrid flexible robot according to claim 6, wherein, The flexibility space solving method of the hybrid flexible robot specifically includes: S901, the joint angle of the flexible robot is generated according to the Monte Carlo method, and the pose of the end relative to the base is calculated, and the step is repeated for several times to obtain a pre-defined arm type space of the flexible robot; S902, the cross-sectional equation, the sampling range and the sampling interval are given, the position points are uniformly sampled as the position points of the moving platform according to the cross-sectional equation, the maximum sampling range and the sampling interval; S903, for each moving platform position point, the joint angle combination in the pre-defined arm type space of the flexible robot is combined into a generalized pose; S904, the statics balance of each generalized pose obtained in S903 is judged according to the statics model of the hybrid flexible robot, and the number of combinations satisfying the statics balance is calculated; S905, the flexibility of the hybrid flexible robot on the moving platform position point obtained in S902 is calculated according to the number of combinations satisfying the statics balance. The above S902 to S905 are cycled until the position points of the S902 cross-section equation are uniformly sampled, and the position points obtained by the S902 and the flexibility of the mixed flexible robot obtained by the S905 constitute a flexibility space, which is used to determine the operation space size of the flexible robot when the moving platform is at different positions in actual application, and guide the arrangement of the mixed flexible robot, so that the flexible robot operation space covers the target object.

8. A hybrid flexible robot workspace analysis system, comprising: The system is used to perform the workspace analysis method according to any one of claims 1-7, and comprises the following modules: A forward kinematics model construction module is configured to construct a forward kinematics model of the mixed flexible robot by considering the minimization of the rope length error, and obtain an end pose of the mixed flexible robot, wherein the mixed flexible robot comprises a flexible robot arm and a rope-driven parallel robot; An inverse kinematics model construction module is configured to construct an inverse kinematics model of the mixed flexible robot based on the end pose of the mixed flexible robot, and obtain a generalized joint angle control quantity of the mixed flexible robot; A statics analysis model construction module is configured to construct a statics analysis model of the mixed flexible robot, and obtain a static force balance condition of the robot; A control module is configured to construct a workspace of the mixed flexible robot in combination with the end pose of the mixed flexible robot, the generalized joint angle control quantity and the static force balance condition, and control a working state of the mixed flexible robot according to the workspace.

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