A global path smoothing method and system considering robot redundancy characteristics

Abstract

This invention belongs to the technical field of robot path smoothing, and discloses a global path smoothing method and system that considers the redundancy characteristics of robots. The method includes generating discrete tool position points, tool directions, and redundancy angles; constructing a system based on the discrete tool position points that satisfies C 2 The tool position spline is obtained by continuously generating five global PH splines; the tool direction is converted into Euler angles, using C... 2 A continuous global 5th-order PH spline is used to obtain the tool orientation spline. The arc length parameter of each path point is calculated based on the tool position spline. A piecewise 5th-order polynomial spline is established for the arc length parameter and the corresponding redundant angle. The objective function and constraints are constructed and quadratic programming is performed to obtain the redundant angle spline. The piecewise 5th-order polynomial spline is obtained by synchronizing the tool position spline parameter, tool orientation spline parameter, redundant angle spline parameter and arc length parameter to obtain the synchronization relationship. The smooth interpolation trajectory of the robot's six joints is obtained by solving the global velocity planning method.

Description

Technical Field

[0001] This invention belongs to the technical field of robot path smoothing, and more specifically, relates to a global path smoothing method and system that takes into account the redundancy characteristics of robots. Background Technology

[0002] With the rapid development of science and technology, robotics technology is also constantly advancing. Compared to five-axis CNC machine tools, robots are increasingly being applied in the machining field due to their advantages such as high flexibility and low cost. A 6-joint robot has six degrees of freedom, and when performing five-axis machining tasks, it has one redundant degree of freedom. This redundant degree of freedom does not affect the actual machining posture of the robot's end effector, but it does influence the joint configuration during machining. Existing methods for optimizing redundant angles mostly focus on the machining path point generation level, and primarily optimize discrete redundant angles by improving stiffness and avoiding singularities. They do not delve into the interpolation commands, which are the direct commands executed by the robot during machining. Therefore, researching the global redundant angle smoothing of robots performing five-axis machining tasks is of great significance for improving the robot's motion characteristics.

[0003] However, most existing robot posture optimization methods that consider robot redundancy characteristics focus on the robot path planning level, optimizing discrete redundancy angles without considering global redundancy angle optimization at the command interpolation level. Since robot path smoothing includes tool tip position smoothing, tool direction smoothing, and redundancy angle smoothing, it requires rigorous theoretical guidance and involves significant computational difficulty and complexity. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a global path smoothing method and system that takes into account the redundancy characteristics of the robot. Its purpose is to provide global optimization of the robot's position point, orientation angle and redundancy angle, and solve the technical problems of poor dynamic characteristics, low processing efficiency and large joint vibration of the robot when performing five-axis machining tasks.

[0005] To achieve the above objectives, according to one aspect of the present invention, a global path smoothing method considering robot redundancy characteristics is provided, the method comprising: S1: generating discrete tool position points, tool orientation, and redundancy angles using computer-aided manufacturing software; S2: constructing a system based on the discrete tool position points that satisfies C 2 A series of global 5-fold PH splines are used to smooth the tool position points and obtain the tool position spline; simultaneously, the tool direction is converted into Euler angle representation, and in Euler angle space, a method satisfying C is used. 2S3: Continuous global 5th degree PH splines are used to smooth the tool direction, resulting in a tool direction spline; S4: The arc length parameter of each path point is calculated based on the tool position spline, and a piecewise 5th degree polynomial spline of the arc length parameter and the corresponding redundant angle is established. An objective function is constructed for the piecewise 5th degree polynomial spline with the goal of minimizing acceleration. The redundant angle spline is obtained by quadratic programming with the position point, first derivative, and second derivative of the piecewise 5th degree polynomial spline as constraints. The piecewise 5th degree polynomial spline is:

[0006]

[0007] Where s is the arc length parameter corresponding to the q-th path point, γ q c is the redundant angle corresponding to the q-th path point. q,j S4: Synchronize the tool position spline parameters, tool direction spline parameters, redundant angle spline parameters, and arc length parameters to obtain the synchronization relationship; S5: Use the global velocity planning method to solve for the smooth interpolation trajectory of the robot's six joints.

[0008] Preferably, step S2 constructs a system based on the discrete tool position points that satisfies C. 2 The continuous global 5-times pH spline is as follows:

[0009] Based on the initial discrete tool position point P i =[P i,x ,P i,y ,P i,z ] T Construct the i-th 5th-order PH spline curve for i = 0, 1, 2…N:

[0010]

[0011] Where u is the tool position spline parameter, B i,j For spline control points, The basis functions are 5th order PH splines.

[0012] Preferably, step S2 is performed in Euler angle space, using the method that satisfies C 2 Five consecutive global PH splines were used to smooth the tool direction, resulting in the following tool direction spline:

[0013] Direct the tool direction O i =[O i,x O i,y O i,z ] T Converting i = 0, 1, 2…N to Euler angles Θ i =[α i ,β i ] Ti = 0, 1, 2…N, Construct the i-th 5th-order pH spline curve Θ i (ω);

[0014]

[0015] Where ω is the tool direction spline parameter, {M i,j} represents the spline control points. The basis functions are 5th order PH splines.

[0016] Preferably, the objective function F is:

[0017]

[0018] Where N is the number of path points, γ is the redundancy angle, and s i This represents the arc length of each path segment.

[0019] Preferably, the synchronization relationship is (u(s),ω(s),γ(s)).

[0020] Preferably, step S5 specifically includes: using a global velocity planning method to obtain the optimal robot interpolation trajectory that satisfies the position, orientation and acceleration constraints, and substituting the optimal robot interpolation trajectory into the robot kinematics inverse function for inverse kinematics solution to obtain the smooth interpolation trajectory of the robot's six joints.

[0021] Preferably, the optimal robot interpolation trajectory expression is:

[0022]

[0023]

[0024] Where, θ min θ represents the maximum range of motion of each joint. max v represents the minimum range of motion for each joint. max a is the maximum speed of the robot joint. max j is the maximum acceleration of the robot's joints. max The maximum jerk value for the robot joints.

[0025] θ(t)=IK([P(s(t)),Θ(s(t)),γ(s(t))])

[0026] Where IK(·) is the inverse kinematics function of the robot, θ(t) is the joint value at time t, and [P(s(t)),Θ(s(t)),γ(s(t))] is the optimal robot interpolation trajectory.

[0027] According to another aspect of the present invention, a global path smoothing system considering robot redundancy characteristics is provided, comprising: a parameter generation module for generating discrete tool position points, tool orientation, and redundancy angles using computer-aided manufacturing software; and a first acquisition module for constructing a system that satisfies C based on the discrete tool position points. 2 A series of global 5-fold PH splines are used to smooth the tool position points and obtain the tool position spline; simultaneously, the tool direction is converted into Euler angle representation, and in Euler angle space, a method satisfying C is used. 2 A continuous global 5th degree PH spline is used to smooth the tool direction, resulting in a tool direction spline. The second acquisition module calculates the arc length parameter for each path point based on the tool position spline, establishes a piecewise 5th degree polynomial spline of the arc length parameter and corresponding redundant angle, constructs an objective function for the piecewise 5th degree polynomial spline with the goal of minimizing acceleration, and performs quadratic programming using the position point, first derivative, and second derivative of the piecewise 5th degree polynomial spline as constraints to obtain a redundant angle spline. The piecewise 5th degree polynomial spline is as follows:

[0028]

[0029] Where s is the arc length parameter corresponding to the g-th path point, γ q c is the redundant angle corresponding to the g-th path point. q，j The coefficients are the spline coefficients of a fifth-order polynomial;

[0030] The third acquisition module is used to synchronize the tool position spline parameters, tool direction spline parameters, redundant angle spline parameters, and arc length parameters to obtain the synchronization relationship; the solution module is used to solve for the smooth interpolation trajectory of the robot's six joints using a global velocity planning method.

[0031] In summary, compared with the prior art, the global path smoothing method and system considering robot redundancy characteristics provided by the present invention have the following advantages:

[0032] 1. This application constructs a system that satisfies C 2 By constructing a global optimization method for tool position splines, tool direction splines, and redundant angle splines using continuous global 5th-order PH splines and piecewise 5th-order polynomial splines for redundant angles, global optimization of toolpaths is achieved. This fully leverages the dynamic characteristics of the robot when performing five-axis machining tasks, improves machining efficiency, and reduces robot joint vibration.

[0033] 2. By constructing piecewise quintic polynomial splines with arc length parameters and corresponding redundant angles, an objective function is constructed for the piecewise quintic polynomial splines with the goal of minimizing acceleration. The redundant angle splines are obtained by quadratic programming with the position points, first derivatives, and second derivatives of the piecewise quintic polynomial splines as constraints. This enables attitude planning for robots performing redundant machining tasks, thereby improving robot machining efficiency. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the global path smoothing method considering robot redundancy characteristics in an embodiment of this application.

[0035] Figure 2 This is a schematic diagram illustrating the redundancy characteristics of robot processing in an embodiment of this application;

[0036] Figure 3 This is a schematic diagram of the robot tool position smoothing according to an embodiment of this application;

[0037] Figure 4 This is a schematic diagram of the robot tool direction smoothing in an embodiment of this application;

[0038] Figure 5 This is a schematic diagram of a fifth-order polynomial spline for the robot redundancy angle in an embodiment of this application;

[0039] Figure 6 This is a schematic diagram showing the synchronization of tool position spline parameters, orientation angle spline parameters, and redundant angle spline parameters in an embodiment of this application;

[0040] Figure 7 This is a schematic diagram of the instance path selected in the embodiments of this application;

[0041] Figure 8A This is the result of tool position smoothing using the example path selected in the embodiments of this application;

[0042] Figure 8B This is the result of tool direction smoothing using the example path selected in the embodiments of this application;

[0043] Figure 8C This is the result of tool redundancy angle smoothing of the example path selected in the embodiments of this application;

[0044] Figure 9 This is the speed planning result of the example selected in the embodiments of this application. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0046] The first aspect of this application provides a global path smoothing method that considers the redundancy characteristics of a robot, such as... Figure 1 As shown, the method includes the following steps S1 to S5.

[0047] S1: Use computer-aided manufacturing software to generate discrete tool position points, tool direction and redundancy angles.

[0048] In the workpiece coordinate system, such as Figure 2 As shown, discrete tool position points P = [P] are generated by computer-aided manufacturing (CAM) software. x P y P z ] T Tool direction o = [O x O y O z ] T And the redundant angle γ.

[0049] S2: Construct a system based on the discrete tool position points that satisfies C 2 A series of global 5-fold PH splines are used to smooth the tool position points and obtain the tool position spline; simultaneously, the tool direction is converted into Euler angle representation, and in Euler angle space, a method satisfying C is used. 2 Five consecutive global PH splines are used to smooth the tool direction and obtain the tool direction spline.

[0050] like Figure 3 As shown, based on the discrete tool position points, a system is constructed that satisfies C. 2 The continuous global 5-times pH spline is as follows:

[0051] Based on the initial discrete tool position point P i =[P i，x P i，y P i，z ] T Construct the i-th 5th-order PH spline curve for i = 0, 1, 2…N:

[0052]

[0053] Where u is the tool position spline parameter, B i,j For spline control points, The basis functions are 5th order PH splines.

[0054] To construct the PH spline, with respect to the quaternion coefficients q0, q1, ..., q N+1 The polynomial equation is used to determine the derivative of the PH spline:

[0055] P i ′(u)=w i (u)iw i * (u)

[0056] w i (u)=w i,0 (1-u) 2 +2w i,1 (1-u)u+w i,2 u 2

[0057]

[0058] Among them, P i ′(u) is P i The first derivative of (u), w i (u) is a quaternion equation, w i * (u) is w i (u) conjugate.

[0059] To calculate the quaternion coefficient q, we can integrate the above expression from 0 to 1 to obtain:

[0060]

[0061] The above formula can establish N equations about q, and since q has N+2 variables, the condition for adding the first and last tangent vectors of the spline is:

[0062]

[0063] The solution to the quaternion polynomial is not unique. We propose using Newton's iteration method to find the solution, establishing a cubic B-spline structure. i (u) To construct the initial solution, calculate the tangent vector c′ (u=0,0.5,1) for each B-spline segment. Therefore, the initial solution of the quaternion is calculated using the following formula:

[0064]

[0065] Shaped like AiA * =c, the solution is as follows:

[0066]

[0067] Where (λ,u,v)=c / |c|.

[0068] Solving equation (5) yields the result that satisfies C. 2 For continuous initial solutions, the iterative equation is:

[0069]

[0070] Since the expression contains an imaginary number i, it cannot be iterated using differentiation; therefore, a linearization method is chosen:

[0071]

[0072] Through the above iterative process, the quaternion coefficients q0, q1, ..., q that meet the required accuracy can be obtained. N+1 The method for calculating pH spline control points is as follows:

[0073]

[0074] The arc length s is calculated as follows:

[0075]

[0076] Where σ i =[σ i,0 ,σ i,1 ,σ i,2 ,σ i,3 ,σ i,4 The following formula can be used to calculate:

[0077]

[0078] In a further preferred embodiment, step S2 takes place in Euler angle space and uses the condition C. 2 Five consecutive global pH splines were used to smooth the tool direction, such as... Figure 4 As shown, the tool direction spline is obtained as follows:

[0079] Direct the tool direction O i =[O i,x O i,y O i,z ] T Converting i = 0, 1, 2…N to Euler angles Θ i =[α i ,β i ] T i = 0, 1, 2…N, Construct the i-th 5th-order pH spline curve Θ i (ω);

[0080]

[0081] Where ω is the tool direction spline parameter, {M i,j} represents the spline control points. These are the basis functions for the 5th-order PH spline. The method for constructing the planar 5th-order PH spline is the same as described above, and will not be repeated here.

[0082] S3: Calculate the arc length parameter for each path point based on the tool position spline, such as... Figure 5 As shown, a piecewise 5th-order polynomial spline is established for the arc length parameter and the corresponding redundant angle. An objective function is constructed for the piecewise 5th-order polynomial spline with the goal of minimizing acceleration. A quadratic programming operation is then performed using the position points, first derivative, and second derivative of the piecewise 5th-order polynomial spline as constraints to obtain the redundant angle spline. The piecewise 5th-order polynomial spline is as follows:

[0083]

[0084] Where s is the arc length parameter corresponding to the q-th path point, γ q c is the redundant angle corresponding to the q-th path point. q,j The coefficients are 5th-order polynomial splines; in a further optimized scheme, the objective function F for establishing the minimum acceleration using polynomial splines is:

[0085]

[0086] Where N is the number of path points, γ is the redundancy angle, and s i This represents the arc length of each path segment.

[0087] The optimization function for the i-th spline segment can be expressed as:

[0088]

[0089] This can be represented in matrix form as follows:

[0090]

[0091] Therefore, the optimization function can be transformed into a quadratic programming form:

[0092]

[0093] The continuity condition of the position points of the spline segment can be expressed as:

[0094] γ i (0)=γ i-1 ,γ i (s i )=γ i For i = 1, 2, ..., N-1, N:

[0095]

[0096] Represented in matrix form as follows:

[0097]

[0098] The first-order and second-order continuity conditions are:

[0099]

[0100]

[0101] Represented in matrix form as follows:

[0102]

[0103] The conditions for the first and last points are:

[0104]

[0105] Therefore, the final optimization function is:

[0106]

[0107]

[0108] The above optimization function (23) can be solved using MATLAB's optimization function toolbox.

[0109] S4: As Figure 6 As shown, the tool position spline parameters, tool direction spline parameters, redundant angle spline parameters, and arc length parameters are synchronized to obtain the synchronization relationship.

[0110] Due to the analytical property of the arc length of the PH spline, the tool position spline parameters and the arc length are established through the analytical relationship of PH, thus establishing u(s).

[0111] The tool direction spline parameter ω(s) is:

[0112] In a further optimized scheme, the synchronization relationship is: (u(s),ω(s),γ(s)).

[0113] S5: The smooth interpolation trajectory of the robot's six joints is obtained by using the global velocity planning method.

[0114] This step specifically includes:

[0115] The optimal robot interpolation trajectory that satisfies position, orientation and acceleration constraints is obtained by using a global velocity planning method. The optimal robot interpolation trajectory is then substituted into the robot kinematics inverse function for inverse kinematics solution to obtain the smooth interpolation trajectory of the robot's six joints.

[0116] In this embodiment, the optimal robot interpolation trajectory expression is:

[0117]

[0118]

[0119] Where, θ min θ represents the maximum range of motion of each joint. max v represents the minimum range of motion for each joint. max a is the maximum speed of the robot joint. max j is the maximum acceleration of the robot's joints. max The maximum jerk value for the robot joints.

[0120] By solving the above optimization function, the end interpolation vector [P(s(t)),Θ(s(t)),γ(s(t))] is obtained.

[0121] Based on the obtained robot end-effector interpolation data, substitute it into the robot's inverse kinematics function to obtain the robot joint interpolation command:

[0122] θ(t)=IK([P(s(t)),Θ(s(t)),γ(s(t))])

[0123] Where IK(·) is the inverse kinematics function of the robot, θ(t) is the angle value of each joint at time t, and [P(s(t)),Θ(s(t)),γ(s(t))] is the optimal robot interpolation trajectory, such as Figure 7 , Figure 8A , Figure 8B , 8C as well as Figure 9 As shown.

[0124] The second aspect of this application provides a global path smoothing system that takes into account the redundancy characteristics of a robot, including a parameter generation module, a first acquisition module, a second acquisition module, a third acquisition module, and a solution module.

[0125] Parameter generation module: used to generate discrete tool position points, tool orientation, and redundant angles using computer-aided manufacturing software;

[0126] First acquisition module: used to construct a system that satisfies C based on the discrete tool position points. 2 A series of global 5-fold PH splines are used to smooth the tool position points and obtain the tool position spline; simultaneously, the tool direction is converted into Euler angle representation, and in Euler angle space, a method satisfying C is used. 2 Five consecutive global PH splines are used to smooth the tool direction and obtain the tool direction spline.

[0127] The second acquisition module is used to calculate the arc length parameter of each path point based on the tool position spline, establish a piecewise quintic polynomial spline of the arc length parameter and the corresponding redundant angle, construct an objective function for the piecewise quintic polynomial spline with the goal of minimizing acceleration, and perform quadratic programming using the position point, first derivative, and second derivative of the piecewise quintic polynomial spline as constraints to obtain the redundant angle spline, wherein the piecewise quintic polynomial spline is:

[0128]

[0129] Where s is the arc length parameter corresponding to the q-th path point, γ q c is the redundant angle corresponding to the q-th path point. q,j The coefficients are the spline coefficients of a fifth-order polynomial;

[0130] The third acquisition module is used to synchronize the tool position spline parameters, tool direction spline parameters, redundant angle spline parameters and arc length parameters to obtain the synchronization relationship.

[0131] The solver module is used to solve for the smooth interpolation trajectory of the robot's six joints using a global velocity planning method.

[0132] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0133] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is 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 within the scope of protection of the present invention.

Claims

1. A global path smoothing method considering robot redundancy characteristics, characterized in that, Comprise: S1: using computer aided manufacturing software to generate discrete tool position points, tool direction and redundancy angle; S2: Construct a continuous global 5th order PH spline that satisfies C 2 a continuous global 5th order PH spline to perform tool position point fairing to obtain a tool position spline; meanwhile, the tool orientation is converted into Euler angle representation, and a continuous global 5th order PH spline is adopted in the Euler angle space to perform tool orientation fairing to obtain a tool orientation spline; C 2 a continuous global 5th order PH spline to perform tool position point fairing to obtain a tool position spline; meanwhile, the tool orientation is converted into Euler angle representation, and a continuous global 5th order PH spline is adopted in the Euler angle space to perform tool orientation fairing to obtain a tool orientation spline; S3: according to the tool position spline, the arc length parameter of each path point is calculated, the segmented quintic polynomial spline of the arc length parameter and the corresponding redundancy angle is established, the objective function is constructed with the minimum acceleration as the target of the segmented quintic polynomial spline, and the redundancy angle spline is obtained by quadratic programming with the position point, first derivative and second derivative of the segmented quintic polynomial spline as constraint conditions, wherein the segmented quintic polynomial spline is: wherein, s is the arc length parameter corresponding to the q th path point, is the redundant angle corresponding to the q th path point, is a quintic polynomial spline coefficient; S4: synchronize the tool position spline parameter, the tool direction spline parameter, the redundancy angle spline parameter and the arc length parameter to obtain a synchronization relationship; S5: using global velocity planning method to solve and obtain the smooth interpolation trajectory of the six joints of the robot; Step S2 is to perform tool direction fairing in the Euler angle space using a continuous global 5th order PH spline that satisfies C 2 The tool direction spline is obtained by performing tool direction fairing using a continuous global 5th order PH spline that satisfies Convert the tool orientation to Euler angle representation , The first i segment 5th order PH spline curve : wherein, is the tool direction spline parameter, is the spline control point, is the basis function of the 5th order PH spline; The objective function is: wherein, N is the number of path points, is the redundancy angle, is the first i segment path arc length.

2. The global path smoothing method of claim 1, wherein, Step S2 constructs a global 5th order PH spline that satisfies C 2 The continuous global 5th order PH spline is specifically: According to the initial discrete tool position points , a first i segment 5th order PH spline curve is constructed wherein, is the tool position spline parameter, is the spline control point, is the basis function of the 5th order PH spline.

3. The global path smoothing method of claim 1, wherein, The synchronization relationship is ; wherein, is a tool position spline parameter, is a tool orientation spline parameter, is a redundancy angle.

4. The global path smoothing method of claim 1, wherein, Step S5 specifically comprises: using global velocity planning method to obtain the optimal robot interpolation trajectory satisfying position, direction and acceleration constraints, and bringing the optimal robot interpolation trajectory into the robot kinematics inverse function to obtain the smooth interpolation trajectory of the six joints of the robot.

5. The global path smoothing method of claim 4, wherein, The optimal robot interpolation trajectory expression is: wherein, is a maximum value of the range of motion of each joint, is a minimum value of the range of motion of each joint, is a maximum value of the velocity of the robot joint, is a maximum value of the acceleration of the robot joint, is a maximum value of the jerk of the robot joint.

6. The global path smoothing method of claim 4 or 5, wherein, The kinematics inverse function is: wherein, is a robot kinematics inverse function, is an angle value of each joint at time t, is an optimal robot interpolation trajectory.

7. A global path smoothing system that takes into account the robot's redundancy characteristics, characterized in that, The system for implementing the global path smoothing method of any one of the above claims 1-6 comprises: Parameter generation module: for using computer aided manufacturing software to generate discrete tool position points, tool direction and redundancy angle; The first obtaining module is configured to construct a continuous global 5th order PH spline according to the discrete tool position points to perform tool position point fairing and obtain a tool position spline; meanwhile, the tool orientation is converted into Euler angle representation, and a continuous global 5th order PH spline is adopted in the Euler angle space to perform tool orientation fairing and obtain a tool orientation spline. C 2 The first obtaining module is configured to construct a continuous global 5th order PH spline according to the discrete tool position points to perform tool position point fairing and obtain a tool position spline; meanwhile, the tool orientation is converted into Euler angle representation, and a continuous global 5th order PH spline is adopted in the Euler angle space to perform tool orientation fairing and obtain a tool orientation spline. C 2 The first obtaining module is configured to construct a continuous global 5th order PH spline according to the discrete tool position points to perform tool position point fairing and obtain a tool position spline; meanwhile, the tool orientation is converted into Euler angle representation, and a continuous global Second acquisition module: for calculating the arc length parameter of each path point according to the tool position spline, establishing the segmented quintic polynomial spline of the arc length parameter and the corresponding redundancy angle, constructing the objective function with the minimum acceleration as the target of the segmented quintic polynomial spline, and obtaining the redundancy angle spline by quadratic programming with the position point, first derivative and second derivative of the segmented quintic polynomial spline as constraint conditions, wherein the segmented quintic polynomial spline is: wherein, s is an arc length parameter corresponding to the q th path point, is a redundant angle corresponding to the q th path point, is a quintic polynomial spline coefficient; Third acquisition module: for synchronizing the tool position spline parameter, the tool direction spline parameter, the redundancy angle spline parameter and the arc length parameter to obtain a synchronization relationship; Solving module: for using global velocity planning method to solve and obtain the smooth interpolation trajectory of the six joints of the robot.

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