Robot time optimal speed planning method and system considering robot contour error constraint

Abstract

The invention belongs to the field of robot speed planning, and particularly relates to a robot time optimal speed planning method and system considering robot contour error constraints, and the method comprises the steps: firstly building a prediction model related to robot joint tracking errors according to a robot joint control loop; then, according to a robot joint tracking error model and a Frenet framework of a robot path, a linear prediction model of a robot tail end contour error about joint speed, acceleration and jerk is achieved; and finally, according to a typical constraint equation of robot speed planning, a contour error constraint model is added, and time optimal speed planning meeting robot contour error constraint is realized.

Description

Technical Field

[0001] The present invention belongs to but is not limited to the technical field of robot speed planning, and in particular relates to a robot time optimal speed planning method and system considering robot contour error constraints. Background Art

[0002] At present, with the improvement of the accuracy of industrial robots, robots are increasingly widely used in high-speed and high-precision machining fields, such as robot high-speed milling, high-speed welding and other industries. This kind of operation scenario often requires the robot's motion efficiency to be improved without sacrificing the robot's motion accuracy, especially the robot's contour error accuracy in the working space. Existing robot speed planning often only considers the robot's joint servo constraints to achieve the optimal robot speed, but does not consider the robot's terminal contour error caused by the robot's joint servo tracking error. Therefore, when planning the robot speed, it is necessary to consider the robot's terminal contour error constraint implementation to achieve high-precision and high-speed robot speed planning. However, most of the existing robot contour error modeling methods are nonlinear modeling methods, which are difficult to directly use in robot speed planning to achieve high-efficiency contour error prediction. Therefore, it is necessary to establish a contour error prediction model that can be used for robot speed planning.

[0003] Through the above analysis, the problems and defects of the prior art are as follows:

[0004] (1) The existing robot velocity planning does not take into account the contour error constraint and cannot guarantee the end-of-robot motion accuracy.

[0005] (2) Existing robot contour error modeling methods are difficult to directly use as constraints during robot velocity planning. Summary of the invention

[0006] In view of the problems existing in the prior art, the present invention provides a robot time optimal speed planning method and system taking into account the robot contour error constraints.

[0007] The present invention is implemented as follows: a robot time optimal speed planning method considering robot contour error constraints and the method comprises:

[0008] S1, based on the robot joint control loop, establish a prediction model for the robot joint tracking error.

[0009] S2, based on the robot joint tracking error model and the Frenet framework of the robot path, realize the linear prediction model of the robot end contour error with respect to the joint velocity, acceleration, and jerk;

[0010] S3, according to the typical constraint equation of robot speed planning, the constraint model of contour error is added to achieve the time-optimal speed planning under the robot contour error constraint;

[0011] Furthermore, in step S1, a prediction model for robot joint tracking error is established according to the robot joint control loop, specifically:

[0012] The tracking error of each joint of the robot can be expressed by the transfer function:

[0013] q i,e (s) = G i,e (s)q i,r (s), i=1L6 (1)

[0014] where q i,e (s) is the tracking error of the ith joint, G i,e (s) is the error transfer function of the i-th joint, q i,r (s) is the input command of the i-th joint, and s is the Laplace operator. G i,e The third-order Maclaurin expansion of (s) at s = 0 gives:

[0015]

[0016] Since the steady-state error design value of the robot is 0, the first term of the above formula is 0, so the above formula can be converted into:

[0017] G i,e (s) = K i,vel s+K i,acc s 2 +K i,jer s 3 (3)

[0018] Where K i,vel , K i,acc , K i,jer is the model coefficient.

[0019] Converting the above formula from frequency domain to time domain, we can get the time domain expression of tracking error:

[0020]

[0021] In step S2, according to the robot joint tracking error model and the Frenet framework of the robot path, a linear prediction model of the robot end contour error with respect to joint velocity, acceleration, and jerk is implemented, specifically:

[0022] Step S1 obtains the tracking error model of each joint of the robot, and the tracking error of the robot end can be expressed by kinematic solution calculation as:

[0023] [P e ,O e ]=FK(qr )-FK(q r -q e ) (5)

[0024] Among them [P e ,O e ] is the position tracking error and direction tracking error of the robot end, FK() is the forward kinematics of the robot, q r and q e are the robot's input instructions and tracking errors.

[0025] Due to the nonlinear relationship in forward kinematics, the posture tracking error can be regarded as the end differential motion result caused by the differential motion equivalent to the robot joint tracking error through Jacobi matrix transformation:

[0026] [ ω P e , ω O e ] T = J(q r )q e (6)

[0027] in[ ω P e , ω O e ] is the position tracking error accuracy of the robot in a fixed coordinate system, satisfying P e = ω P e J is the robot Jacobian matrix. The robot direction tracking error needs to be converted into:

[0028]

[0029] Among them [O α ,O β ] is the robot's zyz Euler angle.

[0030] The above formula has realized the linear estimation of the robot end tracking error with respect to the robot joint velocity, acceleration, and jerk. In order to realize the estimation of the contour error, since the position and direction of the robot are expressed as spline expressions about the arc length, the tangent vector and normal vector of each path point can be expressed as:

[0031]

[0032] Where [t p ,t o ] is the tangent vector, [n p ,n o] is the normal vector, [P′(s), O′(s)] is the first-order derivative of position and direction with respect to the arc length, and [P″(s), O″(s)] is the second-order derivative of position and direction with respect to the arc length.

[0033] The binormal vector b can be calculated by the right-hand rule as b = n × t, so the tracking error in the base coordinate system [P e ,O e ] can be converted to the Frenet coordinate system of the path as [P pe ,O oe ]:

[0034]

[0035] The prediction model of contour error can be calculated by the following equation and further expressed as a linear expression:

[0036]

[0037] Among them [ε p ,ε o ] are the position contour error and direction contour error of the robot respectively. To simplify the writing, the contour error prediction equation of the robot is written as:

[0038]

[0039] The step S3, according to the typical constraint equation of robot speed planning, adds the constraint model of contour error to achieve the time optimal speed planning under the robot contour error constraint; specifically:

[0040] The constraint equation of convex optimization of robot velocity planning, the typical velocity planning equation that satisfies the third-order constraints of the robot expressed by B-spline velocity square can be expressed as:

[0041]

[0042] Where f is the velocity spline control point, Y(u) is the robot velocity square B-spline, m is the number of checkpoints, δs is the interval between checkpoints, S Σ is the arc length of the robot path, [V max ,A max ,J max ] are the robot terminal velocity, acceleration, and jerk constraints, are the robot joint velocity, acceleration, and jerk constraints. C1(s)≤0 is the first step constraint, C2(s)≤0 is the second step constraint, and Y * (u) is the intermediate variable obtained by the first step constraint, [q′,q″,q″′] is the partial derivative of the robot joint with respect to the end arc length, and [Y′(u),Y″(u)] is the derivative equation of the velocity square spline.

[0043] In order to implement the constraint equation of adding contour error in the above formula, it is necessary to scale the nonlinear terms of robot joint velocity and jerk. The following formula is used to locally amplify and reduce the velocity term as an approximate term:

[0044]

[0045] The approximate term of the acceleration is calculated using the following formula:

[0046]

[0047] By combining the above formulas, the linear expression of the contour error with respect to the speed planning variable can be realized. In order to simplify the writing, the constraint of the contour error is expressed as follows:

[0048]

[0049] The time optimal speed planning equation with the contour error constraint finally added can be expressed as:

[0050]

[0051] The above expression can be used to realize the robot time optimal velocity planning that meets the contour error constraint through two-step linear programming.

[0052] Another object of the present invention is to provide a robot time optimal speed planning system considering robot contour error constraints, which implements the robot time optimal speed planning method and system considering robot contour error constraints, and the system comprises:

[0053] The tracking error prediction module establishes a prediction model of the robot joint tracking error based on the robot control loop;

[0054] The contour error prediction module builds a linear prediction model of the robot end contour error based on the robot tracking error prediction model and the Frene framework;

[0055] The optimization implementation module adds the constraint model of contour error according to the typical equation of robot speed planning to achieve the time-optimal speed planning under the constraint of robot contour error.

[0056] Another object of the present invention is to provide a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the robot time optimal speed planning method considering the robot contour error constraints.

[0057] Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to execute the steps of the robot time optimal velocity planning method considering the robot contour error constraints.

[0058] Another object of the present invention is to provide an information data processing terminal, which is used to implement the robot time optimal speed planning system considering the robot contour error constraints.

[0059] In combination with the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solutions to be protected by the present invention are as follows:

[0060] First, the present invention is a typical robot speed planning problem. By considering the contour error in the robot speed planning, a robot time optimal speed planning method and system considering the robot contour error constraint is realized.

[0061] The present invention aims to solve the problem that the actual motion accuracy of the robot is not considered in the existing robot speed planning, and proposes a robot time optimal speed planning method that takes into account the robot contour error constraint. The existing technology usually fails to fully consider the correlation between the tracking error of the robot joint and the end contour error, resulting in the system being unable to effectively suppress the error in complex paths or high dynamic scenes. The present invention achieves time optimal path planning while ensuring accuracy by establishing a joint error prediction model and a linear expression of the contour error, thereby solving the problem of the difficulty in balancing efficiency and accuracy in traditional methods.

[0062] Compared with the prior art, the present invention has made significant technical progress in the following aspects: First, by combining the joint error model with the path Frenet framework, the end contour error is accurately predicted and incorporated into the speed planning constraint, which significantly improves the accuracy of the robot path tracking. Secondly, the nonlinear term of the contour error constraint is innovatively converted into a linear expression, which effectively reduces the computational complexity of the planning model and improves the planning efficiency. In addition, the time-optimal speed planning is achieved through two-step linear programming, which maximizes the speed efficiency while maintaining high accuracy.

[0063] The technical solution of the present invention is applicable to a variety of industrial robot motion planning scenarios, especially in processing tasks with high precision and high dynamic requirements. The proposed planning method can achieve high-precision robot motion while ensuring the robot motion efficiency. This method improves processing efficiency and product quality, reduces the rework rate caused by errors, and has a wide range of industrial application value in aerospace, precision manufacturing and other fields.

[0064] Second, auxiliary evidence of creativity also has the following important manifestations.

[0065] The present invention proposes a robot time optimal speed planning method considering the robot contour error constraint, which is reasonably designed, easy to implement, and non-invasive. This method does not require the introduction of additional hardware in the existing robot system, and can be applied only by implementing it on the existing control system through the optimization algorithm. This design significantly reduces the implementation cost and complexity, making it possible to widely promote it in the field of industrial automation. Especially in high-precision application scenarios such as grinding, welding, and cutting, this method can improve trajectory tracking accuracy and achieve smoother motion trajectories, thereby improving production efficiency and product quality, and has significant commercial value and market potential.

[0066] The technical solution of the present invention fills the technical gap in the industry at home and abroad. In practical applications, the existing time-optimal speed planning methods for robots often fail to fully consider the contour error of the robot end, resulting in poor position accuracy in high-precision operations. The present invention optimizes the speed planning algorithm by introducing contour error constraints, so that the robot can more accurately control the end position when performing complex tasks, significantly improving the effect of high-precision applications such as force-controlled grinding and polishing. This innovative improvement solves long-standing technical problems in the industry, provides a new technical path for the application of robots in high-precision operations, and promotes the development of robotics technology.

[0067] The present invention also overcomes the technical bias in the prior art. Traditional robot speed planning methods usually only consider fixed motion constraints, ignoring the balance between robot motion accuracy and motion performance in actual operation. The solution proposed by the present invention achieves dual optimization of robot motion efficiency and motion accuracy by comprehensively considering contour errors and motion efficiency. This method not only improves the robot's motion efficiency, enabling it to complete tasks more quickly, but also ensures motion accuracy and meets the needs of high-precision operations. This breakthrough effectively solves the contradiction between efficiency and accuracy faced by robots in practical applications, and significantly improves the overall performance and application value of the robot system. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 A flow chart of a robot speed planning method provided by an embodiment of the present invention;

[0069] Figure 2 A schematic diagram of a speed planning path provided for the implementation of the present invention;

[0070] Figure 3 Comparison of speed planning effects provided by the embodiment of the present invention and the comparison method;

[0071] Figure 4 Contour error comparison between the embodiment of the present invention and the comparative method DETAILED DESCRIPTION

[0072] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0073] like Figure 1 As shown, an embodiment of the present invention provides a robot time optimal speed planning method considering robot contour error constraints, which specifically includes the following steps:

[0074] S1, based on the robot joint control loop, establish a prediction model for the robot joint tracking error.

[0075] S2, based on the robot joint tracking error model and the Frenet framework of the robot path, realize the linear prediction model of the robot end contour error with respect to the joint velocity, acceleration, and jerk;

[0076] S3, according to the typical constraint equation of robot speed planning, the constraint model of contour error is added to achieve the time-optimal speed planning under the robot contour error constraint;

[0077] The system first obtains the input instructions of each joint of the robot and uses the joint control loop to establish a prediction model for joint tracking errors. Through Laplace transform, the error transfer function is expanded into a third-order Maclaurin series and simplified into a time domain expression of joint tracking errors. This model describes the linear calculation relationship between joint tracking errors and velocity, acceleration and jerk, providing a basis for subsequent contour error calculations.

[0078] The modeling module converts the joint tracking error into the terminal posture error based on forward kinematics. Through the Jacobian matrix, the nonlinear relationship is linearized into a differential motion model to describe the dependence of the terminal position and direction error on the joint motion. At the same time, combined with the Frenet framework of the path, the terminal error is converted into the contour error in the path coordinate system through the tangent vector, normal vector and binormal vector, including the position contour error and the direction contour error. This linear prediction model ensures the accuracy of subsequent velocity planning.

[0079] In the planning module, the velocity planning of the robot path is expressed in the form of B-spline velocity square. Combining the terminal velocity, acceleration and jerk constraint equations, as well as the joint velocity, acceleration and jerk constraints, a multi-constraint velocity planning equation is constructed. In order to further ensure the robot's operating accuracy, the system adds a constraint expression based on the contour error prediction model to the velocity planning to achieve coordinated optimization of path accuracy and motion efficiency.

[0080] Since there are nonlinear terms in the joint velocity and jerk in the contour error constraint, the planning module uses a local scaling method to approximate the nonlinear terms into linear expressions. This process simplifies the complex nonlinear constraints through piecewise scaling of velocity and jerk, and ensures that the contour error constraint can be effectively embedded in the velocity planning model. This linearization method improves the solution efficiency while maintaining sufficient calculation accuracy.

[0081] Based on the above constraint model, the system uses a two-step linear programming method to solve the time-optimal speed planning equation. In the first step, the optimal speed curve that satisfies the speed and acceleration constraints is preliminarily calculated; in the second step, the contour error constraint condition is optimized by dynamically adjusting the control points of the speed curve to obtain the final time-optimal speed planning result. This method can maximize speed efficiency while maintaining motion accuracy.

[0082] The execution module controls the robot joint movement according to the planning results, realizes the time-optimal speed planning under the robot contour error constraint, and ensures the high-precision and high-efficiency operation of the robot in complex environments.

[0083] Furthermore, in step S1, a prediction model for robot joint tracking error is established according to the robot joint control loop, specifically:

[0084] The tracking error of each joint of the robot can be expressed by the transfer function:

[0085] q i,e (s) = G i,e (s)q i,r (s), i=1L6 (17)

[0086] where q i,e (s) is the tracking error of the ith joint, G i,e (s) is the error transfer function of the i-th joint, q i,r (s) is the input command of the i-th joint, and s is the Laplace operator. G i,e The third-order Maclaurin expansion of (s) at s = 0 gives:

[0087]

[0088] Since the steady-state error design value of the robot is 0, the first term of the above formula is 0, so the above formula can be converted into:

[0089] G i,e (s) = K i,vel s+K i,acc s 2 +K i,jer s 3 (19)

[0090] Where K i,vel , K i,acc , K i,jer is the model coefficient.

[0091] Converting the above formula from frequency domain to time domain, we can get the time domain expression of tracking error:

[0092]

[0093] In step S2, according to the robot joint tracking error model and the Frenet framework of the robot path, a linear prediction model of the robot end contour error with respect to joint velocity, acceleration, and jerk is implemented, specifically:

[0094] Step S1 obtains the tracking error model of each joint of the robot, and the tracking error of the robot end can be expressed by kinematic solution calculation as:

[0095] [P e ,O e ]=FK(q r )-FK(q r -q e ) (twenty one)

[0096] Among them [P e ,O e ] is the position tracking error and direction tracking error of the robot end, FK() is the forward kinematics of the robot, q r and q e are the robot's input instructions and tracking errors.

[0097] Due to the nonlinear relationship in forward kinematics, the posture tracking error can be regarded as the end differential motion result caused by the differential motion equivalent to the robot joint tracking error through Jacobi matrix transformation:

[0098] [ ω P e , ω O e ] T = J(q r )q e (twenty two)

[0099] in[ ω P e , ω O e ] is the position tracking error accuracy of the robot in a fixed coordinate system, satisfying P e = ω P e J is the robot Jacobian matrix. The robot direction tracking error needs to be converted into:

[0100]

[0101] Among them [O α ,O β ] is the robot's zyz Euler angle.

[0102] The above formula has realized the linear estimation of the robot end tracking error with respect to the robot joint velocity, acceleration, and jerk. In order to realize the estimation of the contour error, since the position and direction of the robot are expressed as spline expressions about the arc length, the tangent vector and normal vector of each path point can be expressed as:

[0103]

[0104] Where [t p ,t o ] is the tangent vector, [n p ,n o ] is the normal vector, [P′(s), O′(s)] is the first-order derivative of position and direction with respect to the arc length, and [P″(s), O″(s)] is the second-order derivative of position and direction with respect to the arc length.

[0105] The binormal vector b can be calculated by the right-hand rule as b = n × t, so the tracking error in the base coordinate system [P e ,O e ] can be converted to the Frenet coordinate system of the path as [P pe ,O oe ]:

[0106]

[0107] The prediction model of contour error can be calculated by the following equation and further expressed as a linear expression:

[0108]

[0109] Among them [ε p ,ε o ] are the position contour error and direction contour error of the robot respectively. To simplify the writing, the contour error prediction equation of the robot is written as:

[0110]

[0111] The step S3, according to the typical constraint equation of robot speed planning, adds the constraint model of contour error to achieve the time optimal speed planning under the robot contour error constraint; specifically:

[0112] The constraint equation of convex optimization of robot velocity planning, the typical velocity planning equation that satisfies the third-order constraints of the robot expressed by B-spline velocity square can be expressed as:

[0113]

[0114] Where f is the velocity spline control point, Y(u) is the robot velocity square B-spline, m is the number of checkpoints, δs is the interval between checkpoints, S Σ is the arc length of the robot path, [V max ,A max ,J max ] are the robot terminal velocity, acceleration, and jerk constraints, are the robot joint velocity, acceleration, and jerk constraints. C1(s)≤0 is the first step constraint, C2(s)≤0 is the second step constraint, and Y * (u) is the intermediate variable obtained by the first step constraint, [q′,q″,q″′] is the partial derivative of the robot joint with respect to the end arc length, and [Y′(u),Y″(u)] is the derivative equation of the velocity square spline.

[0115] In order to implement the constraint equation of adding contour error in the above formula, it is necessary to scale the nonlinear terms of robot joint velocity and jerk. The following formula is used to locally amplify and reduce the velocity term as an approximate term:

[0116]

[0117] The approximate term of the acceleration is calculated using the following formula:

[0118]

[0119] By combining the above formulas, the linear expression of the contour error with respect to the speed planning variable can be realized. In order to simplify the writing, the constraint of the contour error is expressed as follows:

[0120]

[0121] The time optimal speed planning equation with the contour error constraint finally added can be expressed as:

[0122]

[0123] The above expression can be used to realize the robot time optimal velocity planning that meets the contour error constraint through two-step linear programming.

[0124] like Figure 2 As shown, it is the experimental path adopted by the embodiment of the present invention;

[0125] like Figure 3 , Figure 4 As shown, compared with the method of satisfying the contour error constraint by reducing the speed and the method of not considering the contour error constraint, the method proposed in the present invention can achieve a greater reduction in contour error on the basis of a lower speed efficiency decrease, thereby improving the movement accuracy of the robot.

[0126] An embodiment of the present invention provides a robot time optimal speed planning system considering robot contour error constraints that implements the robot time optimal speed planning method considering robot contour error constraints, the system comprising:

[0127] The tracking error prediction module establishes a prediction model of the robot joint tracking error based on the robot control loop;

[0128] The contour error prediction module builds a linear prediction model of the robot end contour error based on the robot tracking error prediction model and the Frenet framework;

[0129] The optimization implementation module adds the constraint model of contour error according to the typical equation of robot speed planning to achieve the time-optimal speed planning under the constraint of robot contour error.

[0130] An embodiment of the present invention provides a computer device, which includes a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor executes the steps of the robot time optimal speed planning method considering the robot contour error constraints.

[0131] An embodiment of the present invention provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the processor executes the steps of the robot time optimal speed planning method considering the robot contour error constraint.

[0132] An embodiment of the present invention provides an information data processing terminal, which is used to implement the robot time optimal speed planning system considering the robot contour error constraint.

[0133] Three groups of experiments were designed to verify the effectiveness of the proposed velocity planning method considering contour error constraints. In all experimental groups, the acceleration and jerk constraints were set to A and B, respectively. max =1500mm / s 2 and J max =15000mm / s. The experimental groups are as follows:

[0134] Group 1: Time-optimal velocity planning methods considering contour error constraints.

[0135] Group 2: The control group without considering the contour error constraint and without changing the maximum feed rate.

[0136] Group 3: Control group with reduced maximum feed rate to meet contour error constraints.

[0137] Figure 3 Velocity planning results in Cartesian space are shown for the three experimental groups. Figure 4 The simulated and actual contour errors of the three groups are shown. It can be observed that the proposed method successfully achieves velocity planning that satisfies all three given constraints. Compared with Group 2, which does not consider the contour error constraint, the proposed method reduces the maximum position contour error from 1.080mm to 0.586mm, a reduction of 45.71%. The maximum directional contour error is reduced from 0.0091rad to 0.0064rad, a reduction of 29.67%. The motion efficiency is only reduced by 13.34%, which shows that the proposed algorithm can achieve a significant reduction in contour error with a relatively small sacrifice in motion efficiency. Group 3 reduces the contour error by reducing the maximum feed rate. In contrast, the method proposed in this patent makes full use of the given contour error tolerance. Under the condition of satisfying the contour error constraint, the robot's motion efficiency is improved by 12.80%. The proposed robot time optimal velocity planning method considering the robot contour error constraint can effectively improve the robot's motion efficiency while satisfying the contour error tolerance constraint.

[0138] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware part can be implemented using dedicated logic; the software part can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. It can be understood by a person of ordinary skill in the art that the above-mentioned devices and methods can be implemented using computer executable instructions and / or contained in a processor control code, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. Such code is provided on the carrier medium. The device and its modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, and can also be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0139] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principle of the present invention should be covered by the protection scope of the present invention.

Claims

1. A robot time optimal velocity planning method considering robot contour error constraints, characterized in that: The velocity planning that is suitable for considering the robot motion profile error characteristics includes the following steps: (1) Based on the robot joint control loop, a prediction model for the robot joint tracking error is established; (2) Based on the robot joint tracking error model and the Frenet framework of the robot path, a linear prediction model of the robot end contour error with respect to joint velocity, acceleration, and jerk is established; (3) Based on the typical constraint equations of robot velocity planning and combined with the constraint model of contour error, time-optimal velocity planning is performed.

2. The speed planning method considering robot contour error as claimed in claim 1, characterized in that: In the step (1), the established robot joint tracking error prediction model is converted into a tracking error model expressed in the time domain through a pull-type transformation.

3. The speed planning method considering robot contour error as claimed in claim 1, characterized in that: In the step (2), the robot forward kinematics and Jacobian matrix are used to equivalently represent the end position tracking error as the end motion result caused by the differential motion of the joint tracking error.

4. The speed planning method considering robot contour error as claimed in claim 1, characterized in that: In the step (2), based on the path Frenet framework, the tracking error in the base coordinate system is converted to the path coordinate system through the path tangent vector, normal vector and binormal vector.

5. The speed planning method considering robot contour error as claimed in claim 1, characterized in that: In the step (3), the constraint equation of velocity planning is expressed by B-spline velocity square, and convex optimization is performed in combination with the constraint equations of robot velocity, acceleration, and jerk.

6. The speed planning method considering robot contour error as claimed in claim 1, characterized in that: In the step (3), the contour error constraint is converted into a linear constraint by locally scaling and approximating the nonlinear terms of the robot joint velocity and jerk.

7. The speed planning method considering robot contour error as claimed in claim 1, characterized in that: In the step (3), the time-optimal speed planning equation is solved by two-step linear programming to obtain a time-optimal speed planning solution that satisfies the contour error constraint.

8. A robot time optimal velocity planning system considering robot contour error constraints, comprising: The modeling module is used to establish a prediction model for the robot joint tracking error based on the linear model of the robot joint tracking error and calculate the end contour error through the Frenet framework; The planning module is connected with the modeling module and is used to combine the constraints of velocity, acceleration and jerk and the contour error constraint model to perform time-optimal velocity planning considering the contour error of the robot; The execution module is connected to the planning module and is used to control the movement of the robot joints according to the planning results.

9. The robot time optimal speed planning system considering robot contour error constraints as claimed in claim 8, characterized in that: The planning module includes: A speed planning unit, used for expressing a robot speed square curve by using a B-spline speed square; A contour error constraint unit, used to convert the contour error constraint into a linear expression by local scaling of the nonlinear term; The optimization unit is used to solve the speed planning equation through two-step linear programming to achieve the time optimal planning that meets the contour error constraints.

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