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

Abstract

The present invention belongs to the field of robot velocity planning, and more particularly relates to a method and system for time-optimal velocity planning of a robot that considers robot contour error constraints. The method comprises: first, establishing a prediction model for robot joint tracking error based on the robot joint control loop; then, implementing a linear prediction model for the robot end contour error with respect to joint velocity, acceleration, and jerk based on the robot joint tracking error model and the Frenet framework of the robot path; and finally, incorporating a contour error constraint model based on typical constraint equations for robot velocity planning to achieve time-optimal velocity planning that satisfies the robot contour error constraints.

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 precision 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. Such operation scenarios often require the robot's motion efficiency to be improved without sacrificing the robot's motion accuracy, especially the accuracy of the robot's contour error 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 end 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 end contour error constraint 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 existing technology are as follows:

[0004] (1) The existing robot velocity planning does not consider the contour error constraint, and the robot end motion accuracy cannot be guaranteed.

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

[0006] In response to 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 achieved by providing a robot time optimal velocity planning method considering robot contour error constraints, the method comprising:

[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 joint velocity, acceleration, and jerk;

[0010] S3, based on 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;

[0011] Furthermore, in step S1, a prediction model for robot joint tracking error is established based on 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 i-th 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 of the robot is designed to be 0, the first term of the above formula is 0, and the above formula can be converted to:

[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, a linear prediction model of the robot end contour error with respect to joint velocity, acceleration, and jerk is implemented based on the robot joint tracking error model and the Frenet framework of the robot path, 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:

[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 commands and tracking errors.

[0025] Due to the nonlinear relationship in forward kinematics, the pose tracking error can be regarded as the end differential motion result caused by the differential motion equivalent to the robot joint tracking error through Jacobian 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 the following formula:

[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. To realize the estimation of the contour error, since the position and orientation of the robot are expressed as spline expressions with respect to 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 arc length, and [P″(s), O″(s)] is the second-order derivative of position and direction with respect to 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 the contour error can be calculated by the following equation and further expressed as a linear expression:

[0036]

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

[0038]

[0039] The step S3 is to add the constraint model of contour error according to the typical constraint equation of robot velocity planning to achieve the time-optimal velocity planning under the constraint of robot contour error; 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 using B-spline velocity square representation 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 constraint step, [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] To implement the constraint equation for the contour error in the above equation, it is necessary to scale the nonlinear terms of the robot joint velocity and jerk. The following equation is used to locally scale and reduce the velocity term as an approximate term:

[0044]

[0045] The approximate term of 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 achieved. 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 time-optimal velocity planning of the robot 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 that implements the robot time optimal speed planning method and system considering robot contour error constraints, the system comprising:

[0053] Tracking error prediction module, which builds a prediction model of 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 a contour error constraint model based on the typical equation of robot speed planning to achieve time-optimal speed planning under the robot contour error constraint.

[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, causes the processor to execute the steps of the robot time optimal velocity planning method considering the robot contour error constraint.

[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 constraint.

[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] This paper addresses the problem that existing robot velocity planning fails to consider the actual motion accuracy of the robot. It proposes a time-optimal velocity planning method for robots that takes into account the robot's contour error constraints. Existing technologies often fail to fully consider the correlation between the tracking error of the robot's joints and the contour error of the end point, resulting in the system's inability to effectively suppress errors in complex paths or highly dynamic scenarios. By establishing a joint error prediction model and a linearized representation of the contour error, this paper achieves time-optimal path planning while ensuring accuracy, thus resolving the difficulty in balancing efficiency and accuracy in traditional methods.

[0062] Compared to existing technologies, this invention achieves significant technological advancements in the following areas: First, by combining the joint error model with the path Frenet framework, the end-point contour error is accurately predicted and incorporated into the velocity planning constraints, significantly improving the accuracy of the robot's path tracking. Second, the nonlinear terms of the contour error constraints are innovatively converted into linear expressions, effectively reducing the computational complexity of the planning model and improving planning efficiency. Furthermore, time-optimal velocity planning is achieved through two-step linear programming, maximizing velocity efficiency while maintaining high accuracy.

[0063] The technical solution of this invention is applicable to a variety of industrial robot motion planning scenarios, especially in machining tasks requiring high precision and high dynamics. The proposed planning method achieves high-precision robot motion while maintaining efficient motion. This method improves machining efficiency and product quality, reduces rework due to errors, and has broad industrial application value in aerospace, precision manufacturing, and other fields.

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

[0065] This paper proposes a time-optimal robot velocity planning method that considers robot contour error constraints. The method features a rational design, easy implementation, and non-invasive nature. This method eliminates the need for additional hardware in existing robotic systems and can be implemented simply through an optimization algorithm within existing control systems. This design significantly reduces implementation costs and complexity, making it feasible for widespread adoption in industrial automation. This method can improve trajectory tracking accuracy, achieving smoother motion trajectories, and thus enhancing production efficiency and product quality, particularly in high-precision applications such as grinding, welding, and cutting. It possesses significant commercial value and market potential.

[0066] The technical solution of the present invention fills a technological gap in the industry both domestically and internationally. Existing time-optimal speed planning methods for robots often fail to fully consider the contour error of the robot's end in practical applications, resulting in poor position accuracy in high-precision operations. The present invention optimizes the speed planning algorithm by introducing contour error constraints, enabling the robot to more accurately control the end position when performing complex tasks, significantly improving the effectiveness 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 error 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, meeting 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 the speed planning path provided for the implementation of the present invention;

[0070] Figure 3 Comparison of the speed planning effects provided by the embodiment of the present invention and the comparative 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 solutions 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 intended 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 joint velocity, acceleration, and jerk;

[0076] S3, based on 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;

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

[0078] The modeling module, based on forward kinematics, converts joint tracking errors into end-point pose errors. Using the Jacobian matrix, it linearizes nonlinear relationships into a differential kinematic model, describing the dependence of end-point position and orientation errors on joint motion. Furthermore, incorporating the Frenet framework of the path, the end-point errors are converted into contour errors in the path coordinate system using tangent vectors, normal vectors, and binormal vectors. This linear prediction model ensures the accuracy of subsequent velocity planning.

[0079] In the planning module, the robot's path velocity is expressed as a squared B-spline velocity. This multi-constraint velocity planning equation is constructed by combining the terminal velocity, acceleration, and jerk constraint equations with the joint velocity, acceleration, and jerk constraints. To further ensure the robot's operational accuracy, the system incorporates a constraint expression based on a contour error prediction model into the velocity planning, achieving a coordinated optimization of path accuracy and motion efficiency.

[0080] Because the joint velocities and jerks in the contour error constraints contain nonlinear terms, the planning module uses a local scaling method to approximate the nonlinear terms into linear expressions. This process simplifies the complex nonlinear constraints by piecewise scaling the velocities and jerks and ensures that the contour error constraints can be effectively embedded in the velocity planning model. This linearization method improves solution efficiency while maintaining sufficient computational accuracy.

[0081] Based on the aforementioned constraint model, the system employs a two-step linear programming approach to solve the time-optimal velocity planning equation. In the first step, an optimal velocity curve that satisfies velocity and acceleration constraints is preliminarily calculated. In the second step, the control points of the velocity curve are dynamically adjusted to optimize the contour error constraints, ultimately achieving the time-optimal velocity planning result. This approach maximizes velocity efficiency while maintaining motion accuracy.

[0082] The execution module controls the robot joint motion 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 based on 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 i-th 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 of the robot is designed to be 0, the first term of the above formula is 0, and the above formula can be converted to:

[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, a linear prediction model of the robot end contour error with respect to joint velocity, acceleration, and jerk is implemented based on the robot joint tracking error model and the Frenet framework of the robot path, 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:

[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 commands and tracking errors.

[0097] Due to the nonlinear relationship in forward kinematics, the pose tracking error can be regarded as the end differential motion result caused by the differential motion equivalent to the robot joint tracking error through Jacobian 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 the following formula:

[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. To realize the estimation of the contour error, since the position and orientation of the robot are expressed as spline expressions with respect to 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 arc length, and [P″(s), O″(s)] is the second-order derivative of position and direction with respect to 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 the contour error can be calculated by the following equation and further expressed as a linear expression:

[0108]

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

[0110]

[0111] The step S3 is to add the constraint model of contour error according to the typical constraint equation of robot velocity planning to achieve the time-optimal velocity planning under the constraint of robot contour error; 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 using B-spline velocity square representation 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 constraint step, [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] To implement the constraint equation for the contour error in the above equation, it is necessary to scale the nonlinear terms of the robot joint velocity and jerk. The following equation is used to locally scale and reduce the velocity term as an approximate term:

[0116]

[0117] The approximate term of 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 achieved. 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 time-optimal velocity planning of the robot that meets the contour error constraint through two-step linear programming.

[0124] like Figure 2 As shown, this is the experimental path adopted in 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] Tracking error prediction module, which builds a prediction model of 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 a contour error constraint model based on the typical equation of robot speed planning to achieve time-optimal speed planning under the robot contour error constraint.

[0130] An embodiment of the present invention provides a computer device, comprising 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 constraint.

[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 velocity 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 for the three groups are shown. It can be observed that the proposed method successfully achieves velocity planning that satisfies all three given constraints. Compared to Group 2, which does not consider contour error constraints, the proposed method reduces the maximum position contour error from 1.080 mm to 0.586 mm, a reduction of 45.71%. The maximum directional contour error is reduced from 0.0091 rad to 0.0064 rad, a reduction of 29.67%. The motion efficiency is only reduced by 13.34%, indicating that the proposed algorithm can achieve a significant reduction in contour error with a relatively small sacrifice in motion efficiency. Group 3 reduces contour error by reducing the maximum feed rate. In contrast, the method proposed in this patent fully utilizes 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's contour error constraints 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 portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, 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. The devices and 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, 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, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

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

Claims

1. A robot time-optimal velocity planning method considering robot contour error constraints, characterized in that: The velocity planning method that takes into account the error characteristics of the robot motion profile 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 the constraint model of contour error, time-optimal velocity planning is performed; In step (3), the constraint equation of velocity planning is expressed by the B-spline velocity square, and convex optimization is performed in combination with the constraint equations of robot velocity, acceleration, and jerk; In the step (3), the contour error constraint is converted into a linear constraint by locally scaling the nonlinear terms of the robot joint velocity and jerk; 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 meets the contour error constraint.

2. The speed planning method considering robot contour error according to 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 according to 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 according to claim 1, characterized in that: In the step (2), based on the Frenet framework of the path, 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. 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 to the modeling module and is used to combine the constraints of velocity, acceleration and jerk with 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; The planning module includes: A speed planning unit, used to represent a robot speed square curve 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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