Robot time optimal speed planning method and system based on two-step linear programming

Abstract

The present invention belongs to the technical field of robot speed planning, and in particular relates to a robot time optimal speed planning method and system based on two-step linear programming. The method comprises: based on a cubic B-spline curve, converting the robot speed time optimal speed planning optimization equation into a linearized function about the B-spline control points; according to the derivative analytical characteristics of the B-spline, converting the speed and acceleration constraints in the joint space and the Cartesian space in the robot speed planning into linear constraints expressed by the B-spline control points; scaling the acceleration constraint into a linear constraint equation by an inequality scaling method, and linearizing the dynamic torque constraint equation by adopting the inequality scaling method for the dynamic torque constraint; decoupling the robot speed planning optimization equation into two linear programming sub-equations, and realizing the time optimal speed planning that satisfies the third-order constraint and the dynamic constraint by a two-step linear optimization method.

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 based on two-step linear programming. Background Art

[0002] Robots are widely used in engineering applications such as milling, grinding, polishing, and welding due to their great flexibility and low cost. Robot velocity planning is the most important part of ensuring the efficiency of robot motion. The purpose of robot velocity planning is to maximize the efficiency of robot motion while satisfying the motion constraints of the robot joint space and the end Cartesian space. The constraints of the robot Cartesian space include the end velocity, acceleration, and jerk constraints; the robot joint space constraints include the robot joint velocity, acceleration, jerk, and robot joint torque constraints, i.e., the robot joint dynamics constraints. Existing robot velocity planning methods often perform transition scaling on the jerk to achieve linearization of the third-order constraints, which will result in the robot being unable to fully utilize the constraint tolerance. In addition, when linearizing the robot joint dynamics torque constraints, existing robot velocity planning methods usually simplify the robot joint friction constraints to achieve constraint linearization, which will also affect the actual robot velocity planning effect.

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

[0004] (1) The overscaling of the linearization of third-order constraints in existing robot velocity planning methods will result in the robot velocity planning being unable to fully utilize the robot constraint tolerance.

[0005] (2) The existing robot velocity planning algorithm simplifies the robot joint friction constraints when linearizing the robot joint dynamic constraints, which does not conform to the actual robot joint friction phenomenon. 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 based on two-step linear programming.

[0007] The present invention is implemented as follows: a robot time optimal speed planning system based on two-step linear programming, comprising:

[0008] A processor, configured to execute the speed planning optimization step;

[0009] A memory for storing a cubic B-spline curve, a linearization function of a B-spline control point, a velocity and acceleration constraint equation, and a dynamic torque constraint equation;

[0010] Execution module, configured as:

[0011] Based on the cubic B-spline curve, the robot speed time optimal speed planning optimization equation is transformed into a linearized function about the B-spline control points;

[0012] According to the analytical characteristics of B-spline derivation, the velocity and acceleration constraints in joint space and Cartesian space in robot velocity planning are transformed into linear constraints expressed by B-spline control points.

[0013] The jerk constraint is scaled down to a linear constraint equation by the inequality scaling method, and the dynamic torque constraint equation is linearized by the inequality scaling method.

[0014] The robot velocity planning optimization equation is decoupled into two linear programming sub-equations, and the time-optimal velocity planning that satisfies third-order constraints and dynamic constraints is achieved through a two-step linear optimization method.

[0015] Input and output interface, used to receive robot motion trajectory data and output optimized speed planning results.

[0016] Furthermore, the processor and memory are connected via a bus to ensure efficient transmission of data and instructions.

[0017] Furthermore, the execution module further includes:

[0018] A linearization module is used to linearize the speed planning optimization equation based on a cubic B-spline curve;

[0019] Constraint conversion module, used to convert velocity and acceleration constraints into linear constraints;

[0020] Inequality scaling module, used to convert nonlinear constraints into linear constraint equations;

[0021] Optimization module for decoupling the optimization equations and performing two-step linear optimization.

[0022] Furthermore, a computer program for implementing the steps of the execution module is pre-installed in the memory.

[0023] Furthermore, the input and output interface includes:

[0024] A data input unit is used to receive the robot's current motion trajectory and status data;

[0025] The data output unit is used to output the optimized speed planning instructions to the robot control system.

[0026] Furthermore, the processor is configured to process multiple robot speed planning tasks in parallel to improve the overall processing efficiency and response speed of the system.

[0027] The present invention also provides a robot time optimal speed planning method based on two-step linear programming, the method comprising:

[0028] S1, based on the cubic B-spline curve, the robot speed time optimal speed planning optimization equation is converted into a linearized function about the B-spline control point;

[0029] S2, based on the analytical characteristics of B-spline derivation, the velocity and acceleration constraints in the joint space and Cartesian space in the robot velocity planning are converted into linear constraints expressed by B-spline control points;

[0030] S3, scale the jerk constraint into a linear constraint equation by using the inequality scaling method, and linearize the dynamic torque constraint equation by using the inequality scaling method for the dynamic torque constraint;

[0031] S4, decouples the robot velocity planning optimization equation into two linear programming sub-equations, and achieves the time-optimal velocity planning that satisfies the third-order constraints and dynamic constraints through a two-step linear optimization method.

[0032] Furthermore, step S1 converts the robot speed time optimal speed planning optimization equation into a linearized convex function about the B-spline control point based on the cubic B-spline curve. Specifically, the robot time optimal speed planning method can be expressed as solving the following optimization equation:

[0033]

[0034] Where t represents the total optimization time, S Σ represents the total arc length of the path, Respectively represent the speed, acceleration, and jerk of the robot’s terminal operation. max ,A max ,J max They represent the maximum values ​​of the robot's terminal velocity, acceleration, and jerk, respectively. They represent the velocity, acceleration, and jerk of the robot joints respectively. Represent the maximum values ​​of robot joint velocity, acceleration, and jerk respectively. represents the robot joint torque, τ max Indicates the maximum value of the joint torque.

[0035] In order to achieve a stable solution for feed rate planning, this paper uses the cubic B-spline Y(u) to represent the square value of the feed rate along the tool path, which is defined as the feed rate spline:

[0036]

[0037] where f=[f0,f1,…,f n-1] The control points of the spline, n is the number of control points, which is the number of points that the planned path is discretized into with equal arc length. i,3 (u) is the basis function of the spline, which can be calculated by the following formula:

[0038]

[0039] Where k = 1, 2, 3.

[0040] In order to make the velocity of the path initial point and end point 0, 4 repeated nodes are selected at the start and end when constructing the B-spline. The node vector is defined as:

[0041]

[0042] where u i =(i-3) / (n-3)

[0043] Due to the characteristics of the B-spline curve, the derivatives of each order of the B-spline can be expressed as a linear combination of the control points f:

[0044]

[0045] where Y′(u) and Y″(u) are the first and second order derivatives of the pseudo velocity curve with respect to the parameter u, respectively.

[0046] Based on the pseudo-velocity curve, the optimization objective of optimizing the robot's motion time is transformed into a function that maximizes the sum of the squares of the feed velocities at each checkpoint on the robot's path. This optimization objective then becomes a linear optimization equation with the B-spline control points as optimization variables:

[0047]

[0048] Where m is the number of checkpoints, which is defined as the number of checkpoints generated by segmenting the path with equal arc length using a smaller spacing δs to check whether the points on the path violate the constraints. Because the initial and terminal points are already set to 0 due to the characteristics of B-spline, they are not calculated here.

[0049] Furthermore, in step S2, based on the analytical characteristics of the derivation of B-splines, the velocity and acceleration constraints in the joint space and Cartesian space in the robot velocity planning are converted into linear constraints expressed by B-spline control points. In step S3, the jerk constraint is scaled into a linear constraint equation by the inequality scaling method, and the dynamic torque constraint equation is linearized by the inequality scaling method for the dynamic torque constraint. The specific steps are:

[0050] The velocity, acceleration, and jerk equations of the robot end can be expressed as equations about the B-spline control points:

[0051]

[0052] where u = s / S Σ ,s=i·δs,i=1…m-2, which is also defined in the subsequent parts of this patent.

[0053] The first and third terms of the above equation have nonlinear terms about the control point The first term can be obtained by squaring the equation to obtain the terminal velocity constraint equation:

[0054]

[0055] In order to satisfy the jerk:

[0056]

[0057] Introduce the inequality equation:

[0058]

[0059] where Y * (u) is an intermediate variable obtained through the first linear optimization. The first optimization will be introduced in step S4. It satisfies the following formula:

[0060] Y(u)≤Y * (u)≤V 2 max (11)

[0061] Therefore, the jerk constraint equation in Cartesian space can be converted into a linear expression:

[0062]

[0063] The same robot joint space constraints can also be expressed using the same strategy as follows:

[0064]

[0065] Where [q′,q″,q″′] is the third-order partial derivative of the robot joint with respect to the end arc length, which can be calculated by the following formula:

[0066]

[0067] The dynamic model of the robot can be expressed using the Newton-Euler equation:

[0068]

[0069] where τ 6×1 Represents the robot joint torque, M 6×6is the inertia matrix, C 6×6 is the Coriolis force matrix, G 6×1 is the gravitational torque, τ f6×1 represents the friction torque of the robot joint, τ load6×1 Represents the joint torque due to the end load of the robot.

[0070] The joint friction torque can be calculated by the following formula:

[0071]

[0072] Among them F c , F v is the friction parameter and sign is the sign function.

[0073] The robot joint torque caused by external load can be expressed as:

[0074] τ load =J T (q)Γ (17)

[0075] Among them J 6×6 is the robot Jacobian matrix, Γ 6×1 is the robot end load.

[0076] The joint torque equation is expressed as the end tangential equation:

[0077]

[0078] It can be seen that in the above formula, there is only one nonlinear term in the friction term. The following two inequalities are scaled down to:

[0079]

[0080] Therefore, the expression of the robot joint dynamics constraint using control point linearization is:

[0081]

[0082] To simplify writing, the robot dynamic joint torque constraint equation is abbreviated as:

[0083] -τ max ≤τ(Y(u),Y′(u),Y * (u))≤τ max (twenty one)

[0084] Furthermore, in step S4, the robot velocity planning optimization equation is decoupled into two linear programming sub-equations, and the time-optimal velocity planning that satisfies the third-order constraints and dynamic constraints is achieved through a two-step linear optimization method. The specific steps are:

[0085] After the calculations in steps S1, S2, and S3, the robot's velocity planning equation can be expressed as the following optimization equation based on whether scaling is performed:

[0086]

[0087] The constraint equation C1(s) does not contain the intermediate variable Y * (u) indicates that it has not been scaled. C2(s) contains the intermediate variable Y * (u) indicates that it has been scaled.

[0088] The above optimization equation is a typical linear optimization equation, which can be calculated by a commonly used linear optimization toolbox. The patent embodiment uses MATLAB's optimization toolbox YALMP to perform two-step linear optimization calculations. Since this calculation does not belong to the original content of the invention patent, it will not be described here. The specific two-step linear optimization steps are: the first step is to obtain the intermediate variable Y by linear optimization to satisfy C1(s)≤0. * (u); the second step is to * Substitute (u) into C2(s) and optimize to satisfy both C1(s)≤0 and C2(s)≤0 to obtain the final speed optimization result.

[0089] Another object of the present invention is to provide a robot time optimal speed planning system based on two-step linear programming for implementing the robot time optimal speed planning method based on two-step linear programming, the system comprising:

[0090] Robot pseudo velocity spline construction module: According to the robot motion path, a velocity square B-spline curve about the robot arc length is established.

[0091] Optimization model building module: Based on the established pseudo-velocity spline building module, a linear mixed constraint equation that satisfies the robot's Cartesian space third-order constraints, joint space third-order constraints, and dynamic constraints is established.

[0092] The planning implementation module is connected with the constraint equation establishment module. According to the mixed constraint conditions, the two-step linear programming method is used to realize the time optimal speed planning solution of the robot.

[0093] 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 based on two-step linear programming.

[0094] 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 speed planning method based on two-step linear programming.

[0095] 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 based on two-step linear programming.

[0096] 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:

[0097] First, the present invention is a typical robot speed planning problem. By transforming the constraints in the robot speed planning, the time-optimal speed planning of the robot that satisfies the third-order constraints and dynamic constraints is achieved.

[0098] This paper addresses the challenges of existing robot velocity planning methods, which suffer from high optimization complexity, low computational efficiency, and difficulty balancing path accuracy and motion efficiency. By proposing a time-optimal velocity planning method based on two-step linear programming, the paper addresses the problems of high optimization complexity, low computational efficiency, and difficulty balancing path accuracy and motion efficiency. Existing technologies often employ nonlinear optimization algorithms to address multi-constraint problems in Cartesian and joint space, resulting in computationally complex and prone to local optimality. This paper linearizes pseudo-velocity splines and constraint equations and employs a two-step linear programming approach to efficiently solve the problem of time-optimal velocity planning for robots under complex constraints.

[0099] Compared with the existing technology, the present invention achieves the following technological advances: first, a pseudo-velocity square function is constructed through a cubic B-spline curve, ensuring the smoothness and accuracy of path planning; second, nonlinear constraints are linearized through the inequality scaling method, and the acceleration and dynamic torque constraints are simplified into linear expressions, which significantly reduces the computational complexity; finally, a two-step linear programming method is adopted to decouple the optimization problem into two sub-problems for solution, which improves the solution efficiency while ensuring the smoothness of the motion and the accuracy of the path.

[0100] The technical solution of this invention has significant application value in a variety of industrial robot applications, particularly in high-precision and high-dynamic tasks such as high-speed milling, welding, and assembly. This method improves motion efficiency while maintaining path tracking accuracy, shortening production cycles and enhancing product quality. By reducing computational complexity and improving planning efficiency, this invention reduces the deployment and operating costs of industrial robots and has broad industrial application prospects.

[0101] Second, as auxiliary evidence for the inventiveness of the claims of the present invention, it is also reflected in the following important aspects:

[0102] (1) The expected benefits and commercial value of the technical solution of the present invention after transformation are:

[0103] The present invention proposes a robot time optimal speed planning method based on two-step linear programming, which can be mainly used in the field of industrial automation in actual commercial applications to improve the efficiency of robot speed planning, increase the robot's motion rhythm, and improve production efficiency.

[0104] (2) The technical solution of the present invention fills the technical gap in the industry at home and abroad:

[0105] Existing robot velocity planning has excessive scaling when considering the robot's third-order constraints and robot dynamic torque constraints, which makes the robot unable to fully utilize the robot constraint tolerance and thus reduces the robot's motion efficiency.

[0106] Third, the methods provided by the embodiments of the present invention solve multiple problems of the prior art in industrial applications and bring about significant technological progress. The following is a detailed explanation of these progress and problem solutions:

[0107] 1) Technical problem solving:

[0108] Full utilization of nonlinear constraints: Existing methods lack effective linearization in dealing with acceleration constraints and dynamic constraints, making it impossible to directly incorporate these constraints into the optimization problem, limiting the efficiency and accuracy of planning.

[0109] 2) Technological progress:

[0110] Improve speed planning efficiency: By introducing the B-spline curve of the square of the speed, the feed speed planning problem is converted into a linear optimization problem, which can improve planning efficiency and ensure solution stability.

[0111] In summary, the technical solution of the present invention not only solves the problems of the existing technology, but also brings about significant technological progress and provides strong support for the industrial application of robots. BRIEF DESCRIPTION OF THE DRAWINGS

[0112] Figure 1 A flow chart of a robot speed planning method provided by an embodiment of the present invention;

[0113] Figure 2 A schematic diagram of the speed planning path provided for the implementation of the present invention;

[0114] Figure 3 Comparison of the speed planning effects provided by the embodiment of the present invention and the comparative method;

[0115] Figure 4 The motion efficiency comparison between the embodiment of the present invention and the comparative method is provided. DETAILED DESCRIPTION

[0116] 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.

[0117] Example 1: Speed ​​Optimization of Welding Robots on Automobile Manufacturing Production Lines

[0118] In automotive manufacturing production lines, welding robots undertake critical welding tasks. The accuracy and efficiency of their motion trajectories directly impact welding quality and production efficiency. This embodiment applies the present invention's time-optimal robot velocity planning method based on two-step linear programming to optimize the welding robot's velocity planning, achieving efficient and high-precision welding operations.

[0119] First, the welding robot generates a predetermined welding path based on a cubic B-spline curve. Step 1 transforms the time-optimal velocity planning optimization equation into a linearized function with respect to the B-spline control points. Next, step 2 transforms the robot's velocity and acceleration constraints in joint and Cartesian space into linear constraints expressed by the B-spline control points. This allows the system to precisely control the welding robot's motion, ensuring smooth movement and high-precision positioning along complex welding paths.

[0120] In step three, the jerk and dynamic torque constraints are linearized using an inequality scaling method to ensure that all physical constraints are satisfied during the optimization process. Subsequently, in step four, the velocity planning optimization equation is decoupled into two linear programming sub-equations, using a two-step linear optimization method to achieve time-optimal velocity planning that satisfies third-order and dynamic constraints. The optimized welding robot can complete welding tasks in the shortest possible time while maintaining high-precision trajectory tracking, significantly improving production efficiency and welding quality while reducing energy consumption and equipment wear.

[0121] Example 2: Speed ​​Control of Precision Assembly Robots on Electronic Assembly Lines

[0122] On electronic product assembly lines, precision assembly robots must complete complex and high-precision assembly tasks, such as chip soldering and component installation, within a limited timeframe. This embodiment utilizes the present invention's time-optimal robot speed planning method based on two-step linear programming to optimize the assembly robot's speed control, improving assembly efficiency and product quality.

[0123] The assembly robot first designs its motion trajectory based on a cubic B-spline curve. In step one, the time-optimal velocity planning optimization equation is linearized as a function of the B-spline control points. Then, in step two, the robot's velocity and acceleration constraints in joint and Cartesian space are converted into linear constraints of the B-spline control points, ensuring smooth and efficient robot motion during high-precision assembly tasks.

[0124] In step three, the system linearizes the jerk and dynamic torque constraints using an inequality scaling method, thereby simplifying the complexity of the optimization problem. In step four, a two-step linear optimization method is used to decompose the velocity planning optimization equation into two linear programming sub-equations, each solving a different optimization objective. The optimized assembly robot is able to minimize operation time while ensuring high-precision assembly, thereby improving the overall production efficiency of the assembly line. Furthermore, the optimization method effectively reduces energy consumption and mechanical wear during robot operation, extending the service life of the equipment and improving the economic efficiency and reliability of the production line.

[0125] The above two embodiments respectively demonstrate the specific applications of the present invention in the fields of automobile manufacturing and electronic assembly. Through the robot time optimal speed planning method based on two-step linear programming, high efficiency and high precision of robot movement are achieved, which significantly improves production efficiency and product quality, and meets the needs of modern industry for high-performance robot control.

[0126] The pseudo-velocity spline construction module generates a squared velocity B-spline curve based on the robot's motion path. By discretizing the path into segmented checkpoints of equal arc length, a cubic B-spline curve is constructed and its knot vectors are defined, ensuring that the velocity at the initial and final points is zero. The derivatives of the B-spline curve can be expressed as linear combinations of control points, providing a foundational expression for subsequent constraint models and optimization solutions.

[0127] The optimization model building module uses the spline curves generated by the pseudo-velocity spline building module to establish linear mixed constraint equations that satisfy the robot's motion constraints. Specifically, this involves converting velocity, acceleration, and jerk constraints in Cartesian and joint space into linearized representations. It also uses inequality scaling to convert nonlinear terms in dynamic torque constraints into linear constraints, ultimately forming a complete linear mixed constraint equation. These constraint equations ensure that the robot's path planning maintains computational simplicity while satisfying third-order motion and dynamic constraints.

[0128] The planning implementation module solves the time-optimal speed planning equation using a two-step linear programming method. In the first step, a basic optimization equation without intermediate variables is calculated through linear optimization to obtain intermediate variables that satisfy basic constraints. In the second step, the intermediate variables calculated in the first step are substituted into the final optimization equation and linear optimization is performed again to obtain the time-optimal speed planning result that satisfies third-order kinematic and dynamic constraints.

[0129] This system can be integrated into a computer device, using memory to store the relevant programs, which are then executed by a processor to implement the functions of the aforementioned modules. Through program execution, the construction of pseudo-velocity splines, the establishment of mixed constraint equations, and the solution of two-step linear optimization are all automated. Furthermore, an information data processing terminal monitors the robot's motion planning results in real time and provides visual feedback. It also supports dynamic adjustment of input path parameters and constraints to meet the application requirements of different scenarios.

[0130] The embodiment of the present invention provides a robot time optimal speed planning method based on two-step linear programming, which specifically includes the following steps:

[0131] S1, based on the cubic B-spline curve, the robot speed time optimal speed planning optimization equation is converted into a linearized function about the B-spline control point;

[0132] S2, based on the analytical characteristics of B-spline derivation, the velocity and acceleration constraints in the joint space and Cartesian space in the robot velocity planning are converted into linear constraints expressed by B-spline control points;

[0133] S3, scale the jerk constraint into a linear constraint equation by using the inequality scaling method, and linearize the dynamic torque constraint equation by using the inequality scaling method for the dynamic torque constraint;

[0134] S4, decouples the robot velocity planning optimization equation into two linear programming sub-equations, and achieves the time-optimal velocity planning that satisfies the third-order constraints and dynamic constraints through a two-step linear optimization method.

[0135] Industrial Application Example 1: Robotic High-Speed ​​Milling

[0136] In the application scenario of robot high-speed milling, the improvement of robot motion efficiency can greatly improve the robot milling production cycle. The proposed speed planning method can effectively improve the robot milling efficiency.

[0137] Specific implementation steps include:

[0138] 1) Construct the speed planning target equation: According to the robot milling path and based on the cubic B-spline curve, the robot speed time optimal speed planning optimization equation is converted into a linearized function about the B-spline control points.

[0139] 2) Linearized constraint equations: Based on the analytical characteristics of B-spline derivation, the velocity and acceleration constraints in the joint space and Cartesian space in the robot velocity planning are converted into linear constraints expressed by B-spline control points; the jerk constraint is scaled into a linear constraint equation by the inequality scaling method, and the dynamic torque constraint equation is linearized by the inequality scaling method for the dynamic torque constraint

[0140] 3) Speed ​​planning solution: The robot speed planning optimization equation is decoupled into two linear programming sub-equations, and the time-optimal speed planning that satisfies third-order constraints and dynamic constraints is achieved through a two-step linear optimization method.

[0141] Through this method, the efficiency of robot high-speed milling can be effectively improved.

[0142] like Figure 1 As shown, an embodiment of the present invention provides a robot time optimal speed planning method based on two-step linear programming, the method comprising:

[0143] S1, based on the cubic B-spline curve, the robot speed time optimal speed planning optimization equation is converted into a linearized function about the B-spline control point;

[0144] S2, based on the analytical characteristics of B-spline derivation, the velocity and acceleration constraints in the joint space and Cartesian space in the robot velocity planning are converted into linear constraints expressed by B-spline control points;

[0145] S3, scale the jerk constraint into a linear constraint equation by using the inequality scaling method, and linearize the dynamic torque constraint equation by using the inequality scaling method for the dynamic torque constraint;

[0146] S4, decouples the robot velocity planning optimization equation into two linear programming sub-equations, and achieves the time-optimal velocity planning that satisfies the third-order constraints and dynamic constraints through a two-step linear optimization method.

[0147] Furthermore, step S1 converts the robot speed time optimal speed planning optimization equation into a linearized convex function about the B-spline control point based on the cubic B-spline curve. Specifically, the robot time optimal speed planning method can be expressed as solving the following optimization equation:

[0148]

[0149] Where t represents the total optimization time, S Σ represents the total arc length of the path, Respectively represent the speed, acceleration, and jerk of the robot’s terminal operation. max ,A max,J max They represent the maximum values ​​of the robot's terminal velocity, acceleration, and jerk, respectively. They represent the velocity, acceleration, and jerk of the robot joints respectively. Represent the maximum values ​​of robot joint velocity, acceleration, and jerk respectively. represents the robot joint torque, τ max Indicates the maximum value of the joint torque.

[0150] In order to achieve a stable solution for feed rate planning, this paper uses cubic B-spline to represent the square value of the feed rate along the tool path, which is defined as the feed rate spline:

[0151]

[0152] where f=[f0,f1,…,f n-1 ] The control points of the spline, n is the number of control points, which is the number of points that the planned path is discretized into with equal arc length. i,3 (u) is the basis function of the spline, which can be calculated by the following formula:

[0153]

[0154] Where k = 1, 2, 3.

[0155] In order to make the velocity of the path initial point and end point 0, 4 repeated nodes are selected at the start and end when constructing the B-spline. The node vector is defined as:

[0156]

[0157] where u i =(i-3) / (n-3)

[0158] Due to the characteristics of the B-spline curve, the derivatives of each order of the B-spline can be expressed as a linear combination of the control points f:

[0159]

[0160] where Y′(u) and Y″(u) are the first and second order derivatives of the pseudo velocity curve with respect to the parameter u, respectively.

[0161] Based on the pseudo-velocity curve, the optimization objective of optimizing the robot's motion time is transformed into a function that maximizes the sum of the squares of the feed velocities at each checkpoint on the robot's path. This optimization objective then becomes a linear optimization equation with the B-spline control points as optimization variables:

[0162]

[0163] Where m is the number of checkpoints, which is defined as the number of checkpoints generated by segmenting the path with equal arc length using a smaller spacing δs to check whether the points on the path violate the constraints. Because the initial and terminal points are already set to 0 due to the characteristics of B-spline, they are not calculated here.

[0164] Furthermore, in step S2, based on the analytical characteristics of the derivation of B-splines, the velocity and acceleration constraints in the joint space and Cartesian space in the robot velocity planning are converted into linear constraints expressed by B-spline control points. In step S3, the jerk constraint is scaled into a linear constraint equation by the inequality scaling method, and the dynamic torque constraint equation is linearized by the inequality scaling method for the dynamic torque constraint. The specific steps are:

[0165] The velocity, acceleration, and jerk equations of the robot end can be expressed as equations about the B-spline control points:

[0166]

[0167] where u = s / S Σ ,s=i·δs,i=1…m-2, which is also defined in the subsequent parts of this patent.

[0168] The first and third terms of the above equation have nonlinear terms about the control point The first term can be obtained by squaring the equation to obtain the terminal velocity constraint equation:

[0169]

[0170] In order to satisfy the jerk:

[0171]

[0172] Introduce the inequality equation:

[0173]

[0174] where Y * (u) is an intermediate variable obtained through the first linear optimization. The first optimization will be introduced in step S4. It satisfies the following formula:

[0175] Y(u)≤Y * (u)≤V 2 max (33)

[0176] Therefore, the jerk constraint equation in Cartesian space can be converted into a linear expression:

[0177]

[0178] The same robot joint space constraints can also be expressed using the same strategy as follows:

[0179]

[0180] Where [q′,q″,q″′] is the third-order partial derivative of the robot joint with respect to the end arc length, which can be calculated by the following formula:

[0181]

[0182] The dynamic model of the robot can be expressed using the Newton-Euler equation:

[0183]

[0184] where τ 6×1 Represents the robot joint torque, M 6×6 is the inertia matrix, C 6×6 is the Coriolis force matrix, G 6×1 is the gravitational torque, τ f6×1 represents the friction torque of the robot joint, τ load6×1 Represents the joint torque due to the end load of the robot.

[0185] The joint friction torque can be calculated by the following formula:

[0186]

[0187] Among them F c , F v is the friction parameter and sign is the sign function.

[0188] The robot joint torque caused by external load can be expressed as:

[0189] τ load =J T (q)Γ (39)

[0190] Among them J 6×6 is the robot Jacobian matrix, Γ 6×1 is the robot end load.

[0191] The joint torque equation is expressed as the end tangential equation:

[0192]

[0193] It can be seen that in the above formula, there is only one nonlinear term in the friction term. The following two inequalities are scaled down to:

[0194]

[0195] Therefore, the expression of the robot joint dynamics constraint using control point linearization is:

[0196]

[0197] To simplify writing, the robot dynamic joint torque constraint equation is abbreviated as:

[0198] -τ max ≤τ(Y(u),Y′(u),Y * (u))≤τ max (43)

[0199] Furthermore, in step S4, the robot velocity planning optimization equation is decoupled into two linear programming sub-equations, and the time-optimal velocity planning that satisfies the third-order constraints and dynamic constraints is achieved through a two-step linear optimization method. The specific steps are:

[0200] After the calculations in steps S1, S2, and S3, the robot's velocity planning equation can be expressed as the following optimization equation based on whether scaling is performed:

[0201]

[0202] The constraint equation C1(s) does not contain the intermediate variable Y * (u) indicates that it has not been scaled. C2(s) contains the intermediate variable Y * (u) indicates that it has been scaled.

[0203] The above optimization equation is a typical linear optimization equation, which can be calculated by a commonly used linear optimization toolbox. The patent embodiment uses MATLAB's optimization toolbox YALMP to perform two-step linear optimization calculations. Since this calculation does not belong to the original content of the invention patent, it will not be described here. The specific two-step linear optimization steps are: the first step is to obtain the intermediate variable Y by linear optimization to satisfy C1(s)≤0. * (u); the second step is to * Substitute (u) into C2(s) and optimize to satisfy both C1(s)≤0 and C2(s)≤0 to obtain the final speed optimization result.

[0204] like Figure 2 The figure shows a schematic diagram of a speed planning path provided by the embodiment of the present invention;

[0205] Figure 3 and Figure 4 The figure shows the planning effect of the present invention compared with the traditional speed planning scaling strategy. The robot speed planning provided by the present invention can fully utilize the robot's motion constraint tolerance and improve the robot's motion efficiency.

[0206] Another object of the present invention is to provide a robot time optimal speed planning system based on two-step linear programming for implementing the robot time optimal speed planning method based on two-step linear programming, the system comprising:

[0207] Robot pseudo velocity spline construction module: According to the robot motion path, a velocity square B-spline curve about the robot arc length is established.

[0208] Optimization model building module: Based on the established pseudo-velocity spline building module, a linear mixed constraint equation that satisfies the robot's Cartesian space third-order constraints, joint space third-order constraints, and dynamic constraints is established.

[0209] The planning implementation module is connected with the constraint equation establishment module. According to the mixed constraint conditions, the two-step linear programming method is used to realize the time optimal speed planning solution of the robot.

[0210] 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 based on two-step linear programming.

[0211] 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 based on two-step linear programming.

[0212] An embodiment of the present invention provides an information data processing terminal, which is used to implement the robot time optimal speed planning system based on two-step linear programming.

[0213] To verify the effectiveness of the proposed speed planning algorithm, two common speed planning methods were used for comparison. The feed rate, acceleration and jerk limits are set as follows: V max =400mm / s, A max =1500mm / s 2 and J max =15000mm / s 3 Comparison method 1: Use a one-step method for velocity planning, and use the maximum given velocity to linearize the acceleration in the rectangular coordinate space and joint space instead; Comparison method 2 uses a two-step method to generate an intermediate variable Y under the acceleration constraint. * (u). The scaling method proposed in this patent is not adopted.

[0214] The optimization results of feed rate planning are as follows: Figure 3As shown in Figure 2, it can be seen that the proposed method makes more effective use of the jerk constraint. Figure 4 As shown in Figure 3, the proposed method improves the motion efficiency by 8.96% and 33.68% on the butterfly trajectory compared to the other two methods. This improvement is attributed to the scaling and two-step optimization strategies introduced in the proposed method, which better utilize the robot's jerk tolerance to improve motion efficiency.

[0215] 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.

[0216] 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 speed planning system based on two-step linear programming, characterized in that: include: A processor, configured to execute the speed planning optimization step; A memory for storing a cubic B-spline curve, a linearization function of a B-spline control point, a velocity and acceleration constraint equation, and a dynamic torque constraint equation; Execution module, configured as: Based on the cubic B-spline curve, the robot speed time optimal speed planning optimization equation is transformed into a linearized function about the B-spline control points; According to the analytical characteristics of B-spline derivation, the velocity and acceleration constraints in joint space and Cartesian space in robot velocity planning are transformed into linear constraints expressed by B-spline control points. The jerk constraint is scaled down to a linear constraint equation by the inequality scaling method, and the dynamic torque constraint equation is linearized by the inequality scaling method. The robot velocity planning optimization equation is decoupled into two linear programming sub-equations, and the time-optimal velocity planning that satisfies third-order constraints and dynamic constraints is achieved through a two-step linear optimization method. Input and output interface, used to receive robot motion trajectory data and output optimized speed planning results.

2. The robot time optimal speed planning system based on two-step linear programming according to claim 1, characterized in that: The processor and the memory are connected via a bus to ensure efficient transmission of data and instructions.

3. The robot time optimal speed planning system based on two-step linear programming as claimed in claim 1, characterized in that: The execution module further includes: A linearization module is used to linearize the speed planning optimization equation based on a cubic B-spline curve; Constraint conversion module, used to convert velocity and acceleration constraints into linear constraints; Inequality scaling module, used to convert nonlinear constraints into linear constraint equations; Optimization module for decoupling the optimization equations and performing two-step linear optimization.

4. The robot time optimal speed planning system based on two-step linear programming as claimed in claim 1, characterized in that: The memory is pre-installed with a computer program for implementing the steps of the execution module.

5. The robot time optimal speed planning system based on two-step linear programming as claimed in claim 1, characterized in that: The input and output interface includes: A data input unit is used to receive the robot's current motion trajectory and status data; The data output unit is used to output the optimized speed planning instructions to the robot control system.

6. The robot time optimal speed planning system based on two-step linear programming as claimed in claim 1, characterized in that: The processor is configured to process multiple robot speed planning tasks in parallel to improve the overall processing efficiency and response speed of the system.

7. A robot time optimal speed planning method based on two-step linear programming, characterized in that: The following steps are involved: (1) Based on the cubic B-spline curve, the robot speed time optimal speed planning optimization equation is converted into a linearized function about the B-spline control points; (2) Based on the analytical characteristics of B-spline derivation, the velocity and acceleration constraints in the joint space and Cartesian space in the robot velocity planning are converted into linear constraints expressed by B-spline control points; (3) The jerk constraint is scaled down to a linear constraint equation by the inequality scaling method, and the dynamic torque constraint equation is linearized by the inequality scaling method for the dynamic torque constraint; (4) The robot velocity planning optimization equation is decoupled into two linear programming sub-equations, and the time-optimal velocity planning that satisfies the third-order constraints and dynamic constraints is achieved through a two-step linear optimization method.

8. The method according to claim 7, wherein In step (1), the robot path is discretized into segments of equal arc length to generate checkpoints, a pseudo-velocity square function on the path is constructed using a cubic B-spline curve, and the velocities of the initial and end points of the path are set to zero.

9. The method according to claim 7, wherein In step (2), the velocity and acceleration of the robot end and the velocity and acceleration constraints in the joint space are converted into linear expressions about the control points through the relationship between the derivatives of each order of the B-spline.

10. The method according to claim 7, wherein: In step (3), we scale by inequality Method, the nonlinear terms in the robot's acceleration constraint and dynamic torque constraint are converted into linear constraints, The dynamic model is expressed using the Newton-Euler equations.

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