Method for controlling the speed of an industrial robot based on a bezier curve and system therefor

Abstract

The application discloses a kind of industrial robot speed control method and system based on Bezier curve, it is related to industrial robot technical field, including: using preset acceleration and deceleration control model, the speed curve shape of acceleration stage and deceleration stage of robot is adjusted, wherein the acceleration and deceleration control model is constructed based on by preset control point defined Bezier polynomial.This scheme is based on the acceleration and deceleration control model constructed by Bezier polynomial, realizes the dynamic adjustment of acceleration and deceleration process, to effectively improve the control precision and stability of system under different load and environmental conditions.

Description

Technical Field

[0001] This application relates to the field of industrial robot technology, and in particular to a method and system for industrial robot speed control based on Bézier curves. Background Technology

[0002] Currently, six-degree-of-freedom articulated industrial robots on the market mainly consist of a teach pendant, controller, AC servo driver, motor, articulated robotic arm, and reducer. Among them, the controller is the core component of the articulated industrial robot, and its main function is to control the AC servo driver and motor to work according to speed, position, and attitude commands.

[0003] To achieve high precision in workpiece machining, acceleration and deceleration control is required between motion control segments at corners to prevent impacts, loss of steps, overtravel, or oscillations during start-up, shutdown, or speed changes in industrial robots. Especially in high-speed, high-precision machining, frequent start-ups and shutdowns and short transition times mean that prioritizing the shortest possible time while neglecting dynamic acceleration and deceleration control will severely impact the robot body and actuators, affecting normal operation, potentially damaging components, and shortening equipment lifespan.

[0004] Currently, the commonly used acceleration and deceleration control methods in articulated industrial robots mainly include linear acceleration and deceleration, exponential acceleration and deceleration, and S-curve acceleration and deceleration. However, these existing technologies have the following drawbacks:

[0005] When linear acceleration and deceleration are applied at the beginning and end of the acceleration and deceleration phase, there are sudden acceleration changes, which can lead to soft impacts and affect the smoothness of motion. Compared with linear acceleration and deceleration, the velocity change is smoother, but the acceleration is not smooth at the beginning and end, which may still cause impacts. Although S-curve acceleration achieves continuous acceleration change and reduces soft impacts, its acceleration is still discontinuous at some points, which may lead to system impacts and vibrations. In addition, its computational workload is huge, making it difficult to meet the requirements of real-time control. Summary of the Invention

[0006] The main objective of this application is to provide a speed control method and system for industrial robots based on Bézier curves, aiming to solve the technical problem of how to improve the accuracy and stability of speed control for industrial robots based on Bézier curves.

[0007] To achieve the above objectives, this application proposes a speed control method for industrial robots based on Bézier curves, the speed control method for industrial robots based on Bézier curves comprising:

[0008] Using a preset acceleration / deceleration control model, the shape of the velocity curves during the robot's acceleration and deceleration phases is adjusted. The acceleration / deceleration control model is constructed based on Bessel polynomials defined by preset control points.

[0009] In one embodiment, before the step of adjusting the velocity curve shape of the robot's acceleration and deceleration phases using a preset acceleration / deceleration control model, the following steps are included:

[0010] By combining the Bessel polynomials defined by the preset control points and the Bernstein basis functions, an acceleration / deceleration control model is constructed, resulting in the preset acceleration / deceleration control model.

[0011] In one embodiment, the step of constructing an acceleration / deceleration control model by combining the Bessel polynomial defined by the preset control points and the Bernstein basis functions to obtain the preset acceleration / deceleration control model includes:

[0012] Based on the Bessel polynomial defined by the preset control points and the Bernstein basis functions, a velocity curve expression is constructed.

[0013] Expand the Bernstein basis functions and extract the Bezier curve coefficients from the velocity curve expression;

[0014] Based on preset boundary conditions, the Bézier curve coefficients are simplified to obtain simplified Bézier curve coefficients.

[0015] Based on the simplified Bézier curve coefficients, the velocity curve expression is determined;

[0016] Differentiate the velocity curve expression to obtain acceleration and jerk, and construct the acceleration / deceleration control model based on the acceleration and jerk.

[0017] In one embodiment, the preset control points include the motion start point, the start and end points of the uniform speed phase, the motion end point, the curve shape control point, and the slope change control point;

[0018] The step of simplifying the Bézier curve coefficients according to preset boundary conditions to obtain simplified Bézier polynomial coefficients includes:

[0019] Based on the starting point of the motion, the starting and ending points of the uniform velocity phase, the ending point of the motion, the curve shape control point, and the slope change control point, the initial velocity and the target velocity are set.

[0020] Based on the initial velocity and the target velocity, and combined with preset boundary conditions, the Bézier curve coefficients are simplified to obtain simplified Bézier curve coefficients.

[0021] In one embodiment, in each interpolation cycle, the interpolation speed of the robot at a preset interpolation time is calculated based on the current normalized time and the speed curve expression, including:

[0022] Convert the Bézier curve coefficients and the current normalized time in the velocity curve expression from floating-point numbers to fixed-point numbers.

[0023] Based on the Bézier curve coefficients in the form of fixed-point numbers and the current normalized time, fixed-point arithmetic is used to calculate the interpolation speed of the robot at the preset interpolation time.

[0024] In one embodiment, after the step of differentiating the velocity curve expression to obtain acceleration and jerk, and constructing the acceleration / deceleration control model based on the acceleration and jerk, the method further includes:

[0025] Analyze the extreme values ​​of the acceleration and the extreme values ​​of the jerk, and determine whether the extreme value of the acceleration exceeds a preset maximum acceleration threshold and whether the extreme value of the jerk exceeds a preset maximum jerk threshold.

[0026] If the extreme value of the acceleration exceeds the preset maximum acceleration, or the extreme value of the jerk exceeds the preset maximum jerk, then the acceleration / deceleration time and target speed are adjusted, and the acceleration / deceleration control model is reconstructed.

[0027] In one embodiment, the step of adjusting the velocity curve shape during the acceleration and deceleration phases using the acceleration / deceleration control model includes:

[0028] The velocity curves of the acceleration phase and the deceleration phase are time-symmetric about the midpoint of the total motion time, wherein the control point sequence of the acceleration phase and the control point sequence of the deceleration phase satisfy a numerical symmetry relationship.

[0029] Furthermore, to achieve the above objectives, this application also proposes an industrial robot speed control system based on Bézier curves, wherein the industrial robot speed control system based on Bézier curves includes:

[0030] The control module is used to adjust the velocity curve shape of the robot's acceleration and deceleration phases using a preset acceleration and deceleration control model, wherein the acceleration and deceleration control model is constructed based on Bezier polynomials defined by preset control points.

[0031] Furthermore, to achieve the above objectives, this application also proposes an industrial robot speed control device based on Bézier curves, the device comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, the computer program being configured to implement the steps of the industrial robot speed control method based on Bézier curves as described above.

[0032] In addition, to achieve the above objectives, this application also proposes a storage medium, which is a computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the steps of the industrial robot speed control method based on Bézier curves as described above.

[0033] In addition, to achieve the above objectives, this application also provides a computer program product, which includes a computer program that, when executed by a processor, implements the steps of the industrial robot speed control method based on Bézier curves as described above.

[0034] This application proposes a method and system for industrial robot speed control based on Bézier curves. The method includes adjusting the shape of the speed curves during the robot's acceleration and deceleration phases using a preset acceleration / deceleration control model. The acceleration / deceleration control model is constructed based on Bézier polynomials defined by preset control points. This scheme, based on the acceleration / deceleration control model constructed using Bézier polynomials, achieves dynamic adjustment of the acceleration / deceleration process, thereby effectively improving the control accuracy and stability of the system under different load and environmental conditions. Attached Figure Description

[0035] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0036] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0037] Figure 1 This is a flowchart illustrating an embodiment of the industrial robot speed control method based on Bézier curves provided in this application.

[0038] Figure 2 This is a schematic diagram of the fifth-order Bézier curve acceleration / deceleration control provided in Embodiment 1 of this application;

[0039] Figure 3 This is a schematic diagram comparing linear and quintic Bezier curve acceleration / deceleration control provided in Embodiment 1 of this application;

[0040] Figure 4 This is a flowchart illustrating Embodiment 2 of the industrial robot speed control method based on Bézier curves provided in this application.

[0041] Figure 5This is a flowchart illustrating Embodiment 3 of the industrial robot speed control method based on Bézier curves provided in this application;

[0042] Figure 6 This is a schematic diagram of the module structure of the industrial robot speed control system based on Bézier curves according to an embodiment of this application;

[0043] Figure 7 This is a schematic diagram of the equipment structure of the hardware operating environment involved in the speed control method for industrial robots based on Bézier curves in the embodiments of this application.

[0044] The purpose, features, and advantages of this application will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0045] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0046] To better understand the technical solution of this application, a detailed description will be provided below in conjunction with the accompanying drawings and specific implementation methods.

[0047] The main solution of this application embodiment is: to adjust the shape of the velocity curves of the robot's acceleration and deceleration phases using a preset acceleration and deceleration control model, wherein the acceleration and deceleration control model is constructed based on Bessel polynomials defined by preset control points.

[0048] In this embodiment, for ease of description, the following description uses a speed control system for industrial robots based on Bézier curves as the execution subject.

[0049] Currently, the commonly used acceleration and deceleration control methods in articulated industrial robots mainly include: linear acceleration and deceleration, exponential acceleration and deceleration, and S-curve acceleration and deceleration. However, these existing technologies have the following drawbacks:

[0050] When linear acceleration and deceleration are applied at the beginning and end of the acceleration and deceleration phase, there are sudden acceleration changes, which can lead to soft impacts and affect the smoothness of motion. Compared with linear acceleration and deceleration, the velocity change is smoother, but the acceleration is not smooth at the beginning and end, which may still cause impacts. Although S-curve acceleration achieves continuous acceleration change and reduces soft impacts, its acceleration is still discontinuous at some points, which may lead to system impacts and vibrations. In addition, its computational workload is huge, making it difficult to meet the requirements of real-time control.

[0051] This application provides an acceleration / deceleration control method based on Bézier curves to achieve speed control of a six-DOF articulated industrial robot. By improving the curve model and introducing advanced control strategies, dynamic adjustments to the acceleration and deceleration process can be achieved, thereby effectively improving the control accuracy and stability of the system under different load and environmental conditions. Furthermore, the smooth characteristics of Bézier curves make them highly suitable for the speed trajectory of servo motors. The speed planning method in this application features fast calculation, smoothness, and continuity, enabling stable acceleration and deceleration and avoiding vibration and excessive impact caused by speed changes.

[0052] It should be noted that the executing entity in this embodiment can be a computing service device with data processing, network communication, and program execution functions, such as a tablet computer, personal computer, or mobile phone, or an electronic device capable of performing the above functions. The following description uses a personal computer as an example to illustrate this embodiment and the subsequent embodiments.

[0053] Based on this, the embodiments of this application provide a speed control method for industrial robots based on Bézier curves, referring to... Figure 1 , Figure 1 This is a flowchart illustrating the first embodiment of the industrial robot speed control method based on Bézier curves of this application.

[0054] In this embodiment, the industrial robot speed control method based on Bézier curves includes steps S10~S20:

[0055] Step S10: Using a preset acceleration / deceleration control model, adjust the velocity curve shape of the robot's acceleration and deceleration phases. The acceleration / deceleration control model is constructed based on Bessel polynomials defined by preset control points.

[0056] In this embodiment, in order to achieve high stability and high-precision trajectory tracking during the robot's motion, a pre-built acceleration and deceleration control model is used to dynamically adjust the shape of the velocity curves during the acceleration and deceleration phases.

[0057] The acceleration / deceleration control model is constructed based on Bessel polynomials defined by preset control points. This model allows for flexible adjustment of the velocity curve's transition characteristics during start-stop phases, ensuring continuous acceleration and jerk, effectively suppressing mechanical vibration, impact, and overshoot, and improving motion smoothness and positioning repeatability.

[0058] Specifically, before step S10, step S01 is also included:

[0059] Step S01: Combine the Bessel polynomial defined by the preset control point and the Bernstein basis function to construct an acceleration / deceleration control model, thus obtaining the preset acceleration / deceleration control model.

[0060] It should be noted that Bézier polynomials are a parametric curve representation based on control points, and are widely used in computer graphics and motion trajectory planning.

[0061] Bernstein basis functions are a set of polynomial functions defined on the unit interval [0,1] and are the core mathematical tools for constructing Bézier curves.

[0062] In this embodiment, to ensure continuous changes in velocity, acceleration, and jerk, a fifth-order Bessel polynomial is used as the acceleration / deceleration control model for the velocity curve. The Bessel polynomial uses six control points to define the curve shape. These six control points are set symmetrically and include the motion start point, the start and end points of the uniform velocity phase, the motion end point, a curve shape control point defining the curve shape, and a slope change control point defining the curve slope change.

[0063] Step S01 includes steps S011 to S015:

[0064] Step S011: Construct the initial velocity curve expression using the preset Bessel polynomial and Bernstein basis functions;

[0065] It should be noted that Bernstein basis functions are a set of polynomial functions defined on the unit interval [0,1], and are the core mathematical tool for constructing Bézier curves.

[0066] In this embodiment, the velocity curve expression is constructed based on a mathematical model built using a fifth-order Bessel polynomial. This model generates a continuous and smooth velocity change curve through a linear combination of a set of preset control points and Bernstein basis functions, thereby achieving precise control over the robot's acceleration and deceleration processes.

[0067] Specifically, the initial velocity curve expression is as follows:

[0068]

[0069] In the formula, This represents the velocity value at the normalized time t, which is the output of the entire acceleration / deceleration control model; t is the normalized time, with a value of [0, 1]. ~ Indicates the preset control point; ~ This represents the Bernstein basis functions.

[0070] The Bernstein basis function expansion is as follows:

[0071] ;

[0072] ;

[0073] ;

[0074] + ;

[0075] ;

[0076] ;

[0077] In the formula, t represents the normalized time.

[0078] This step introduces a fifth-order Bessel polynomial and Bernstein basis functions, combined with preset control points, to construct a velocity curve expression with high continuity and adjustability, providing a mathematical foundation and implementation path for subsequent interpolation calculations, acceleration / deceleration control model establishment, and dynamic optimization.

[0079] Step S012: Expand the Bernstein basis function and extract the Bezier curve coefficients from the initial velocity curve expression;

[0080] It should be noted that the Bézier curve coefficients here do not refer to the control points in the original form of the Bézier curve, but rather to the combination coefficients of the powers of each term after the velocity curve expression has been converted from the Bézier basis representation to the standard polynomial form.

[0081] In this embodiment, to facilitate efficient calculation of the interpolation velocity in the system, the initial velocity curve expression based on Bernstein basis functions is converted into a standard fifth-degree polynomial form. Specifically, the expansions of each Bernstein basis function are substituted into the initial velocity expression, and by combining like terms, the initial velocity expression is rewritten in the following standard polynomial form:

[0082]

[0083] Among them, coefficients A, B, C, D, E, and F are determined by preset control points. ~ It is composed of linear combinations, and the specific expression is as follows:

[0084] ;

[0085] ;

[0086] ;

[0087] ;

[0088] ;

[0089] ;

[0090] In summary, by extracting the Bézier curve coefficients, the complex parameterized velocity model is transformed into a standard polynomial form that can be efficiently computed. This significantly improves the real-time performance of subsequent interpolation calculations and reduces the computational burden on the controller without sacrificing the continuity of the jerk.

[0091] Step S013: According to the preset boundary conditions, the Bézier curve coefficients are simplified to obtain the simplified Bézier curve coefficients.

[0092] In this embodiment, to ensure smooth start and stop of the robot during acceleration and deceleration, and to avoid mechanical shock and vibration, it is necessary to ensure that the acceleration and jerk are continuous and zero at the start and end of the motion. Therefore, this embodiment sets the following boundary conditions:

[0093] At the beginning of the acceleration or deceleration phase, both the initial acceleration and the initial jerk are zero.

[0094] At the end of the acceleration or deceleration phase, the target acceleration and target jerk are also zero.

[0095] Based on the mathematical properties of quintic Bézier curves, the aforementioned requirement for dynamic continuity can be achieved by appropriately setting control points. Specifically, let:

[0096] : Represents the initial velocity value;

[0097] : Indicates the target speed value.

[0098] Substituting the control point configuration into the Bézier curve coefficient expression extracted in step S012 and performing algebraic simplification, the simplified Bézier curve coefficients are obtained as follows:

[0099] ;

[0100] ;

[0101] ;

[0102] D=0;

[0103] E=0;

[0104] F= ;

[0105] By following the steps above, while ensuring the continuity of acceleration and jerk throughout the process, the computational complexity of the Bézier curve coefficients is significantly reduced, the number of control parameters is decreased, and the efficiency of model building and the real-time performance of interpolation are improved.

[0106] Step S014: Determine the final velocity curve expression based on the simplified Bézier curve coefficients;

[0107] In this embodiment, after step S012, the Bernstein basis functions are expanded and the Bézier curve coefficients are extracted. In step S013, the coefficients are simplified according to preset boundary conditions (such as the initial / terminal acceleration and jerk being zero) to obtain a set of simplified polynomial coefficients A, B, C, D, E, F.

[0108] After using this set of simplified Bézier curve coefficients, this step constructs the final speed curve expression that is directly executed in the actual control system, which is used for subsequent interpolation calculations and speed command output.

[0109] Specifically, the expression for the final velocity curve is as follows:

[0110] (0 <= t <= 1)

[0111] in, This represents the instantaneous velocity value at the normalized time; t is the normalized time; A, B, and C are the coefficients of the fifth, fourth, and third orders, respectively; F = , where is a constant term and is the initial velocity of the acceleration / deceleration phase.

[0112] Furthermore, in practical motion control systems, the time interval of the interpolation cycle may not be completely consistent due to coefficient scheduling, external interruptions, or dynamic speed regulation requirements, resulting in the normalization time not being able to increase in a fixed step size, i.e., "non-uniform step size calculation" is adopted. For example, in high dynamic response scenarios, the system may shorten the interpolation cycle to improve control accuracy; or it may automatically adjust according to the path curvature to achieve adaptive interpolation.

[0113] Because the variation of t lacks both equal intervals and periodicity, interpolation results cannot be obtained from a pre-production speed table or by looking up a table. Therefore, the current normalized time must be obtained within each interpolation cycle. Then, the current normalized time is substituted into the final velocity curve expression above, and the calculation is performed point by point. The speed command for the current cycle is obtained and output to the servo drive for execution. This mechanism ensures the accuracy and real-time performance of speed calculation at any t value, making it particularly suitable for precision control applications requiring high motion smoothness.

[0114] Through the above steps, the initial velocity expression from the theoretical modeling stage is transformed into an executable final velocity curve expression applicable to actual control systems. This expression is not only simplified in structure and computationally efficient, but also supports point-by-point solutions under non-uniform time steps, balancing motion smoothness, real-time control, and engineering practicality. It is a key technical step in realizing high-performance robot acceleration and deceleration control.

[0115] Step S015: Differentiate the final velocity curve expression to obtain acceleration and jerk, and construct the acceleration / deceleration control model based on the acceleration and jerk.

[0116] In this embodiment, in order to achieve precise dynamic control of the robot's motion process, it is necessary to ensure that not only the speed is continuous during acceleration and deceleration, but also the acceleration and jerk are continuous, so as to suppress mechanical shock, vibration and noise, and improve motion stability and positioning accuracy.

[0117] Therefore, this step performs mathematical differentiation on the final velocity curve expression determined in step S14, and sequentially obtains the analytical expressions for acceleration and jerk, and constructs a complete acceleration and deceleration control model based on these expressions.

[0118] First, by taking the first derivative of the final velocity curve expression with respect to normalized time, the acceleration function is obtained. This acceleration function reflects the rate of change of velocity with time, and its value is determined by the target velocity value, the initial velocity value, and the normalized time. After further simplification, it can be seen that the acceleration is zero at both the start and end times, satisfying the smooth start and stop requirement of zero acceleration at both ends; and the acceleration curve exhibits a bell-shaped distribution, with gentle changes and no abrupt changes.

[0119] Next, the acceleration function is differentiated again to obtain the jerk function. This jerk function describes the rate of change of acceleration with time and is also determined by the target velocity value, the initial velocity value, and the normalized time. Analysis shows that at a specific time point, the jerk is zero, achieving continuity of jerk; at other time points, the jerk changes continuously without jumps or infinity.

[0120] Based on the above analysis of velocity, acceleration, and jerk, a complete acceleration / deceleration control model is constructed. This model supports the synchronous calculation of acceleration and jerk in each interpolation cycle to determine whether they exceed the physical limitations of the servo system or mechanical structure. If acceleration or jerk exceeds the limit, a corresponding processing strategy is triggered. Simultaneously, based on the vibration conditions during actual operation, the initial velocity value, target velocity value, or control point distribution are adjusted in reverse to optimize the curve shape. Furthermore, acceleration and jerk are used as feedforward terms input to the servo controller to improve trajectory tracking accuracy.

[0121] Through the above steps, the derivative of the final velocity curve expression is obtained, and the explicit analytical expressions of acceleration and jerk are obtained. Based on this, an acceleration and deceleration control model containing three accelerations of velocity, acceleration, and jerk is constructed to ensure high smoothness during the motion process.

[0122] After constructing the acceleration and deceleration control model, the control points are further set reasonably using the model to control the shape of the speed curves during the acceleration and deceleration phases of the robot. This ensures consistent start-stop characteristics of the industrial robot, improves trajectory repeatability and system stability, and facilitates unified management and tuning of control parameters.

[0123] Step S10 may include step S11:

[0124] Step S11: Make the velocity curves of the acceleration phase and the deceleration phase time-symmetric about the midpoint of the total motion time, wherein the control point sequence of the acceleration phase and the control point sequence of the deceleration phase satisfy a numerical symmetry relationship.

[0125] Specifically, let the total time of the entire motion process be... The midpoint time is = / 2. By configuring the control points for the acceleration and deceleration phases, the following can be achieved:

[0126] Acceleration phase (from t=0 to t= velocity curve ;

[0127] Deceleration phase (from t= to t= velocity curve ;

[0128] It satisfies the following time symmetry relationship:

[0129]

[0130] In the formula, t represents the total time of the entire motion process; t represents the current normalized time. The speed during the deceleration phase; The speed of the acceleration phase; Indicates the start time of the deceleration phase; This indicates the end time of the acceleration phase.

[0131] To achieve this symmetry, the control point sequences of the acceleration and deceleration phases must satisfy a numerical symmetry relationship. Take a quintic Bézier curve as an example:

[0132] Let the control point for the acceleration phase be:

[0133]

[0134] Among them, the Indicates the starting point of the acceleration phase; the... Indicates the end point of the acceleration phase; intermediate control point Used to adjust the characteristics of speed change during acceleration, such as curvature and slope.

[0135] The control points for the deceleration phase should then be set as follows:

[0136]

[0137] Among them, the This indicates the start point of the deceleration phase and the corresponding end point of the acceleration phase. The This indicates the end point of the deceleration phase and the corresponding start point of the acceleration phase. ; , , , This is the intermediate control point.

[0138] Right now:

[0139]

[0140] Under this configuration, if the acceleration phase starts from the initial speed Smoothly ascend to target speed The deceleration phase will then start from Smoothly descend to the final speed in a mirror manner. This ensures that the acceleration curve is symmetrical; and the jerk curve is symmetrical; and that energy consumption and mechanical stress distribution are balanced.

[0141] Please refer to Figure 2 , Figure 2 This is a schematic diagram of acceleration / deceleration control using a fifth-order Bézier curve. Figure 2 It can be seen that the temporal symmetry between the acceleration and deceleration segments, as well as the continuity and consistency of the derivative curves, verify the effectiveness of step S11.

[0142] Please refer to Figure 3 , Figure 3This diagram illustrates the comparison between linear and fifth-order Bézier curve acceleration / deceleration control. Compared to the traditional linear acceleration / deceleration method, the fifth-order Bézier curve acceleration / deceleration method proposed in this embodiment results in a smooth transition of the position curve without obvious inflection points, exhibiting an overall "S"-shaped distribution, ensuring the continuity and stability of the motion process. Using fifth-order polynomial interpolation, a "bell-shaped" distribution is formed, with the maximum velocity occurring near the midpoint of the total time, and the velocities at both ends approaching zero, avoiding velocity jumps. Simultaneously, the acceleration curve exhibits a "double-peak" distribution, with the peak occurring at the inflection point between acceleration and deceleration, and the acceleration in the middle section remaining nearly constant, avoiding shocks caused by sudden changes. Furthermore, although the acceleration curve shows significant fluctuations at the beginning and during acceleration / deceleration, it remains continuous overall without jumps, meeting the requirements for smooth dynamics.

[0143] In summary, by utilizing the established acceleration and deceleration control model, active adjustment of the velocity curve shape during acceleration and deceleration phases was achieved. Particularly in the implementation using a time-symmetric design, the numerical symmetry of control points ensured the dynamic consistency of the start-stop process, significantly improving the smoothness, repeatability, and control accuracy of the robot's motion.

[0144] The above-described embodiments utilize a preset acceleration / deceleration control model to adjust the velocity curve shapes during the robot's acceleration and deceleration phases. This acceleration / deceleration control model is constructed based on Bessel polynomials defined by preset control points. This scheme, based on an acceleration / deceleration control model constructed using Bessel polynomials, enables dynamic adjustment of the acceleration / deceleration process, thereby effectively improving the system's control accuracy and stability under different load and environmental conditions.

[0145] Based on the first embodiment of this application, in the second embodiment of this application, the content that is the same as or similar to that in Embodiment 1 above can be referred to the above description, and will not be repeated hereafter. Based on this, please refer to... Figure 4 Following step S014, the industrial robot speed control method based on Bézier curves further includes step A1:

[0146] Step A1: In each interpolation cycle, calculate the robot's interpolation speed at the preset interpolation time based on the current normalized time and the final speed curve expression.

[0147] Because traditional floating-point arithmetic operations are too time-consuming, this implementation proposes a method to convert mathematical operations into the use of fixed-point values ​​to achieve real-time calculations, thereby reducing computational costs.

[0148] In one feasible embodiment, step A1 includes steps A11 to A12:

[0149] A11, convert the Bézier curve coefficients and the current normalized time in the velocity curve expression from floating-point numbers to fixed-point numbers;

[0150] In practical embedded control systems, although floating-point arithmetic operations (such as single-precision float) offer high accuracy, their computational overhead and long execution cycle make them difficult to meet the real-time requirements of high-speed interpolation scenarios. For example, in applications where the drive pulse frequency needs to reach 250,000 steps per second (i.e., 250kHz interpolation frequency), using floating-point operations will significantly increase the CPU load and may even lead to interpolation delays or missed steps.

[0151] Therefore, in this embodiment, the coefficients and normalized time parameters in the final velocity curve expression, which were originally represented in floating-point form, are uniformly converted into fixed-point form to achieve efficient and low-latency integer operations.

[0152] Specifically, fixed-point encoding is performed using the Qm.n format, where m represents the number of integer digits and n represents the number of decimal digits.

[0153] Then, based on the system's maximum interpolation frequency and speed dynamic range, and combined with the mathematical expression for the Bessel coefficients, the parameters are quantitatively designed as follows:

[0154] t: Unsigned Q0.32 fixed-point number (0 ≤ t < 1) | Range 0 to 0xFFFFFFFF (unsigned);

[0155] A: Signed Q24.7 fixed-point number | Range = ±250000 * 6 * 128 = ±192000000 = 0x0B71B000 | 28 data bits + sign bit;

[0156] B: Signed Q24.7 fixed-point number | Range = ±250000 * 15 * 128 = ±480000000 = 0x1C9C3800 | 29 data bits + sign bit;

[0157] C: Signed Q24.7 fixed-point number | Range = ±250000 * 10 * 128 = ±320000000 = 0x1312D000 | 29 data bits + sign bit;

[0158] F: Signed Q24.7 fixed-point number | Range = ±250000 * 128 = ±32000000 = 0x01E84800 | 25 data bits + sign bit.

[0159] In addition, to avoid overflow during the operation and to reserve enough protection bits, the system reserves an extra 2 bits for intermediate calculation expansion to ensure the stability of fixed-point operation.

[0160] Furthermore, this embodiment does not separately process and store the sign bit for each coefficient; instead, it stores the absolute value and marks the sign of coefficient A, thereby saving storage space for the sign bit. According to the rule, the sign always satisfies: sign(A) = -sign(B) = sign(C). Therefore, the final range of values ​​for the coefficient is:

[0161] t: Unsigned number (0 ≤ t < 1) | Range 0 to 0xFFFFFF (unsigned) A: Signed fixed-point number in Q24 format, range = 250000 * 6 = 1500000 = 0x16E360 | 21 bits;

[0162] B: Signed fixed-point number in Q24 format, range = 250000 * 15 = 3750000 = 0x393870 | 22 bits; C: Signed fixed-point number in Q24 format, range = 250000 * 10 = 2500000 = 0x1312D0 | 21 bits; F: Signed fixed-point number in Q24 format, range = 250000 = 250000 = 0x0ED090 | 20 bits;

[0163] For each curve, the Bézier curve coefficients are calculated using the following function:

[0164] void calcBezierCurveCoeffs(int32_t v0, int32_t v1, uint32_t av)

[0165] {

[0166] if (v1 <v0) {

[0167] A_negative = true;

[0168] bezier_A = 6 * (v0 - v1);

[0169] bezier_B = 15 * (v0 - v1);

[0170] bezier_C = 10 * (v0 - v1);

[0171] }

[0172] else {

[0173] A_negative = false;

[0174] bezier_A = 6 * (v1 - v0);

[0175] bezier_B = 15 * (v1 - v0);

[0176] bezier_C = 10 * (v1 - v0);

[0177] }

[0178] bezier_F = v0;

[0179] }

[0180] In summary, step S141 lays the foundation for subsequent high-speed interpolation calculations by converting floating-point parameters into high-precision, low-overhead fixed-point numbers.

[0181] Step A12: Based on the fixed-point Bézier curve coefficients and the current normalized time, fixed-point arithmetic is used to calculate the interpolation speed of the robot at the preset interpolation time.

[0182] After completing the fixed-point conversion of coefficients and time variables, this step uses fixed-point arithmetic operations (such as shifting, multiplication and addition, truncation, etc.) to calculate the instantaneous velocity value within the current interpolation period. Specifically, this is achieved through the following function:

[0183] int32_t evalBezierCurveVelocity(int32_t currDist)

[0184] {

[0185] uint32_t t = bezier_AV * currDist;

[0186] ………

[0187] int64_t Vc = (int64_t) bezier_F<<31;

[0188] ………

[0189] return (int32_t) Vc;

[0190] }

[0191] This function is called once in each interpolation cycle, and the output is the robot's interpolation speed command at that moment, which is sent to the servo driver or position planning module for execution.

[0192] The methods described above collectively form a crucial bridge from theoretical models to engineering implementation. By converting Bézier curve coefficients and normalized time into fixed-point numbers and performing efficient fixed-point arithmetic based on this, this invention significantly reduces computational complexity without sacrificing motion smoothness, achieving real-time, high-precision speed interpolation on resource-constrained embedded platforms.

[0193] Based on the first embodiment of this application, in the third embodiment of this application, the content that is the same as or similar to that in the first embodiment described above can be referred to the above description, and will not be repeated hereafter. Based on this, please refer to... Figure 5 Following step S015, the industrial robot speed control method based on Bézier curves further includes steps B1-B2:

[0194] Step B1: Analyze the extreme values ​​of the acceleration and the extreme values ​​of the jerk, and determine whether the extreme value of the acceleration exceeds a preset maximum acceleration threshold and whether the extreme value of the jerk exceeds a preset maximum jerk threshold.

[0195] Step B2: If the extreme value of the acceleration exceeds the preset maximum acceleration, or the extreme value of the jerk exceeds the preset maximum jerk, then adjust the acceleration / deceleration time and target speed, and reconstruct the acceleration / deceleration control model.

[0196] In this embodiment, considering the dynamic performance constraints of the industrial robot, the acceleration and jerk must not exceed their maximum values. , Differentiating the velocity curve expression yields functions of acceleration and jerk as a function of time, from which the maximum and minimum values ​​of acceleration and jerk within that segment can be determined.

[0197]

[0198] In the formula, t d V d The controller interpolates the time and target speed; This represents the extreme value of acceleration; This represents the extreme value of the jerk.

[0199] When acceleration or jerk exceeds limits, it indicates that the currently set motion parameters (such as target speed and total interpolation time) exceed the robot's dynamic performance boundaries. Direct execution will result in equipment damage, inaccurate positioning, or alarm shutdown. Therefore, this embodiment readjusts the acceleration / deceleration phase time and target speed. For example, reducing the rate of change of speed reduces acceleration and jerk, thereby extending the acceleration / deceleration phase time; reducing the speed difference ( This directly reduces the amplitude of the Bézier curve coefficients, thereby suppressing higher-order dynamic components and reducing the target velocity. Subsequently, based on the adjusted motion parameters, steps S11 to S14 are re-executed to reconstruct the acceleration / deceleration control model.

[0200] In addition, it is necessary to check whether the feed rate components on each joint axis within the speed constraint segment exceed the maximum speed limit of each axis (e.g., through Jacobian matrix mapping) to prevent local axis overload.

[0201] The motion command is only allowed to be executed when all constraints (velocity, acceleration, jerk) are satisfied; otherwise, the parameter adjustment mechanism is triggered until the model is feasible.

[0202] By analyzing the extreme values ​​of acceleration and jerk and comparing them with preset thresholds, potential risks can be identified in a timely manner. Once the limits are exceeded, the acceleration / deceleration model is reconstructed by adjusting the time and target speed of the acceleration / deceleration phases, ensuring that motion commands always remain within the robot's dynamic capabilities. This mechanism significantly improves the safety, stability, and adaptability of the control system and is a key element in achieving highly reliable industrial robot motion planning.

[0203] It should be noted that the above examples are only for understanding this application and do not constitute a limitation on the industrial robot speed control method based on Bézier curves in this application. Any simple modifications based on this technical concept are within the protection scope of this application.

[0204] This application also provides a speed control system for industrial robots based on Bézier curves; please refer to [reference needed]. Figure 6 The Bézier curve-based industrial robot speed control system includes:

[0205] The control module 10 is used to adjust the shape of the velocity curves of the robot's acceleration and deceleration phases using a preset acceleration and deceleration control model, wherein the acceleration and deceleration control model is constructed based on Bessel polynomials defined by preset control points.

[0206] The Bézier curve-based industrial robot speed control system provided in this application, employing the Bézier curve-based industrial robot speed control method described in the above embodiments, can solve the technical problem of how to improve the accuracy and stability of industrial robot speed control based on Bézier curves. Compared with the prior art, the beneficial effects of the Bézier curve-based industrial robot speed control system provided in this application are the same as those of the Bézier curve-based industrial robot speed control method provided in the above embodiments, and other technical features in the Bézier curve-based industrial robot speed control system are the same as those disclosed in the methods of the above embodiments, and will not be repeated here.

[0207] This application provides a speed control device for industrial robots based on Bézier curves. The speed control device for industrial robots based on Bézier curves includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute the speed control method for industrial robots based on Bézier curves in the above embodiment 1.

[0208] The following is for reference. Figure 7 This document illustrates a structural schematic diagram of a Bézier curve-based industrial robot speed control device suitable for implementing embodiments of this application. The Bézier curve-based industrial robot speed control device in this application embodiment may include, but is not limited to, mobile terminals such as mobile phones, laptops, digital radio receivers, PDAs (Personal Digital Assistants), PADs (Portable Application Description), PMPs (Portable Media Players), and in-vehicle terminals (e.g., in-vehicle navigation terminals), as well as fixed terminals such as digital TVs and desktop computers. Figure 7 The industrial robot speed control device based on Bézier curves shown is merely an example and should not impose any limitations on the functionality and scope of use of the embodiments of this application.

[0209] like Figure 7As shown, the speed control device for industrial robots based on Bézier curves may include a processing unit 1001 (e.g., a central processing unit, a graphics processing unit, etc.), which can perform various appropriate actions and processes according to a program stored in a read-only memory 1002 or a program loaded from a storage device 1003 into a random access memory 1004. The random access memory 1004 also stores various programs and data required for the operation of the speed control device for industrial robots based on Bézier curves. The processing unit 1001, the read-only memory 1002, and the random access memory 1004 are interconnected via a bus 1005. An input / output interface 1006 is also connected to the bus. Typically, the following systems can be connected to the input / output interface 1006: input devices 1007 including, for example, touchscreens, touchpads, keyboards, mice, image sensors, microphones, accelerometers, gyroscopes, etc.; output devices 1008 including, for example, liquid crystal displays (LCDs), speakers, vibrators, etc.; storage devices 1003 including, for example, magnetic tapes, hard disks, etc.; and communication devices 1009. Communication device 1009 allows the Bézier curve-based industrial robot speed control device to communicate wirelessly or wiredly with other devices to exchange data. While the figure shows Bézier curve-based industrial robot speed control devices with various systems, it should be understood that implementation or possession of all the systems shown is not required. More or fewer systems may be implemented alternatively.

[0210] Specifically, according to the embodiments disclosed in this application, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from storage device 1003, or installed from read-only memory 1002. When the computer program is executed by processing device 1001, it performs the functions defined in the methods of the embodiments disclosed in this application.

[0211] The Bézier curve-based industrial robot speed control device provided in this application, employing the Bézier curve-based industrial robot speed control method described in the above embodiments, can solve the technical problem of how to improve the accuracy and stability of industrial robot speed control based on Bézier curves. Compared with the prior art, the beneficial effects of the Bézier curve-based industrial robot speed control device provided in this application are the same as those of the Bézier curve-based industrial robot speed control method provided in the above embodiments, and other technical features in this Bézier curve-based industrial robot speed control device are the same as those disclosed in the previous embodiment method, and will not be repeated here.

[0212] It should be understood that the various parts disclosed in this application can be implemented using hardware, software, firmware, or a combination thereof. In the description of the above embodiments, specific features, structures, materials, or characteristics can be combined in any suitable manner in one or more embodiments or examples.

[0213] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0214] This application provides a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon, the computer-readable program instructions being used to execute the Bézier curve-based industrial robot speed control method in the above embodiments.

[0215] The computer-readable storage medium provided in this application may be, for example, a USB flash drive, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems or devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system or device. The program code contained on the computer-readable storage medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (Radio Frequency), etc., or any suitable combination thereof.

[0216] The aforementioned computer-readable storage medium may be included in a Bézier curve-based industrial robot speed control device; or it may exist independently and not be assembled into a Bézier curve-based industrial robot speed control device.

[0217] The aforementioned computer-readable storage medium carries one or more programs that, when executed by a Bézier curve-based industrial robot speed control device, cause the Bézier curve-based industrial robot speed control device to: adjust the shape of the speed curves during the acceleration and deceleration phases of the robot using a preset acceleration / deceleration control model, wherein the acceleration / deceleration control model is constructed based on Bézier polynomials defined by preset control points.

[0218] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a Local Area Network (LAN) or a Wide Area Network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0219] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0220] The modules described in the embodiments of this application can be implemented in software or hardware. The names of the modules do not necessarily limit the functionality of the unit itself.

[0221] The readable storage medium provided in this application is a computer-readable storage medium that stores computer-readable program instructions (i.e., a computer program) for executing the above-described Bézier curve-based industrial robot speed control method. This solves the technical problem of how to improve the accuracy and stability of industrial robot speed control based on Bézier curves. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as those of the Bézier curve-based industrial robot speed control method provided in the above embodiments, and will not be repeated here.

[0222] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the above-described industrial robot speed control method based on Bézier curves.

[0223] The computer program product provided in this application can solve the technical problem of how to improve the accuracy and stability of industrial robot speed control based on Bézier curves. Compared with the prior art, the beneficial effects of the computer program product provided in this application are the same as those of the industrial robot speed control method based on Bézier curves provided in the above embodiments, and will not be repeated here.

[0224] The above description is only a part of the embodiments of this application and does not limit the patent scope of this application. All equivalent structural transformations made under the technical concept of this application and using the contents of the specification and drawings of this application, or direct / indirect applications in other related technical fields, are included in the patent protection scope of this application.

Claims

1. A method for velocity control of an industrial robot based on a Bezier curve, characterized by, The Bezier curve-based industrial robot speed control method comprises: combining a Bezier polynomial defined by preset control points and a Bernstein basis function to construct an acceleration / deceleration control model, obtaining a preset acceleration / deceleration control model, comprising: constructing an initial speed curve expression based on the Bezier polynomial defined by the preset control points and the Bernstein basis function; expanding the Bernstein basis function to extract Bezier curve coefficients in the initial speed curve expression; simplifying the Bezier curve coefficients according to preset boundary conditions to obtain simplified Bezier curve coefficients; determining a final speed curve expression based on the simplified Bezier curve coefficients; deriving the final speed curve expression to obtain acceleration and jerk, and constructing the acceleration / deceleration control model based on the acceleration and the jerk; adjusting the speed curve shape of the acceleration and deceleration stages of the robot using the preset acceleration / deceleration control model, wherein the acceleration / deceleration control model is constructed based on the Bezier polynomial defined by the preset control points.

2. The Bezier curve-based industrial robot velocity control method according to claim 1, characterized in that, The preset control points include a motion starting point, a uniform speed stage starting point and an ending point, a motion ending point, a curve shape control point, and a slope change control point. The step of simplifying the Bezier curve coefficients according to the preset boundary conditions to obtain the simplified Bezier polynomial coefficient comprises: setting an initial speed and a target speed based on the motion starting point, the uniform speed stage starting point and the ending point, the motion ending point, the curve shape control point, and the slope change control point; simplifying the Bezier curve coefficients according to the initial speed and the target speed in combination with the preset boundary conditions to obtain the simplified Bezier curve coefficients.

3. The Bezier curve-based industrial robot velocity control method according to claim 1, characterized in that, After the step of determining the final speed curve expression based on the simplified Bezier curve coefficients, it further comprises: In each interpolation period, calculating the interpolation speed of the robot at the preset interpolation time according to the current normalized time and the final speed curve expression, comprising: Converting the Bezier curve coefficients in the speed curve expression and the current normalized time from floating-point numbers to fixed-point numbers; Based on the fixed-point number form of the Bezier curve coefficients and the current normalized time, using fixed-point operation to calculate the interpolation speed of the robot at the preset interpolation time.

4. The Bezier curve-based industrial robot velocity control method according to any one of claims 1 to 3, characterized in that, After the step of deriving the final speed curve expression to obtain acceleration and jerk, and constructing the acceleration / deceleration control model based on the acceleration and the jerk, it further comprises: analyzing the extreme value of the acceleration and the extreme value of the jerk, and determining whether the extreme value of the acceleration exceeds the preset maximum acceleration threshold and whether the extreme value of the jerk exceeds the preset maximum jerk threshold; if the extreme value of the acceleration exceeds the preset maximum acceleration or the extreme value of the jerk exceeds the preset maximum jerk, adjusting the acceleration / deceleration time and the target speed, and reconstructing the acceleration / deceleration control model.

5. The Bezier curve-based industrial robot velocity control method according to claim 1, characterized in that, The step of adjusting the shape of the velocity curve of the acceleration phase and the deceleration phase of the robot by using the preset acceleration-deceleration control model comprises: The velocity curve of the acceleration phase is time-symmetric with the velocity curve of the deceleration phase about the midpoint of the total motion time, wherein the control point sequence of the acceleration phase and the control point sequence of the deceleration phase satisfy a numerical symmetry relationship.

6. A Bezier curve based speed control system for an industrial robot, characterized by The industrial robot velocity control system based on the Bezier curve comprises: A control module is configured to adjust the shape of the velocity curve of the acceleration phase and the deceleration phase of the robot by using a preset acceleration-deceleration control model, wherein the acceleration-deceleration control model is constructed based on a Bezier polynomial defined by preset control points. The industrial robot velocity control system based on the Bezier curve is further configured to construct the acceleration-deceleration control model by combining the Bezier polynomial defined by the preset control points and Bernstein basis functions to obtain the preset acceleration-deceleration control model, comprising: constructing an initial velocity curve expression based on the Bezier polynomial defined by the preset control points and the Bernstein basis functions; expanding the Bernstein basis functions to extract Bezier curve coefficients in the initial velocity curve expression; simplifying the Bezier curve coefficients according to preset boundary conditions to obtain simplified Bezier curve coefficients; determining a final velocity curve expression based on the simplified Bezier curve coefficients; deriving the final velocity curve expression to obtain acceleration and jerk, and constructing the acceleration-deceleration control model based on the acceleration and the jerk.

7. A Bezier curve-based industrial robot velocity control device, characterized by, The device comprises a memory, a processor, and a computer program stored on the memory and executable on the processor, and the computer program is configured to implement the steps of the industrial robot velocity control method based on the Bezier curve according to any one of claims 1 to 5.

8. A storage medium, characterized by The storage medium is a computer readable storage medium, and the storage medium stores a computer program, and the computer program is executed by the processor to implement the steps of the industrial robot velocity control method based on the Bezier curve according to any one of claims 1 to 5.

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