Trajectory planning method, system, device and storage medium

Abstract

This application discloses a trajectory planning method, system, device, and storage medium, relating to the technical field of underactuated electromechanical systems. The method comprises: dividing the motion trajectory of a payload into four motion segments in geometric proportions; obtaining the payload's swing angle data corresponding to the four motion segments, the swing angle data including a load swing angle threshold, a swing angle angular velocity threshold, and a swing angle angular acceleration threshold; determining a polynomial equation for the payload based on the relationship between the load swing angle and time; obtaining a derivative expression of the polynomial equation at a preset order; and using the swing angle data as a constraint, solving the polynomial equation and the derivative expression for the polynomial coefficients to obtain a swing angle trajectory equation. This application helps control the payload's maximum swing angle and reduce safety accidents.

Description

Technical Field

[0001] The present application relates to the technical field of underactuated electromechanical systems, and in particular to a trajectory planning method, system, device, and storage medium. Background Art

[0002] Underactuated electromechanical systems, such as typical bridge cranes, play a vital role in freight transportation. Load swing during operation not only affects efficiency but also increases the likelihood of accidents. Currently, in most practical applications of these underactuated electromechanical systems, operators manually control the system's motion speed based on experience to mitigate the adverse effects of load swing. However, prolonged manual operation is not conducive to improving the efficiency of underactuated electromechanical systems or reducing the likelihood of accidents. Therefore, a method is needed to predict the trajectory of the payload, thereby controlling the payload's maximum swing angle based on the predicted trajectory and reducing the occurrence of accidents. Summary of the Invention

[0003] The present application aims to solve at least one of the technical problems existing in the prior art. To this end, the present application proposes a trajectory planning method, system, device, and storage medium that help control the maximum swing angle of the payload and reduce the occurrence of safety accidents.

[0004] The first embodiment of the present application provides a trajectory planning method, including:

[0005] Divide the payload's motion trajectory into four motion segments in equal proportions;

[0006] Obtaining swing angle data of the payload corresponding to the four motion segments, the swing angle data including a load swing angle threshold, a swing angle angular velocity threshold, and a swing angle angular acceleration threshold;

[0007] Determining the effective load based on a polynomial equation of a load swing angle versus time;

[0008] Obtaining a derivative expression of the polynomial equation at a preset order;

[0009] The swing angle data is used as a constraint condition, and the polynomial coefficients of the polynomial equation and the derivative expression are solved to obtain the swing angle trajectory equation.

[0010] The first aspect of the present application provides a trajectory planning method, which has at least the following beneficial effects: the trolley will cause the movement of the load during the movement process. The present application divides the time period from the start of the trolley to the stop of the trolley at the destination into four stages in equal proportion. The swing angle data of the load corresponding to the four motion segments are substituted into the polynomial equation and the multiple derivative expressions corresponding to the polynomial equation as constraints to obtain the swing angle trajectory equation. Therefore, in the process from the start of the trolley to the stop of the trolley, the movement of the swing angle is controlled according to the swing angle trajectory equation, and the maximum swing angle of the load can be controlled at the preset swing angle threshold, so that the load swing angle can be controlled, which helps to reduce the occurrence of safety accidents.

[0011] According to some embodiments of the first aspect of the present application, the polynomial equation includes at least five polynomial coefficients to be solved, and using the swing angle data as a constraint condition, solving the polynomial coefficients of the polynomial equation and the derivative expression to obtain the swing angle trajectory equation includes:

[0012] Substituting the first angle data into the polynomial equation and the derivative expression to obtain the first four polynomial coefficients of the polynomial equation; wherein the first angle data is the starting data of the first motion segment corresponding to the swing angle data, and the first motion segment is the initial segment of the motion trajectory of the payload;

[0013] updating the polynomial equation and the derivative expression according to the first four polynomial coefficients;

[0014] Substituting the second angle data into the updated polynomial equation and the updated derivative expression to obtain other polynomial coefficients of the polynomial equation; the second angle data is the angle data in the swing angle data other than the first angle data;

[0015] The swing angle trajectory equation is determined according to the first four polynomial coefficients and the other polynomial coefficients.

[0016] According to some embodiments of the first aspect of the present application, determining the swing angle trajectory equation according to the first four polynomial coefficients and the other polynomial coefficients includes:

[0017] Substituting the first four polynomial coefficients and the other polynomial coefficients into the polynomial equation to obtain an intermediate equation;

[0018] Optimizing the intermediate equation according to a preset convex optimization algorithm to determine the optimal duration of the payload movement;

[0019] The swing angle trajectory equation is determined according to the optimal duration and the intermediate equation.

[0020] According to some embodiments of the first aspect of the present application, the polynomial equation is:

[0021]

[0022]

[0023] Among them, T is the time from the start of the trolley movement to the stop of the trolley movement at the destination, 0≤t≤T, τ is the normalized time quantity, K is the maximum swing angle coefficient, α i is the coefficient of the i-th polynomial, β is the adjustment coefficient, and θ is the swing angle of the load with respect to the vertical direction.

[0024] According to some embodiments of the first aspect of the present application, the swing angle data includes:

[0025] θ(0)=0,

[0026]

[0027]

[0028]

[0029] θ(T)=0,

[0030] in, is the first-order derivative of θ(t), which represents the relationship between the angular velocity of the swing angle and time. is the second-order derivative of θ(t), which characterizes the relationship between the angular acceleration of the swing angle and time, θ(t)≤θ max , θ max 、ω max and a max They are load swing angle threshold, swing angle angular velocity threshold, and swing angle angular acceleration threshold respectively.

[0031] According to some embodiments of the first aspect of the present application, after obtaining the swing angle trajectory equation, the method further includes:

[0032] Determining a dynamic coupling equation between the trolley displacement and the swing angle of the payload;

[0033] The trolley trajectory equation is determined according to the dynamic coupling equation and the swing angle trajectory equation.

[0034] According to some embodiments of the first aspect of the present application, the dynamic coupling equation is:

[0035]

[0036] Among them, X(t) is the displacement equation of the trolley in the horizontal direction, is the second-order derivative of X(t), L is the length of the rope between the trolley and the load, and g is the acceleration due to gravity.

[0037] A second embodiment of the present application provides an underactuated electromechanical system, including:

[0038] The first module is used to divide the motion trajectory of the payload into four motion segments in equal proportions;

[0039] The second module is used to obtain the swing angle data of the payload corresponding to the four motion segments, wherein the swing angle data includes a load swing angle threshold, a swing angle angular velocity threshold, and a swing angle angular acceleration threshold;

[0040] A third module is configured to determine a polynomial equation for the effective load based on a relationship between a load swing angle and time;

[0041] A fourth module is used to obtain a derivative expression of the polynomial equation at a preset order;

[0042] The fifth module is used to use the swing angle data as a constraint condition to solve the polynomial coefficients of the polynomial equation and the derivative expression to obtain the swing angle trajectory equation.

[0043] The second aspect embodiment of the present application provides an under-actuated electromechanical system, which is used to implement a trajectory planning method of the first aspect embodiment of the present application, and therefore has all the beneficial effects of the first aspect embodiment of the present application.

[0044] A third embodiment of the present application provides an electronic device, including:

[0045] at least one memory;

[0046] at least one processor;

[0047] at least one program;

[0048] The program is stored in the memory, and the processor executes at least one of the programs to implement the trajectory planning method as described in any embodiment of the first aspect of the present application.

[0049] An embodiment of the fourth aspect of the present application provides a computer-readable storage medium, which stores a computer-executable signal, and the computer-executable signal is used to execute the trajectory planning method as described in any embodiment of the first aspect of the present application. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Additional aspects and advantages of the present application will become apparent and readily understood from the following description of the embodiments with reference to the accompanying drawings, in which:

[0051] Figure 1 Schematic diagram of a single pendulum model of a bridge crane provided in an embodiment of the present application;

[0052] Figure 2 A schematic diagram of five initial and final states of a load provided in an embodiment of the present application;

[0053] Figure 3 A flow chart of a trajectory planning method provided in an embodiment of the present application;

[0054] Figure 4 A schematic structural diagram of an underactuated electromechanical system provided in an embodiment of the present application;

[0055] Figure 5 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of this application more clear, the following further describes this application in detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain this application and are not intended to limit this application.

[0057] It should be noted that although a logical order is shown in the flowcharts, in some cases, the steps shown or described may be performed in a different order than that shown in the flowcharts. Terms used in the specification, claims, and drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0058] In the description of this application, if there is a description of first or second, it is only for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0059] In the description of this application, unless otherwise clearly defined, terms such as setting, installing, and connecting should be understood in a broad sense, and technicians in the relevant technical field can reasonably determine the specific meanings of the above terms in this application based on the specific content of the technical solution.

[0060] The flowcharts shown in the accompanying drawings are for illustrative purposes only and do not necessarily include all contents and operations / steps, nor must they be executed in the order described. For example, some operations / steps may be decomposed, while others may be combined or partially combined. Therefore, the actual execution order may vary depending on the actual situation.

[0061] Bridge cranes play a vital role in freight transport and are a special type of underactuated electromechanical system. The motion trajectory of the driven object in an underactuated electromechanical system plays a crucial role in the efficiency and safety of transportation tasks. Trajectory planning for bridge cranes requires the following requirements: the payload should have no residual swing angle after reaching the target displacement; the trolley should reach the target displacement in the shortest possible time; and the payload's swing angle should remain within an acceptable range throughout the entire process. However, in most current applications of these underactuated electromechanical systems, operators control the system's motion speed based on experience to minimize the adverse effects of load swing. However, prolonged manual operation can reduce the efficiency of underactuated electromechanical systems and increase their safety risks. Therefore, promoting the automation of underactuated electromechanical systems, particularly bridge cranes, is urgent.

[0062] Existing control methods primarily include optimal control, sliding film control, adaptive control, and trajectory planning. Trajectory planning is further divided into two categories: offline and online. Offline planning generally offers better control results, while online planning eliminates the need for offline iterations and offers excellent real-time response. Both offline and online trajectory planning typically plan the trajectory of the trolley or load to eliminate load sway. This makes it difficult to directly control swing angle changes during transportation, making it impossible to quickly adjust these changes.

[0063] Based on this, the present application proposes a trajectory planning method, system, device and storage medium, which help to control the maximum swing angle of the payload and reduce safety accidents.

[0064] The embodiments of the present application are further described below with reference to the accompanying drawings.

[0065] Reference Figure 1 , Figure 1 A schematic diagram of a simple pendulum model of a bridge crane provided in an embodiment of the present invention includes a payload and a trolley, wherein the payload and the trolley are connected by a rope of length L. The trolley moves linearly along the X-axis under the action of a driving force. The movement of the trolley causes the movement of the payload, and the swing angle of the payload is θ. The model parameters of the simple pendulum model of the bridge crane are shown in Table 1.

[0066] Table 1 Bridge crane system model parameters

[0067]

[0068]

[0069] based on Figure 1The crane pendulum model is used. Using the Lagrange dynamics equation, we can get equations (1) and (2):

[0070]

[0071]

[0072] Reference Figure 2 , Figure 2 In order to describe the swinging process of the payload from the start of the bridge crane's movement to the stop at the destination, it is divided into four movement stages: the initial acceleration to the first stage where the swing angle reaches the maximum; the payload accelerates to the stage where the swing angle is equal to the trolley displacement for the first time, that is, the swing angle returns to zero again, but at this time the speed of the payload is greater than the speed of the trolley; the second stage where the swing angle reaches the maximum, the maximum amplitude of the swing angle is equal to the first maximum amplitude, that is, the stage where the trolley catches up with the payload; the second stage where the effective payload and the trolley displacement are equal, at this time the trolley just catches up with the payload, and the trolley stops at the target position at the same time. The four movement stages correspond to five initial and end states. Figure 2 The rope length is always considered constant during the entire motion. This division method is conducive to obtaining the optimal trajectory corresponding to each maximum swing angle.

[0073] based on Figure 1 and Figure 2 , refer to Figure 3 ,Figure ,3 is a flow chart of a trajectory planning method provided by an embodiment of the present invention, ,which includes but is not limited to the following steps 301 to 303.

[0074] Step 301: Divide the motion trajectory of the payload into four motion segments in equal proportions;

[0075] Step 302: Obtaining the swing angle data of the payload corresponding to the four motion segments, the swing angle data including the load swing angle threshold, the swing angle angular velocity threshold, and the swing angle angular acceleration threshold;

[0076] Step 303: Determine the effective load based on a polynomial equation of the relationship between the load swing angle and time;

[0077] Step 304: Obtaining a derivative expression of the polynomial equation at a preset order;

[0078] Step 305: Using the swing angle data as a constraint condition, the polynomial coefficients of the polynomial equation and the derivative expression are solved to obtain the swing angle trajectory equation.

[0079] It should be noted that the swing angle data includes load swing angle thresholds, swing angle angular velocity thresholds, and swing angle angular acceleration threshold data corresponding to the five initial and final states respectively.

[0080] In one embodiment, the polynomial equation includes at least five polynomial coefficients to be solved. Step 305: using the swing angle data as a constraint condition, solving the polynomial coefficients of the polynomial equation and the derivative expression to obtain the swing angle trajectory equation, including: substituting the first angle data into the polynomial equation and the derivative expression to obtain the first four polynomial coefficients of the polynomial equation; wherein the first angle data is the starting data corresponding to the first motion segment in the swing angle data, and the first motion segment is the initial segment of the motion trajectory of the effective load; updating the polynomial equation and the derivative expression according to the first four polynomial coefficients; substituting the second angle data into the updated polynomial equation and the updated derivative expression to obtain other polynomial coefficients of the polynomial equation; the second angle data is the angle data other than the first angle data in the swing angle data; and determining the swing angle trajectory equation according to the first four polynomial coefficients and other polynomial coefficients.

[0081] In one embodiment, the swing angle trajectory equation is determined based on the first four polynomial coefficients and other polynomial coefficients, including: substituting the first four polynomial coefficients and other polynomial coefficients into the polynomial equation to obtain an intermediate equation; optimizing the intermediate equation according to a preset convex optimization algorithm to determine the optimal duration of the payload movement; and determining the swing angle trajectory equation based on the optimal duration and the intermediate equation.

[0082] In one embodiment, the polynomial equation is:

[0083]

[0084]

[0085] Among them, T is the time from the start of the trolley movement to the stop of the trolley movement at the destination, 0≤t≤T, τ is the normalized time quantity, K is the maximum swing angle coefficient, α i is the coefficient of the i-th polynomial, β is the adjustment coefficient, and θ is the swing angle of the effective load with respect to the vertical direction.

[0086] It should be noted that when we take the derivative of θ(t), we are actually taking the derivative of the equation containing τ i Derivative of each polynomial, for example: the i-th term τ i The first-order derivative equation of is shown in formula (3), where i = 0, 1, 2, 3, ..., 14:

[0087]

[0088] In one embodiment, the swing angle data includes:

[0089] First initial and final state:

[0090] θ(0)=0,

[0091] The second initial and final state:

[0092]

[0093] The third initial and final state:

[0094]

[0095] The fourth state:

[0096]

[0097] The fifth state:

[0098] θ(T)=0,

[0099] in, is the first-order derivative of θ(t), which represents the relationship between the angular velocity of the swing angle and time. is the second-order derivative of θ(t), which characterizes the relationship between the angular acceleration of the swing angle and time, θ(t)≤θ max , θ max 、ω max and a max They are load swing angle threshold, swing angle angular velocity threshold, and swing angle angular acceleration threshold respectively.

[0100] It should be noted that by taking the derivative of θ(t) three times, we obtain three derivative expressions. The first initial and final state is the first angle data. Substituting the first initial and final state into θ(t) and its three derivative expressions, we can obtain the first four polynomial coefficients: α0 = α1 = α2 = α3 = 0. On this basis, substituting the first four polynomial coefficients into the polynomial equation, we can obtain the intermediate equation shown in formula (4):

[0101]

[0102] The r-th order derivative corresponding to formula (4) is shown in formula (5):

[0103]

[0104] Where r is 0, 1, 2, 3, and the second, third, fourth, and fifth initial and final states are substituted into formula (5), and a formula about α4, α5, α6, ..., α can be obtained. 14 By solving the eleven-variable linear equation system, we can get α4, α5, α6...α 14Specifically, α4=8516, α5=84930, α6=366290, α7=900421, α8=1381281, α9=1341035, α 10 =779555,α 11 =219810,α 12 =7,α 13 =10558,α 14 =13.

[0105] After getting α1, α2, α3...α 14 After finding the specific value of , the intermediate equations must be optimized according to the preset convex optimization algorithm to determine the optimal duration T of the payload movement to complete the entire trajectory planning process. Next, by adjusting T, the planned trajectory meets the Y threshold constraints of the swing angle, angular velocity, and angular acceleration. On the other hand, considering that T is the operating time of the trolley, in order to improve the working efficiency of the entire system, T should be made as small as possible. In addition, θ(t)≤θ max , All inequality constraints in are convex constraints. Therefore, the selection of parameter T can be reduced to the following convex optimization problem:

[0106] min T,stθ(t)≤θ max ,

[0107] Use the bisection method to solve the above problem. The specific solution algorithm is shown in the following pseudo code, where: T low , T up ∈R + , T low , T up They represent the lower limit and upper limit of the parameter T to be optimized respectively; ε is the optimization tolerance, which is the judgment standard for the end of optimization and can be set according to actual needs; T target is the optimal value of parameter T that satisfies the constraints.

[0108]

[0109] The above-mentioned α1, α2, α3...α 14 The specific value of T target Substituting into the polynomial equation, the final swing angle trajectory equation is as follows:

[0110]

[0111] It should be noted that the setting of the above constraints can reduce the complexity of trajectory planning, and setting the preset threshold to 0 can achieve a better swing elimination effect.

[0112] In one embodiment, after obtaining the swing angle trajectory equation, the method further includes: determining a dynamic coupling equation between the trolley displacement and the swing angle of the payload; and determining the trolley trajectory equation based on the dynamic coupling equation and the swing angle trajectory equation.

[0113] In one embodiment, the dynamic coupling equations are:

[0114]

[0115] Among them, X(t) is the displacement equation of the trolley in the horizontal direction, is the second-order derivative of X(t), L is the length of the rope between the trolley and the payload, and g is the acceleration due to gravity.

[0116] It should be noted that the above formula (2) is simplified to the following intermediate formula to obtain formula (6):

[0117]

[0118] In addition, combined Figure 1 For the single pendulum model of a bridge crane, the horizontal displacement of the effective load can be expressed by formula (7). According to formula (7) and formula (6), formula (8) can be obtained. Formula (8) characterizes the dynamic coupling relationship between the effective load displacement and the effective load swing angle:

[0119]

[0120]

[0121] From the polynomial equation and equation (8), it can be seen that all states of the payload and the trolley can be expressed as the algebraic sum of θ(t) and its derivatives of different orders. Therefore, by obtaining θ(t), the trolley trajectory equation can be determined. In practical applications, the trolley motion can be controlled based on the trolley trajectory equation. Therefore, the trolley trajectory equation of this application can achieve a good anti-sway effect during the control of the trolley motion process.

[0122] Reference Figure 4 , an underactuated electromechanical system provided by an embodiment of the present invention, comprising:

[0123] The first module is used to divide the motion trajectory of the payload into four motion segments in equal proportions;

[0124] The second module is used to obtain the swing angle data of the effective load corresponding to the four motion segments, and the swing angle data includes the load swing angle threshold, the swing angle angular velocity threshold, and the swing angle angular acceleration threshold;

[0125] A third module is used to determine the effective load based on a polynomial equation of the relationship between the load swing angle and time;

[0126] The fourth module is used to obtain the derivative expression of the polynomial equation at a preset order;

[0127] The fifth module is used to use the swing angle data as a constraint condition to solve the polynomial coefficients of the polynomial equation and the derivative expression to obtain the swing angle trajectory equation.

[0128] It can be understood that the present application divides the time period from the start of the trolley's movement to the stop of the trolley's movement at the destination into four stages in equal proportion, and substitutes the swing angle data of the load corresponding to the four motion segments as constraints into the polynomial equation and multiple derivative expressions corresponding to the polynomial equation to obtain the swing angle trajectory equation. Therefore, in the process from the start of the trolley's movement to the stop of the trolley's movement, the movement of the swing angle is controlled according to the swing angle trajectory equation, and the maximum swing angle of the load can be controlled at the preset swing angle threshold, thereby achieving controllable load swing angle and helping to reduce the occurrence of safety accidents.

[0129] It is understood that the trajectory planning method of the present application can control the maximum swing angle, angular velocity, and angular acceleration of the payload generated during the trolley's motion, and control them within preset thresholds. According to the law of conservation of energy, if the payload does not swing, the work done by the driving force is fully used to increase the kinetic energy of the trolley, that is, to accelerate the trolley's movement speed, so that the trolley reaches the destination in the shortest time, thereby improving work efficiency. In addition, the minimum period T determined by satisfying the upper limit constraints of the swing angle, angular velocity, and angular acceleration mentioned above is also conducive to the trolley reaching the destination in the shortest time, thereby improving work efficiency.

[0130] Reference Figure 5 , Figure 5 The electronic device 500 includes a memory 501, a processor 502, and a computer program stored in the memory 501 and executable on the processor 502. The computer program is used to execute the above method when executed.

[0131] The processor 502 and the memory 501 may be connected via a bus or other means.

[0132] Memory 501, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs, such as the method described in the embodiments of the present invention. Processor 502 implements the above method by executing the non-transitory software programs and instructions stored in memory 501.

[0133] The memory 501 may include a program storage area and a data storage area, wherein the program storage area may store an operating system and applications required for at least one function; the data storage area may store and execute the above method. In addition, the memory 501 may include a high-speed random access memory, and may also include a non-volatile memory, such as at least one storage device memory device, a flash memory device or other non-volatile solid-state memory device. In some embodiments, the memory 501 may optionally include a memory remotely arranged relative to the processor 502, and these remote memories may be connected to the electronic device 500 via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network and a combination thereof.

[0134] The non-transitory software programs and instructions required to implement the above methods are stored in the memory 501 , and when executed by one or more processors 502 , the above methods are performed.

[0135] An embodiment of the present invention further provides a computer-readable storage medium storing computer-executable instructions for executing the above method.

[0136] In one embodiment, the computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are executed by one or more control processors to implement the above method.

[0137] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, i.e., they may be located in one place or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of this embodiment.

[0138] Those skilled in the art will appreciate that all or some of the steps and systems in the method disclosed above can be implemented as software, firmware, hardware, and appropriate combinations thereof. Some physical components or all physical components can be implemented as software executed by a processor, such as a central processing unit, a digital signal processor, or a microprocessor, or implemented as hardware, or implemented as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, and the computer-readable medium can include computer storage media (or non-transitory media) and communication media (or temporary media). As known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory, or other memory technology, CD-ROM, digital versatile disks (DVD), or other optical disk storage, magnetic cassettes, magnetic tapes, storage device storage, or other magnetic storage devices, or any other medium that can be used to store desired information and can be accessed by a computer. Furthermore, as is well known to those skilled in the art, communication media typically includes computer-readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism, and may include any information delivery media.

[0139] It should also be understood that the various implementations provided in the embodiments of the present invention can be combined arbitrarily to achieve different technical effects.

[0140] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the above implementation. Those skilled in the art can make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of the present invention.

Claims

1. A trajectory planning method, characterized in that: include: Divide the payload's motion trajectory into four motion segments in equal proportions; Obtaining swing angle data of the payload corresponding to the four motion segments, the swing angle data including a load swing angle threshold, a swing angle angular velocity threshold, and a swing angle angular acceleration threshold; Determining the effective load based on a polynomial equation of a load swing angle versus time; Obtaining a derivative expression of the polynomial equation at a preset order; Using the swing angle data as a constraint condition, the polynomial equation and the derivative expression are solved for polynomial coefficients to obtain a swing angle trajectory equation; The polynomial equation includes at least five polynomial coefficients to be solved. The polynomial coefficients are solved for the polynomial equation and the derivative expression using the swing angle data as a constraint condition to obtain the swing angle trajectory equation, including: Substituting the first angle data into the polynomial equation and the derivative expression to obtain the first four polynomial coefficients of the polynomial equation; wherein the first angle data is the starting data of the first motion segment corresponding to the swing angle data, and the first motion segment is the initial segment of the motion trajectory of the payload; updating the polynomial equation and the derivative expression according to the first four polynomial coefficients; Substituting the second angle data into the updated polynomial equation and the updated derivative expression to obtain other polynomial coefficients of the polynomial equation; the second angle data is the angle data in the swing angle data other than the first angle data; Determining a swing angle trajectory equation according to the first four polynomial coefficients and the other polynomial coefficients; The polynomial equation is: Among them, T is the time from the start of the trolley movement to the stop of the trolley movement at the destination, 0≤t≤T, τ is the normalized time quantity, K is the maximum swing angle coefficient, α i is the coefficient of the i-th polynomial, β is the adjustment coefficient, and θ is the swing angle of the load with respect to the vertical direction.

2. The method according to claim 1, characterized in that Determining the swing angle trajectory equation according to the first four polynomial coefficients and the other polynomial coefficients includes: Substituting the first four polynomial coefficients and the other polynomial coefficients into the polynomial equation to obtain an intermediate equation; Optimizing the intermediate equation according to a preset convex optimization algorithm to determine the optimal duration of the payload movement; The swing angle trajectory equation is determined according to the optimal duration and the intermediate equation.

3. The method according to claim 1, characterized in that The swing angle data includes: in, is the first-order derivative of θ(t), which represents the relationship between the angular velocity of the swing angle and time. is the second-order derivative of θ(t), which characterizes the relationship between the angular acceleration of the swing angle and time, θ(t)≤θ max , θ max 、ω max and a max They are load swing angle threshold, swing angle angular velocity threshold, and swing angle angular acceleration threshold respectively.

4. The method according to claim 3, characterized in that After obtaining the swing angle trajectory equation, the method further includes: Determining a dynamic coupling equation between the trolley displacement and the swing angle of the payload; The trolley trajectory equation is determined according to the dynamic coupling equation and the swing angle trajectory equation.

5. The method according to claim 4, characterized in that The dynamic coupling equation is: Among them, X(t) is the displacement equation of the trolley in the horizontal direction, is the second-order derivative of X(t), L is the length of the rope between the trolley and the load, and g is the acceleration due to gravity.

6. An underactuated electromechanical system, characterized in that: include: The first module is used to divide the motion trajectory of the payload into four motion segments in equal proportions; The second module is used to obtain the swing angle data of the payload corresponding to the four motion segments, wherein the swing angle data includes a load swing angle threshold, a swing angle angular velocity threshold, and a swing angle angular acceleration threshold; A third module is configured to determine a polynomial equation for the effective load based on a relationship between a load swing angle and time; A fourth module is used to obtain a derivative expression of the polynomial equation at a preset order; a fifth module, configured to use the swing angle data as a constraint condition, solve the polynomial coefficients of the polynomial equation and the derivative expression, and obtain a swing angle trajectory equation; The polynomial equation includes at least five polynomial coefficients to be solved. The polynomial coefficients are solved for the polynomial equation and the derivative expression using the swing angle data as a constraint condition to obtain the swing angle trajectory equation, including: Substituting the first angle data into the polynomial equation and the derivative expression to obtain the first four polynomial coefficients of the polynomial equation; wherein the first angle data is the starting data of the first motion segment corresponding to the swing angle data, and the first motion segment is the initial segment of the motion trajectory of the payload; updating the polynomial equation and the derivative expression according to the first four polynomial coefficients; Substituting the second angle data into the updated polynomial equation and the updated derivative expression to obtain other polynomial coefficients of the polynomial equation; the second angle data is the angle data in the swing angle data other than the first angle data; Determining a swing angle trajectory equation according to the first four polynomial coefficients and the other polynomial coefficients; The polynomial equation is: Among them, T is the time from the start of the trolley movement to the stop of the trolley movement at the destination, 0≤t≤T, τ is the normalized time quantity, K is the maximum swing angle coefficient, α i is the coefficient of the i-th polynomial, β is the adjustment coefficient, and θ is the swing angle of the load with respect to the vertical direction.

7. An electronic device, characterized in that: include: at least one memory; at least one processor; at least one program; The programs are stored in the memory, and the processor executes at least one of the programs to implement the trajectory planning method according to any one of claims 1 to 5.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer-executable signal, and the computer-executable signal is used to execute the trajectory planning method according to any one of claims 1 to 5.

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