Four-wheel steering robot control method and device, storage medium and program product

Abstract

The invention provides a four-wheel steering robot control method and device, a storage medium and a program product. The curvature characteristic of the current position of a four-wheel steering robot on a target track is measured by introducing a curvature dynamic coefficient and a path curvature index; a prediction time domain for future state prediction is dynamically adjusted through a fuzzy control algorithm, and a control time domain is determined to adapt to current curvature characteristics. Discretizing a vehicle control model of the four-wheel steering robot, establishing a mapping relation between a control increment and a motion state of the four-wheel steering robot under a constraint condition, solving an optimal control sequence in a control time domain based on a quadratic programming solver, executing an instruction corresponding to the first-step control increment, and obtaining the optimal control sequence of the four-wheel steering robot. And the motion state of the four-wheel steering robot is updated through a feedback correction mechanism to realize continuous control. According to the method, the calculation load can be reduced, the calculation efficiency can be optimized, and the real-time response capability of the system and the stability of the four-wheel steering robot under complex working conditions can be improved.

Description

Technical Field

[0001] The present invention relates to the field of robot control technology, and in particular to a four-wheel steering robot control method, device, storage medium and program product. Background Art

[0002] In the field of small and light package logistics sorting, four-wheel independently driven automated guided vehicles (AGVs) have become core equipment in logistics sorting systems due to their high load capacity and high maneuverability. Their tracking accuracy directly determines material turnover efficiency and system reliability. This is especially true in high-cargo density environments like logistics factories, where the work surfaces are complex and varied. Robots must be able to flexibly avoid obstacles in dense cargo environments and maintain stable movement despite varying surface characteristics (such as flatness and friction coefficient).

[0003] In the field of autonomous mobile equipment control, model predictive control (MPC) algorithms have become a highly favored advanced control solution due to their forward-looking and constrained optimization capabilities. Based on the current operating state of the device, this algorithm predicts the system's dynamic behavior within a specific future time domain. By optimizing control commands on a rolling basis, it continuously reduces deviations from the target state, achieving precise control while satisfying physical constraints such as device dynamics and kinematics.

[0004] However, traditional trajectory tracking control technologies, such as fixed-time model predictive control (MPC), have significant drawbacks when dealing with curved paths. Among them, there is the problem of error accumulation. Fixed-time control cannot dynamically adapt to changes in path curvature, resulting in tracking errors accumulating as the path curvature increases, affecting sorting efficiency and cargo safety. There is also a problem of insufficient dynamic adaptability. In the case of sudden changes in curvature or complex paths, traditional algorithms have difficulty adjusting control parameters in real time, making it easy for trajectory deviation and unstable robot operation to occur. This is especially true in four-wheel steering mode, where the problem of insufficient control accuracy is even more prominent.

[0005] Therefore, there is an urgent need for a trajectory tracking control algorithm that is adaptive to changes in path curvature to improve the trajectory tracking accuracy and operational stability of four-wheel steering robots in curved paths and high-density cargo environments, and to meet the requirements of modern logistics sorting systems for efficiency and reliability. Summary of the Invention

[0006] In view of this, the present invention provides a four-wheel steering robot control method, device, storage medium and program product to solve the problems of low trajectory tracking accuracy and poor operation stability of four-wheel steering robots in curved paths in high-density cargo environments in the prior art.

[0007] One aspect of the present invention provides a four-wheel steering robot control method, the method comprising the following steps:

[0008] Read the position coordinates of the four-wheel steering robot when it is running on the target trajectory according to the set sampling period, calculate the curvature gradient of the current position, and divide the curvature gradient by the maximum curvature gradient to obtain the curvature dynamic coefficient;

[0009] determining a preview length on the target trajectory according to a set rule based on the current movement speed and the current position, calculating an average curvature within the preview length, and dividing the average curvature by a maximum curvature allowed by the system to obtain a path curvature index;

[0010] The curvature dynamic coefficient and the path curvature index are used as inputs of a fuzzy control algorithm and output as a prediction time domain for future state prediction, such that the larger the curvature dynamic coefficient and the path curvature index, the longer the prediction time domain. The input and output of the fuzzy control algorithm both use triangular membership functions. The curvature dynamic coefficient gain is introduced, and the control time domain is calculated based on the prediction time domain.

[0011] A controller is constructed to discretize a pre-established continuous-state vehicle control model for the four-wheel steering robot, establish multiple constraints within the control time domain, and form a mapping relationship between control increments and the motion state of the four-wheel steering robot; the vehicle control model includes a kinematic model, a lateral dynamics model, and a longitudinal dynamics model;

[0012] A quadratic programming solver is used to solve the optimal control sequence in the control time domain, the instruction corresponding to the first step control increment in the optimal control sequence is executed, and the motion state of the four-wheel steering robot is updated through a feedback correction mechanism to achieve continuous control.

[0013] In some embodiments, the curvature gradient is calculated as:

[0014]

[0015] Among them, C g represents the curvature gradient, k i is the curvature of the current position, k i-1 Indicates the curvature of the position at the previous moment. The current position coordinate is (x i ,y i ), the position coordinate at the previous moment is (x i-1 ,y i-1 );

[0016] The calculation formula of the curvature dynamic coefficient is:

[0017]

[0018] Among them, C gn represents the curvature dynamic coefficient, C gmax Indicates the maximum value of the curvature gradient.

[0019] In some embodiments, the preview length is determined on the target trajectory according to a set rule based on the current motion speed and the current position, and the expression is:

[0020]

[0021] Among them: min is the minimum value of the preview length, l max is the maximum value of the preview length, in m; a l and b l is a constant; ν min is the minimum value of linear velocity, v max is the maximum value of the linear velocity, in m / s;

[0022] Then the calculation formula of the path curvature index is:

[0023]

[0024] Among them, C pn represents the path curvature index, C p represents the forward mean curvature within the preview length, κ k represents the curvature of the kth sampling point, n represents the number of sampling points, κ kmax Indicates the maximum curvature allowed by the system.

[0025] In some embodiments, the curvature dynamic coefficient gain is introduced, and the control time domain is calculated according to the prediction time domain. The calculation formula is:

[0026] N c =round[k m N p (1+k n C gn )];

[0027] Among them, k m represents the time domain weight coefficient, which ranges from 0 to 0.5; k n Indicates the gain coefficient, ranging from 0 to 1; C gn represents the curvature dynamic coefficient; N p represents the prediction time domain; N c represents the control time domain.

[0028] In some embodiments, the method discretizes the vehicle control model using a fourth-order Runge-Kutta method, including:

[0029] Calculating a first state change rate at an initial moment based on the current state and the control input;

[0030] Inferring the state after half the control time domain based on the first state change rate, and calculating the second state change rate at this time;

[0031] Recalculating the state after half the control time domain based on the second state change rate, and calculating the third state change rate at this time;

[0032] Inferring the state after the entire control time domain according to the third state change rate, and calculating the fourth state change rate at this time;

[0033] The first state change rate, the second state change rate, the third state change rate and the fourth state change rate are averaged according to preset weights to obtain an average change rate, and the state at the next sampling point is calculated using the average change rate.

[0034] In some embodiments, the constraints include range constraints on the trajectory tracking error term, the heading angle error term, the yaw rate error term, the control input smoothing term, and the rear wheel steering angle smoothing constraint term, and the constraints further introduce a relaxation factor to ensure solution feasibility;

[0035] The method uses the curvature dynamic coefficient and the path curvature index as inputs of the fuzzy control algorithm and outputs a prediction time domain for future state prediction, and also includes: defuzzifying the output using the centroid method, calculating the centroid of the synthesized fuzzy set, and obtaining the value of the prediction time domain.

[0036] In some embodiments, the method further comprises:

[0037] In response to a received movement instruction, obtaining an initial position of the four-wheel steering robot; the movement instruction includes the end position;

[0038] A moving path from the initial position to the end position is constructed as the target trajectory according to a preset path planning algorithm.

[0039] On the other hand, the present invention also provides a four-wheel steering robot control device, comprising a processor, a memory, and a computer program / instructions stored in the memory, wherein the processor is used to execute the computer program / instructions, and when the computer program / instructions are executed, the device implements the steps of the above method.

[0040] On the other hand, the present invention further provides a computer-readable storage medium having a computer program / instruction stored thereon, which implements the steps of the above method when executed by a processor.

[0041] On the other hand, the present invention also provides a computer program product, comprising a computer program / instruction, which implements the steps of the above method when executed by a processor.

[0042] The four-wheel steering robot control method, device, storage medium, and program product described in the present invention measure the curvature characteristics of the four-wheel steering robot's current position on the target trajectory by introducing a curvature dynamic coefficient and a path curvature index. A fuzzy control algorithm dynamically adjusts the prediction horizon for future state predictions and determines the control horizon to adapt to the current curvature characteristics. By discretizing the vehicle control model of the four-wheel steering robot, a mapping relationship between control increments and the robot's motion state is established under constraints. A quadratic programming solver is used to solve the optimal control sequence within the control horizon, executing the instructions corresponding to the first control increment. A feedback correction mechanism is then used to update the robot's motion state, achieving continuous control. The present invention dynamically adjusts the control horizon based on the path curvature, automatically shortening the prediction horizon for low-curvature straight paths, reducing the dimensionality of the optimization problem, lowering the computational load, optimizing computational efficiency, and significantly enhancing the system's real-time responsiveness. Furthermore, by introducing constraints into the vehicle control model, control accuracy is effectively improved, enhancing the stability of the four-wheel steering robot under complex operating conditions.

[0043] Additional advantages, objects, and features of the present invention will be set forth in part in the following description and will become apparent to those skilled in the art upon examination of the following or may be learned from practice of the present invention. The objects and other advantages of the present invention may be realized and obtained by the structures particularly pointed out in the description and drawings.

[0044] Those skilled in the art will understand that the purposes and advantages that can be achieved by the present invention are not limited to the above specific descriptions, and the above and other purposes that can be achieved by the present invention will be more clearly understood based on the following detailed description. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of this application, and do not constitute a limitation of the present invention. In the drawings:

[0046] Figure 1 The figure is a flow chart of a four-wheel steering robot control method according to an embodiment of the present invention.

[0047] FIG. 2( a ) shows the input-output membership function of the fuzzy control algorithm with respect to the path curvature index in one embodiment of the present invention.

[0048] FIG2( b ) is an input-output membership function of the fuzzy control algorithm with respect to the curvature dynamic index in one embodiment of the present invention.

[0049] FIG2( c ) is an input-output membership function of the fuzzy control algorithm in the prediction time domain according to an embodiment of the present invention.

[0050] Figure 3 This is an input-output response surface diagram of the fuzzy control algorithm in one embodiment of the present invention.

[0051] Figure 4 2 is a flow chart of a control method for a four-wheel steering robot according to an embodiment of the present invention.

[0052] Figure 5 This is a parameter annotation diagram of the dynamic model of a four-wheel steering robot in one embodiment of the present invention.

[0053] Figure 6 This is the trajectory tracking diagram under different prediction time domains at a low speed of 0.5m / s.

[0054] Figure 7 This is the lateral error diagram under different prediction time domains at a low speed of 0.5m / s.

[0055] Figure 8(a) shows the change of heading angle with time at a low speed of 0.5 m / s.

[0056] Figure 8(b) shows the change of heading error over time at a low speed of 0.5 m / s.

[0057] Figure 9 This is a graph showing the change of yaw angular velocity with time at a low speed of 0.5m / s.

[0058] Figure 10(a) shows the change of the front wheel angle with time under different prediction time domains at a low speed of 0.5 m / s.

[0059] Figure 10(b) shows the change of the rear wheel turning angle with time under different prediction time domains at a low speed of 0.5 m / s.

[0060] Figure 11 Trajectory tracking diagrams under different prediction time domains at a high speed of 2m / s.

[0061] Figure 12 This is the lateral error diagram under different prediction time domains at a high speed of 2m / s.

[0062] Figure 13(a) shows the change of heading angle with time at a high speed of 2 m / s.

[0063] Figure 13(b) shows the change of heading error over time at a high speed of 2 m / s.

[0064] Figure 14 This is a graph showing the change of yaw angular velocity with time at a high speed of 2m / s.

[0065] Figure 15(a) shows the change of the front wheel angle with time under different prediction time domains at a high speed of 2 m / s.

[0066] Figure 15(b) shows the change of the rear wheel angle with time under different prediction time domains at a high speed of 2 m / s. DETAILED DESCRIPTION

[0067] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments and the accompanying drawings. Here, the exemplary embodiments of the present invention and their descriptions are used to explain the present invention, but are not intended to limit the present invention.

[0068] It should also be noted that, in order to avoid obscuring the present invention due to unnecessary details, the accompanying drawings only show structures and / or processing steps closely related to the solutions according to the present invention, while other details that are not closely related to the present invention are omitted.

[0069] It should be emphasized that the term "include / comprises" when used herein refers to the existence of features, elements, steps or components, but does not exclude the existence or addition of one or more other features, elements, steps or components.

[0070] In fields such as logistics and sorting, four-wheel independently driven automatic guided robots have become core equipment due to their high load capacity and high maneuverability, and their trajectory tracking accuracy is extremely important. The existing fixed-time domain model predictive control (MPC) algorithm has problems with error accumulation and insufficient dynamic adaptability when dealing with curved paths, making it difficult to meet the needs of high-precision trajectory tracking under complex working conditions. To this end, the present invention aims to solve the problems of insufficient trajectory tracking accuracy of four-wheel steering robots on curved paths and poor adaptability of traditional fixed-time domain MPC algorithms. An adaptive time-domain MPC algorithm based on a fuzzy control algorithm is proposed, which improves the tracking accuracy and operational stability of the robot on curved paths through real-time evaluation of the path curvature characteristics and dynamic adjustment of the prediction time domain.

[0071] Specifically, the present invention provides a four-wheel steering robot control method, such as Figure 1 As shown, the method includes the following steps S101 to S105:

[0072] Step S101: Read the position coordinates of the four-wheel steering robot when it is running on the target trajectory according to the set sampling period, calculate the curvature gradient of the current position, and divide the curvature gradient by the maximum curvature gradient to obtain the curvature dynamic coefficient.

[0073] Step S102: Determine the preview length on the target trajectory according to the current motion speed and current position according to the set rules, calculate the average curvature within the preview length range, and divide the average curvature by the maximum curvature allowed by the system to obtain the path curvature index.

[0074] Step S103: Using the curvature dynamic coefficient and the path curvature index as the input and output of the fuzzy control algorithm to predict the prediction time domain for future state prediction, so that the larger the curvature dynamic coefficient and the path curvature index are, the longer the prediction time domain is. The input and output of the fuzzy control algorithm both use triangular membership functions; the curvature dynamic coefficient gain is introduced, and the control time domain is calculated based on the prediction time domain.

[0075] Step S104: Construct a controller to discretize the pre-established continuous state vehicle control model for the four-wheel steering robot, establish multiple constraints in the control time domain, and form a mapping relationship between the control increment and the motion state of the four-wheel steering robot; the vehicle control model includes a kinematic model, a lateral dynamics model, and a longitudinal dynamics model.

[0076] Step S105: Use a quadratic programming solver to solve the optimal control sequence in the control time domain, execute the instruction corresponding to the first step control increment in the optimal control sequence, and update the motion state of the four-wheel steering robot through a feedback correction mechanism to achieve continuous control.

[0077] Before step S101, the method further includes steps S1011 and S1012:

[0078] Step S1011: In response to the received movement instruction, the initial position of the four-wheel steering robot is acquired; the movement instruction includes the end position.

[0079] Step S1012: constructing a moving path from the initial position to the end position as a target trajectory according to a preset path planning algorithm.

[0080] In this embodiment, the path planning algorithms used may include: Dijkstra algorithm, which is suitable for static environments and can globally search for the shortest path to ensure that the robot reaches the target location. RRT (Rapidly-exploring Random Tree), which is suitable for dynamic and complex environments, can quickly explore feasible paths, and is suitable for emergencies in logistics scenarios. The artificial potential field method uses a virtual potential field to guide the robot to avoid obstacles and move towards the target, but may fall into a local minimum. The graph search-based algorithm is suitable for real-time path updates in dynamic environments and can cope with dynamic changes in logistics scenarios. Deep reinforcement learning algorithms, such as deep Q networks (DQN), allow robots to autonomously learn optimal path strategies through training, and are suitable for long-term logistics robots. These algorithms have their own characteristics, and the appropriate algorithm can be selected according to the specific needs of the logistics scenario.

[0081] In this embodiment, the target trajectory is preset and can be planned based on the end position determined by the movement instruction, or can be directly carried in the movement instruction.

[0082] In steps S101 to S103, the prediction horizon and control horizon are adjusted by analyzing the curvature state corresponding to the four-wheel steering robot's current position in the target trajectory. The prediction horizon and control horizon are the core control variables of the model predictive control system. Their values ​​directly determine the trajectory tracking performance. The rational selection of these two horizon parameters requires a trade-off analysis between control accuracy and computational efficiency. While keeping other control parameters constant, increasing the prediction horizon enhances the system's ability to predict the state of the forward path and improves closed-loop stability by increasing the state observation window during the rolling optimization process. However, an excessively long prediction horizon significantly increases the dimensionality of the optimization problem, leading not only to increased computational complexity but also to the overweighting of long-term errors in the objective function, potentially affecting the optimality of the current control sequence. Shortening the prediction horizon effectively reduces computational resource consumption and improves the system's dynamic response efficiency. However, the limited prediction horizon impairs the controller's ability to predict the vehicle's future motion trends. In particular, when physical constraints exist, steering mechanism hysteresis can lead to accumulated trajectory deviations, ultimately resulting in tracking failure. From the above analysis, it can be seen that the determination of the prediction time domain has a great impact on the accuracy of trajectory tracking.

[0083] First, define the curvature dynamic coefficient, and the calculation formula is:

[0084]

[0085] Among them, C g represents the curvature gradient, k i is the curvature of the current position, k i-1 Indicates the curvature of the position at the previous moment. The current position coordinate is (x i ,y i ), the position coordinate at the previous moment is (x i-1 ,y i-1 ).

[0086] The calculation formula of the curvature dynamic coefficient is:

[0087]

[0088] Among them, C gn represents the curvature dynamic coefficient, C gmax Indicates the maximum value of the curvature gradient.

[0089] Define the preview length, which represents the path the robot will soon travel. The length of the preview length is determined by the robot's speed. Because the robot's trajectory will change at different speeds, the preview length must be adjusted accordingly to ensure the accuracy of the path curvature evaluation metric. Higher speeds increase the preview length. However, when the robot approaches the end of the trajectory, the preview length may exceed the trajectory range. In this case, the end of the preview length becomes the end of the trajectory.

[0090] In some embodiments, the preview length is determined on the target trajectory according to the current motion speed and current position according to a set rule, and the expression is:

[0091]

[0092] Among them: min is the minimum preview length, l max The maximum preview length, in m; a l and b l is a constant; v min is the minimum value of linear velocity, v max It is the maximum value of linear velocity, in m / s.

[0093] A path curvature index is defined, which can more accurately reflect the curvature of the upcoming path. When it is large, it means that the robot is about to enter a path with a large curvature. The robot needs to change the prediction time domain to cope with the curvature. The calculation formula of the path curvature index is:

[0094]

[0095] Among them, C pn represents the path curvature index, C p represents the forward mean curvature within the preview length, κ k represents the curvature of the kth sampling point, n represents the number of sampling points, κ kmax Indicates the maximum curvature allowed by the system.

[0096] When the robot's ideal trajectory is more curved, it is necessary to prepare for the turn earlier and adjust the current driving direction to better track the upcoming curve. To a certain extent, the prediction time domain N is increased. p The four-wheel steering robot can take the curvature of the future trajectory into account in advance and generate more accurate control instructions when entering a curve. Under conditions where the path curvature characteristics are significantly enhanced, the prediction time domain parameter N is dynamically adjusted. pThis approach not only maintains the trajectory fit of the current pose within a reasonable range, but also improves the robustness of tracking complex curvature paths and prevents motion instability. When the path curvature feature is small, indicating that the tracking path is relatively straight, reducing the prediction time domain can enhance the sensitivity of local path tracking while reducing the computational complexity of the optimization problem, effectively balancing the contradiction between trajectory tracking performance and computational resource consumption.

[0097] When other parameters remain unchanged, increasing the control time domain N c The value of usually improves the control accuracy of trajectory tracking, but when N c When it is too large, it will bring about a large amount of calculation, resulting in a decrease in the solution speed of the trajectory tracking controller and affecting the real-time performance of the robot control system. c When the value of is small, in order to minimize the average error of the robot in the prediction time domain, the control action solved by the control method may reduce the accuracy of the current path tracking. Therefore, when the path is relatively curved, increase N c The value of can enhance the robot's control accuracy on curved paths. When the path is less curved, reduce N c The value of can reduce the computing burden of the host and thus improve the real-time response capability of the system.

[0098] Therefore, the present invention uses the curvature dynamic coefficient and the path curvature index to measure the curvature state of the four-wheel steering robot at the current position on the target path, introduces the fuzzy control algorithm to determine the prediction time domain and further calculates the control time domain.

[0099] The present invention adopts a dual-input single-output fuzzy control algorithm. The input variables are the curvature dynamic index and the path curvature index. The triangular membership function is used to divide the curvature dynamic index and the path curvature index into three fuzzy subsets: low, medium and high. The output is the prediction time domain, which is divided into three fuzzy subsets: short, medium and long using the triangular membership function.

[0100] Fuzzy rule design follows the principle that the larger the curvature dynamic index and path curvature index, the longer the prediction horizon. Nine fuzzy rules were designed. Defuzzification was performed using the centroid method. The centroid of the synthesized fuzzy set was calculated to obtain an accurate prediction horizon value, and the control horizon was dynamically adjusted based on the prediction horizon.

[0101] Through the fuzzy control algorithm, the prediction time domain can be changed in real time through the curvature dynamic index and the path curvature index to cope with paths of different degrees of curvature. The following figures are the membership function diagrams of the input parameters and output parameters respectively. The present invention adopts a triangular membership function, which has a smoother shape and avoids the instability problem caused by overly complex shapes. Overly complex membership functions may cause the system to react too sensitively, while triangular membership functions provide a relatively smooth response and have better robustness. Among them, VS, S, MS, M, ML, L and VL represent extremely short to extremely long, and VL, L, M, H to VH represent extremely small to extremely large. Table 1 is the fuzzy rules, and Table 2 is the domain and quantization factor of each variable. Figure 2(a) to Figure 2(c) is the input-output membership function of the fuzzy control algorithm, Figure 3 This is the input-output response surface diagram of the fuzzy control algorithm:

[0102] Table 1

[0103]

[0104] Table 2

[0105]

[0106] In some embodiments, a curvature dynamic coefficient gain is introduced, and the control time domain is calculated based on the prediction time domain. The calculation formula is:

[0107] N c =round[k m N p (1+k n C gn )];

[0108] Among them, k m represents the time domain weight coefficient, which ranges from 0 to 0.5; k n Indicates the gain coefficient, ranging from 0 to 1; C gn represents the curvature dynamic coefficient; N p Represents the prediction time domain; N c Indicates the control time domain.

[0109] N p Directly determine N c The size of N p When N increases, c The synchronous increase causes the controller to incorporate more future state constraints in each sampling period, which is equivalent to achieving more intensive strategy planning at a fixed update frequency, thereby achieving a trajectory tracking effect similar to that of increasing the control frequency.

[0110] In other embodiments, the control frequency may be increased according to a set rule for situations where the path curvature is large within the preview length range. For example, multiple ranges of values ​​are set for the average curvature of the path within the preview length range, with a corresponding control frequency set for each range, such that the higher the average curvature, the higher the control frequency.

[0111] In step S104, the kinematic characteristics of the four-wheel steering robot and its lateral and longitudinal dynamic characteristics are mainly analyzed. These three characteristics are mathematically analyzed and a model is constructed to form a continuous-state vehicle control model. This model ignores the vertical movement of the vehicle (such as up and down bumps) and only focuses on the lateral movement and yaw movement in the two-dimensional plane. A discrete state space equation is established, in which the state vectors are lateral displacement, linear velocity, heading angle, and yaw angular velocity, and the control vectors are the front wheel angle and the rear wheel angle. A state transfer matrix is ​​constructed, which contains information such as vehicle parameters and control cycle, reflecting the impact of the current state on the next state; a control input matrix is ​​constructed to reflect the impact of the front and rear wheel steering angles on the next state. The product of the current state and the state transfer matrix and the sum of the control input matrix and the current control steering control amount are the final result equation.

[0112] In some embodiments, the method uses a fourth-order Runge-Kutta method to discretize the vehicle control model, including steps S201 to S205:

[0113] Step S201: Calculate the first state change rate at the initial moment based on the current state and control input.

[0114] Step S202: Calculate the state after half the control period based on the first state change rate, and calculate the second state change rate at this time.

[0115] Step S203: recalculating the state after half the control time domain according to the second state change rate, and calculating the third state change rate at this time.

[0116] Step S204: inferring the state after the entire control time domain according to the third state change rate, and calculating the fourth state change rate at this time.

[0117] Step S205: Averaging the first state change rate, the second state change rate, the third state change rate, and the fourth state change rate according to preset weights to obtain an average change rate, and using the average change rate to calculate the state at the next sampling point.

[0118] When designing a model predictive controller, the setting of constraints is directly related to the stability, safety, and control effect of the robot control system. Through reasonable constraint design, the controller can ensure that its control behavior meets the needs of the actual environment. In order to ensure the smooth operation of the four-wheel steering robot and that the turning angles of the front and rear wheels meet physical limitations, it is necessary to add corresponding constraints. In some embodiments, the constraints include the range constraints of the trajectory tracking error term, the heading angle error term, the yaw angular velocity error term, the control input smoothing term, and the rear wheel steering angle smoothing constraint term. The constraints also introduce a relaxation factor to ensure the feasibility of the solution.

[0119] In step S105, within the control time domain, a quadratic programming problem is constructed with the motion state (such as position, velocity, acceleration, steering angle, etc.) and control increment (such as wheel speed change, steering angle change, etc.) of the four-wheel steering robot as variables. The objective function is usually a weighted sum of indicators such as the deviation between the robot's motion state and the target trajectory and the size of the control increment, aiming to minimize the energy consumption caused by these deviations and control increments. The constraints in step S104 are introduced for solution, and a quadratic programming solver can be used, such as MATLAB's quadprog function or the open source OSQP (Operator Splitting Quadratic Program) solver. The optimal control sequence that minimizes the objective function within the control time domain is obtained. This sequence contains the optimal control increment corresponding to each moment, which is used to guide the movement of the four-wheel steering robot. From the optimal control sequence obtained, the instruction execution corresponding to the first control increment is extracted. The actual motion state of the four-wheel steering robot after executing the control instruction, including position, speed, direction and other information, is collected in real time through sensors (such as encoders, gyroscopes, and visual sensors) to update the system state and implement feedback correction for continuous control.

[0120] On the other hand, the present invention also provides a four-wheel steering robot control device, comprising a processor, a memory, and a computer program / instructions stored in the memory, wherein the processor is used to execute the computer program / instructions, and when the computer program / instructions are executed, the device implements the steps of the above method.

[0121] On the other hand, the present invention further provides a computer-readable storage medium having a computer program / instruction stored thereon, wherein the computer program / instruction implements the steps of the above method when executed by a processor.

[0122] On the other hand, the present invention also provides a computer program product, comprising a computer program / instruction, which implements the steps of the above method when executed by a processor.

[0123] The present invention will be described below in conjunction with a specific embodiment:

[0124] This embodiment provides a control method for a four-wheel steering robot. A four-wheel steering robot is a device having a moving device, a working device, and a control device, which can move and work autonomously within a certain range, such as a bin handling robot or a package sorting robot. This embodiment uses the method applied to the control device of a four-wheel steering robot as an example to illustrate. Figure 4 The specific steps are as follows:

[0125] S31: Control the four-wheel steering robot to move along the reference trajectory. During the movement, the coordinate information of discrete points is sampled according to a fixed period to construct a path curvature evaluation index.

[0126] S32: A dual-input, single-output fuzzy control algorithm is used. The input variables are the curvature dynamic index and the path curvature index, and the output is the predicted time domain. The centroid method is used for defuzzification. The centroid of the synthesized fuzzy set is calculated to obtain the precise predicted time domain value. The control time domain is adjusted dynamically based on the predicted time domain.

[0127] S33: Establish kinematic, lateral and longitudinal control models for a four-wheel steering robot.

[0128] S34: Build an MPC controller based on the control model of the four-wheel steering robot, establish discrete state-space equations, construct a multi-objective optimization objective function, and set constraints. Within each control cycle, a quadratic programming solver is used to solve the optimal control sequence, executing only the first control instruction and updating the system state through a feedback correction mechanism.

[0129] The method includes the following steps S41 to S44:

[0130] Step S41: construct a path curvature evaluation index and control the robot to move along the reference trajectory. During the movement, the robot reads the coordinates (x i ,y i )、(x i-1 ,y i-1 ). This embodiment uses the Euclidean distance to approximate the calculation of Δs i .

[0131]

[0132]

[0133] C g represents the curvature gradient, k iis the curvature of the current position, k i-1 Indicates the curvature of the position at the previous moment.

[0134] C g The larger the gradient, the faster the curvature of the path changes (for example, when a straight road suddenly turns sharply, the gradient increases significantly).

[0135]

[0136] Among them C gn represents the curvature dynamic coefficient, C gmax Indicates the maximum value of the curvature gradient.

[0137] The curvature of the future path affects the robot's trajectory tracking accuracy, and the robot needs to adjust its prediction time domain based on the future path conditions. Therefore, this embodiment establishes an indicator that can reflect the curvature of the future path and names it the path curvature index.

[0138] First, it is necessary to determine the specific size of the future path. Therefore, the present invention defines a preview length, which represents a section of the path that the robot is about to take. The size of the preview length is determined by the movement speed of the robot. Because the robot travels at different speeds, the trajectory it is about to travel in the same time will also change. It is necessary to change the preview length according to the speed to ensure the accuracy of the path curvature evaluation index. The higher the travel speed, the longer the preview length. When the robot approaches the end point of the entire trajectory, the preview length may exceed the trajectory range. At this time, the end point of the preview length is the end point of the trajectory. Based on the above analysis, the following calculation formula is proposed to calculate the preview length:

[0139]

[0140] Among them: min is the minimum preview length, l max The maximum preview length, in m; a l , b l is a constant; v min is the minimum value of linear velocity, v max It is the maximum value of linear velocity, in m / s.

[0141] Define the forward mean curvature, which represents the mean value of the curvature within the preview length, and the expression is:

[0142]

[0143] Where C p represents the forward mean curvature, κ k represents the curvature of the kth point, and n represents the number of points.

[0144]

[0145] Where C pn represents the path curvature index, κ kmax Indicates the maximum curvature allowed by the system.

[0146] Through the above analysis, the path curvature index can more accurately reflect the curvature of the upcoming path. When it is larger, it means that the robot is about to enter a path with a larger curvature, and the robot needs to change the prediction time domain to cope with the curvature.

[0147] In step S42 , this embodiment uses the curvature dynamic index and the path curvature index as input parameters of the fuzzy control algorithm, and uses the prediction time domain as the output parameter of the fuzzy control algorithm.

[0148] Through the fuzzy control algorithm, the prediction time domain can be changed in real time through the curvature dynamic index and the path curvature index to cope with paths with different degrees of curvature.

[0149] Figure 2(a) to Figure 2(c) The following are membership function diagrams for the input and output parameters, respectively. This embodiment uses a triangular membership function, which has a smoother shape and avoids the instability caused by overly complex shapes. Overly complex membership functions may cause the system to react too sensitively, while triangular membership functions provide a smoother response and better robustness. As shown in Table 1 above, VS to VL represents the shortest to the longest, and VL to VH represents the smallest to the largest. Figure 2(a) to Figure 2(c) It is the input and output membership function of the fuzzy control algorithm, as shown in Table 2 above, which records the domain and quantization factor of each variable.

[0150] Fuzzy rules are a crucial component of designing fuzzy control algorithm systems. Based on fuzzy logic, they are used to map fuzzy inputs to fuzzy outputs. They are typically expressed in an "if-then" form, describing the behavior of a system by defining fuzzy sets of input variables and the relationships between these fuzzy sets.

[0151] Fuzzy rules allow the system to make decisions under uncertainty or fuzzy information, thus being able to handle complex, nonlinear problems. By combining multiple fuzzy rules, the fuzzy control algorithm can adaptively adjust the output according to the actual situation.

[0152] Based on the concept of variable time domain, the fuzzy rules of this invention adhere to the following principle: smaller curvature dynamic index and path curvature index indicate that the current path curvature is not changing much and the future path is relatively straight, thus shortening the prediction time domain. Larger curvature dynamic index and path curvature index indicate a longer prediction time domain. The fuzzy rules designed by this invention are shown in Table 2 above.

[0153] The response surface between fuzzy input and output established according to the above rules is as follows: Figure 3 As shown in Figure 1, defuzzification is the process of converting the fuzzy output value obtained by fuzzy reasoning into an accurate control signal. Since the output of the fuzzy control algorithm is in the form of a fuzzy set, defuzzification must be performed to obtain the actual control command. Common defuzzification methods include the maximum membership method, the weighted average method, and the center of gravity method. Among them, the center of gravity method determines the final output by calculating the center of gravity position of the area under the fuzzy output curve. It can usually more accurately reflect the impact of the entire fuzzy output and meets the design requirements of the present invention. Therefore, the present invention selects the center of gravity method for defuzzification.

[0154] After defuzzification, the value of the prediction time domain can be obtained. Since the prediction time domain has a certain correlation with the control time domain, the size of the control time domain needs to be adjusted according to the prediction time domain. The expression is as follows:

[0155] N c =round[k m N p (1+k n C gn )];

[0156] In this formula, k m Indicates the time domain weight coefficient, its value range is 0 to 0.5, k n Indicates the gain coefficient, ranging from 0 to 1.

[0157] Step S43 constructs a control model for the four-wheel steering robot. This mathematical analysis and model construction allows for a more effective understanding and control of the robot's dynamic behavior, improving its trajectory tracking accuracy and operational stability. This embodiment establishes kinematic, lateral, and longitudinal control models for the four-wheel steering robot.

[0158] Establishing the robot kinematic model: Four-wheel steering is the most flexible mobility solution for a four-wheel robot. All four wheels can be driven and steered independently, requiring the simultaneous control of eight different motors. In this case, the robot's rotation center can freely change within the range of the distance between the wheel axles on both sides of the vehicle body. Figure 5 As shown in the figure, O represents the center of rotation, K represents the lateral distance between the inside tire of the four-wheel steering robot and the center of rotation when turning, S represents the longitudinal distance between the four-wheel steering robot's front wheel and the center of rotation, L represents the front and rear wheel wheelbase, G represents the four-wheel steering robot's center of mass, r1 to r4 represent the turning radius of each wheel, B represents the spacing between the two front wheels or the two rear wheels, a represents the longitudinal distance from the front wheel to G, b represents the longitudinal distance from the rear wheel to G, δ1 to δ4 represent the steering angle of each wheel, and v1 to v4 represent the speed of each wheel. Through geometric derivation, the turning radius of the four wheels and the four-wheel steering robot's center of mass can be calculated, and ultimately the wheel speeds of the four wheels can be obtained.

[0159] The relationship between the reverse rotation angles of the left front and left rear wheels:

[0160]

[0161] The expression of S is:

[0162]

[0163] The expression of K is:

[0164]

[0165] The turning radius of the four wheels is expressed as follows:

[0166]

[0167] The turning radius of the vehicle's center of mass is expressed as:

[0168]

[0169] The speeds of the four wheels are:

[0170]

[0171]

[0172] Where v is the velocity of the robot's center of mass.

[0173] Robot lateral dynamics model: When a four-wheel steering robot is driving normally, it can be assumed that the tire's side slip characteristics are in a linear operating range, and the tire's side slip force and side slip angle are approximately proportional:

[0174] F yf =-C αf α f ;

[0175] F yr =-C ar α r ;

[0176] Where, F yf is the deflection force of the front tire, F yr is the deflection force of the rear tire, α f is the sideslip angle of the front tire, α r Indicates the side slip angle of the rear tire, C αf represents the equivalent cornering stiffness of the front tire, C ar Indicates the equivalent cornering stiffness of the rear tire.

[0177] The lateral force at the center of mass of the robot is:

[0178]

[0179] Where m represents the mass of the robot, represents the acceleration of the robot's center of mass, u c represents the longitudinal velocity of the robot, Indicates the robot's yaw angular velocity.

[0180] The yaw moment at the center of mass of the robot is:

[0181]

[0182] Where, I z represents the moment of inertia at the center of mass of the robot, Indicates the robot's yaw angular acceleration.

[0183] The construction of the four-wheel steering model is based on the balance of the net external torque around the z-axis and the net external force along the y-axis. Both the front and rear wheels participate in the steering. The net external torque around the z-axis and the net external force along the y-axis are:

[0184] ∑M z,4WS =∑M z,FWS +ΔM z ;

[0185] ∑F y,4WS =ΣF y,FWS +ΔF y ;

[0186] Where, ΔM z is the additional torque, M z,4WS represents the net external moment about the z-axis, ΔF y Indicates the additional lateral force associated with the rear wheels of the vehicle, F y,4WS The net external force along the y-axis and the front and rear wheel slip angle formulas are as follows:

[0187]

[0188] Where, δ f represents the front wheel turning angle, δ r Indicates the rear wheel turning angle.

[0189] In four-wheel steering mode, ΔF y and ΔM z It is expressed by the following formula:

[0190]

[0191] The two-degree-of-freedom vehicle dynamics model of the robot's four-wheel steering is shown as follows:

[0192]

[0193] in:

[0194]

[0195] Where, Indicates the heading angle of the robot, P y represents the lateral displacement of the robot, represents the robot's heading angular velocity, represents the equivalent cornering stiffness of the robot’s front tire, represents the equivalent cornering stiffness of the robot's rear tire, and the system state is The control quantity is U=[δ f ,δ r ] T As for the model output, considering that the robot trajectory tracking is mainly evaluated by the size of the lateral deviation and the heading deviation in the subsequent analysis, the lateral position and the heading angle are selected as the output of the model.

[0196] In this embodiment, the robot's motion is described in the vehicle coordinate system. The robot's coordinate position needs to be converted to the earth coordinate system using the following formula:

[0197]

[0198] Robot longitudinal dynamics model: Based on Newton's second law, the longitudinal dynamics model of the four-wheel steering robot in motion can be analyzed as follows:

[0199] F Dem =F a +F G +F R +F D ;

[0200] F a =ma x ;

[0201] F R =f R mg;

[0202] F G =i G mg;

[0203]

[0204] Where, F Dem Indicates the total travel resistance of the robot; F a Indicates the resistance caused by the robot's acceleration; F G Indicates the resistance of the slope; F R Indicates rolling resistance; FD represents the air resistance of the robot, m represents the mass of the four-wheeled robot; a x represents the longitudinal acceleration of the robot; f R represents the friction coefficient of the road surface; g is the acceleration due to gravity; i G Indicates the road slope value; A indicates the robot's frontal area; C D Indicates the air coefficient; ρ a represents the air density; u represents the longitudinal speed of the robot.

[0205] Step S44: Establishing an MPC controller. First, the vehicle control model in the continuous state needs to be discretized. The fourth-order Runge-Kutta method is used for discretization:

[0206] x(k+1)=A4x(k)+B4u(k);

[0207]

[0208] in, u=[δ f ,δ r ].

[0209] Introduce an integral link to eliminate static error and define the control increment:

[0210] Δu(k)=u(k)-u(k-1);

[0211] The system equation is:

[0212] x(k+1)=A4x(k)+B4u(k-1)+B4Δu(k);

[0213] Define the augmented state vector:

[0214]

[0215] The incremental model is:

[0216]

[0217] in,

[0218] The system output is:

[0219]

[0220] Where C = [I 0].

[0221] In order to avoid the possibility of no solution during the solution process, a relaxation factor is added to the objective function. The objective function of the four-wheel steering trajectory tracking controller is as follows:

[0222] J=D1+D2+D3+D4+D5+ρε 2 ;

[0223]

[0224] In the above formula, D1 is the trajectory tracking error term, D2 is the heading error term, D3 is the yaw rate error term, D4 is the control input smoothing term, D5 is the rear wheel steering angle smoothing term, Q is the weight function of the lateral following error, P is the weight function of the heading angle, R is the weight function of the control output increment, and S is the weight function of the yaw angle. v is the weight coefficient, ε is the relaxation factor, Np represents the prediction time domain, and Nc represents the control time domain.

[0225] When designing a model predictive controller, the constraints directly impact the stability, safety, and control effectiveness of the robot's control system. By properly designing constraints, the controller can ensure that its control behavior meets the requirements of the actual environment. To ensure smooth operation of the four-wheel steering robot and that the front and rear wheel angles meet physical constraints, appropriate constraints must be added. The steering tracking controller must solve the following problems during each control cycle:

[0226] min Δu,ε J(Δu,ε);

[0227] Lateral displacement error constraint:

[0228] |P y (k+i|k)-P y，ref (k+i|k)|≤0.1m;

[0229] Yaw rate constraint:

[0230] |φ′(k+i|k)|≤1rad / s;

[0231] Front and rear wheel coordination constraints:

[0232]

[0233] The control quantity of this model is the front and rear wheel angles, with a maximum value set to 0.4 rad. Considering the operating parameters of the steering motor, the maximum value of the angle increment is set to 0.3 rad / s to ensure that the robot's steering action is within the tolerance range of the mechanism and steering motor.

[0234] In each control cycle, the quadratic planner is used to solve the sequence containing the control input increment and the relaxation factor:

[0235] Δu * (k)=[Δu * (k|k),Δu *(k+1|k),.....,Δu * (k+N c -1|k)] T ;

[0236] Normally, the first number of the control sequence obtained in each cycle is used as the actual control input and input into the system to obtain:

[0237] u(k)=u(k-1)+Δu * (k|k);

[0238] After the cycle is completed, it will enter the next control cycle until the model prediction, rolling optimization and feedback correction are completed. Figure 4 shown.

[0239] Corresponding to the above method, the present invention also provides an apparatus / system, which includes a computer device, the computer device includes a processor and a memory, the memory stores computer instructions, and the processor is used to execute the computer instructions stored in the memory. When the computer instructions are executed by the processor, the apparatus / system implements the steps of the method described above.

[0240] An embodiment of the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the aforementioned edge computing server deployment method. The computer-readable storage medium may be a tangible storage medium, such as a random access memory (RAM), a memory, a read-only memory (ROM), an electrically programmable ROM, an electrically erasable programmable ROM, a register, a floppy disk, a hard disk, a removable storage disk, a CD-ROM, or any other form of storage medium known in the art.

[0241] To test the control effect of the adaptive time-domain MPC algorithm provided in this embodiment on the trajectory tracking of the robot on a curved path, simulation experiments were conducted with the robot at low and high speeds. In order to compare the performance difference with the traditional fixed time-domain MPC, it was selected as the baseline method for the simulation comparison experiment.

[0242] The ideal trajectory in this case is a double lane change. When the four-wheel steering robot encounters a fixed obstacle, it needs to bypass the obstacle and return to the original trajectory. For example, if the robot is moving normally and there is a shelf in the forward position, its original walking trajectory is a straight line, but now it needs to change the original path, bypass the shelf, and return to the original path to drive in a straight line.

[0243] Comparison between adaptive time domain and fixed time domain in low-speed state: When the robot speed is set to 0.5m / s, the sampling period is 0.05s, and the prediction time domain is set to 15, 25, 35 and variable time domain respectively. Simulations are performed on these four cases respectively to compare the tracking effects under different prediction time domains.

[0244] like Figure 6 The following figure shows the trajectory tracking at low speeds using different prediction time domains. Both the fixed-domain MPC algorithm and the variable-domain MPC algorithm achieve good tracking results at low speeds, with the robot's actual trajectory essentially aligning with the ideal trajectory. In the early stages of a straight path, both the different prediction time domains and the adaptive time domain performed well. However, when cornering, the optimized algorithm adheres more closely to the ideal trajectory than the fixed-domain algorithm.

[0245] like Figure 7 Figure 2 shows the lateral error at low speeds under different prediction time domains. The variation of lateral displacement error over time demonstrates that the variable-time-domain MPC algorithm outperforms the fixed-time-domain MPC algorithm, stabilizing more quickly when entering a curve. Furthermore, the maximum lateral displacement error for the variable-time-domain MPC algorithm is relatively small. The maximum lateral errors for the three prediction time domains are 6.5cm, 5.8cm, and 5cm, respectively. However, the adaptive time-domain MPC algorithm limits the maximum lateral error to 4.5cm, improving the robot's trajectory tracking accuracy.

[0246] Figures 8(a) and 8(b) show the time-varying course of the heading angle and heading error at low speed. Overall, the adaptive time-domain approach significantly reduces the heading error compared to the time-domain approach. After traversing a curved path, the optimized algorithm stabilizes faster than the time-domain MPC approach and exhibits a smaller overall error.

[0247] Figure 9 The figure shows the temporal variation of the yaw rate at low speeds. As the prediction horizon increases, the yaw rate decreases, reaching a maximum of 3.5° when using the variable horizon. Throughout the entire operation, the adaptive horizon MPC system exhibits a smaller yaw angle than the fixed-horizon MPC system, resulting in more stable vehicle driving.

[0248] Figures 10(a) and 10(b) show the temporal evolution of the front and rear wheel angles at low speeds for different prediction horizons. The adaptive prediction horizon, due to its higher trajectory tracking accuracy, yields larger maximum and larger variations in the front and rear wheel angles. The front and rear wheel angles for each prediction horizon are all within a 0.4 rad range, with no significant abrupt changes, meeting the constraints established above.

[0249] Figure 11The trajectory tracking diagrams for different prediction time domains at a high speed of 2 m / s show that the actual trajectory is significantly less consistent with the ideal trajectory than at 0.5 m / s. In the early stages of a straight path, both the different prediction time domains and the adaptive time domain performed well. However, when cornering, it is clear that the optimized algorithm is more consistent with the ideal trajectory than the fixed time domain algorithm.

[0250] Figure 12 The following figure shows the lateral error at different prediction time domains at high speeds. The time-domain MPC algorithm has a larger error at bends, while the variable-time-domain MPC algorithm has a much smaller error at bends. When the prediction time domain is 15, the maximum lateral error is 14.6cm; when the prediction time domain is 25, the maximum lateral error is 8.5cm; when the prediction time domain is 35, the maximum lateral error is 6.7cm; and the maximum lateral error of the variable-time-domain MPC is 4.6cm. Experiments show that the optimized algorithm has relatively better path tracking performance. In addition, compared to the time-domain MPC algorithm, the variable-time-domain MPC algorithm has a shorter stabilization time and can adapt more quickly to changes in path curvature.

[0251] Figures 13(a) and 13(b) show the time-varying course of the heading angle and heading error at high speed. The red image is the time-varying domain image. It can be seen that the heading error in the time-varying domain is significantly reduced compared to the time-domain image. After traversing a curved path, the optimized algorithm stabilizes faster than the time-domain MPC and exhibits a smaller overall error. The maximum heading error of the optimized algorithm is 2.6°.

[0252] Figure 14 The yaw rate changes with time in high-speed state. The yaw rate of adaptive time-domain MPC is smaller than that of fixed time-domain MPC. Experiments show that the tracking of adaptive time-domain MPC is more stable.

[0253] Figures 15(a) and 15(b) show the time-varying front and rear wheel turning angles at different prediction time domains under high-speed conditions. The front and rear wheel turning angles at different prediction time domains are all within the 0.4 rad range, meeting the constraints set above.

[0254] In summary, the present invention proposes an adaptive time-domain MPC algorithm to achieve dynamic performance optimization: the curvature dynamic index and the path curvature index are used to analyze the path curvature characteristics in real time, and the prediction time domain is dynamically adjusted in combination with the fuzzy control algorithm strategy. In the curved path scenario, the algorithm can plan the control sequence in advance. Compared with the traditional fixed time-domain MPC, the maximum lateral error under high curvature conditions is significantly reduced, and the trajectory tracking accuracy is improved beyond expectations. In the case of a low-curvature straight path, the system automatically reduces the prediction time domain, reduces the amount of calculation by reducing the dimension of the optimization problem, and greatly improves the real-time response efficiency. The four-wheel steering mechanism and the adaptive time-domain control form a synergistic effect, effectively suppressing the fluctuation of the yaw angular velocity, reducing the risk of vehicle body sideslip, and significantly enhancing the operating stability under complex working conditions. The algorithm comprehensively improves the control accuracy through the organic combination of dynamic time-domain adjustment and multi-objective optimization, fully meeting the application requirements of high-precision operation scenarios.

[0255] Therefore, this embodiment proposes an adaptive time-domain MPC algorithm. This algorithm analyzes path curvature characteristics using a curvature dynamic index and a path curvature index, and dynamically adjusts the prediction time domain in conjunction with a fuzzy control algorithm. Preemptive control commands are planned for high-curvature paths, reducing maximum lateral error and improving trajectory tracking accuracy compared to traditional algorithms. For low-curvature straight paths, the time domain is automatically shortened, reducing computational effort and improving real-time response efficiency. Four-wheel steering and adaptive time domain synergistically suppress yaw rate fluctuations, enhancing stability in complex operating conditions. Through dynamic time domain adjustment and multi-objective optimization, the algorithm improves control accuracy and meets the demands of high-precision operations.

[0256] It should be understood by those skilled in the art that the various exemplary components, systems and methods described in conjunction with the embodiments disclosed herein can be implemented in hardware, software or a combination of the two. Whether it is specifically performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of the present invention. When implemented in hardware, it can be, for example, an electronic circuit, an application specific integrated circuit (ASIC), appropriate firmware, a plug-in, a function card, etc. When implemented in software, the elements of the present invention are programs or code segments that are used to perform the required tasks. The program or code segment can be stored in a machine-readable medium, or transmitted on a transmission medium or a communication link via a data signal carried in a carrier.

[0257] It should be understood that the present invention is not limited to the specific configurations and processes described above and illustrated in the figures. For the sake of brevity, a detailed description of known methods is omitted. In the above embodiments, several specific steps are described and illustrated as examples. However, the method of the present invention is not limited to the specific steps described and illustrated. Those skilled in the art may make various changes, modifications, and additions, or change the order of the steps after understanding the spirit of the present invention.

[0258] In the present invention, features described and / or illustrated for one embodiment may be used in the same or similar manner in one or more other embodiments, and / or combined with or replace features of other embodiments.

[0259] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations to the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A four-wheel steering robot control method, characterized in that: The method comprises the following steps: Read the position coordinates of the four-wheel steering robot when it is running on the target trajectory according to the set sampling period, calculate the curvature gradient of the current position, and divide the curvature gradient by the maximum curvature gradient to obtain the curvature dynamic coefficient; determining a preview length on the target trajectory according to a set rule based on the current movement speed and the current position, calculating an average curvature within the preview length, and dividing the average curvature by a maximum curvature allowed by the system to obtain a path curvature index; The curvature dynamic coefficient and the path curvature index are used as inputs and outputs of a fuzzy control algorithm for predicting a prediction time domain for future states, such that the larger the curvature dynamic coefficient and the path curvature index, the longer the prediction time domain; the input and output of the fuzzy control algorithm both use triangular membership functions; the curvature dynamic coefficient gain is introduced, and the control time domain is calculated based on the prediction time domain; A controller is constructed to discretize a pre-established continuous-state vehicle control model for the four-wheel steering robot, establish multiple constraints within the control time domain, and form a mapping relationship between control increments and the motion state of the four-wheel steering robot; the vehicle control model includes a kinematic model, a lateral dynamics model, and a longitudinal dynamics model; A quadratic programming solver is used to solve the optimal control sequence in the control time domain, the instruction corresponding to the first step control increment in the optimal control sequence is executed, and the motion state of the four-wheel steering robot is updated through a feedback correction mechanism to achieve continuous control.

2. The four-wheel steering robot control method according to claim 1, characterized in that: The calculation formula of the curvature gradient is: Among them, C g represents the curvature gradient, k i is the curvature of the current position, k i-1 Indicates the curvature of the position at the previous moment. The current position coordinate is (x i ,y i ), the position coordinate at the previous moment is (x i-1 ,y i-1 ); The calculation formula of the curvature dynamic coefficient is: Among them, C gn represents the curvature dynamic coefficient, C gmax Indicates the maximum value of the curvature gradient.

3. The four-wheel steering robot control method according to claim 2, characterized in that: The preview length is determined on the target trajectory according to the current motion speed and the current position according to the set rules. The expression is: Among them: min is the minimum value of the preview length, l max is the maximum value of the preview length, in m; a l and b l is a constant; ν min is the minimum value of linear velocity, ν max is the maximum value of the linear velocity, in m / s; Then the calculation formula of the path curvature index is: Among them, C pn represents the path curvature index, C p represents the forward mean curvature within the preview length, κ k represents the curvature of the kth sampling point, n represents the number of sampling points, κ kmax Indicates the maximum curvature allowed by the system.

4. The four-wheel steering robot control method according to claim 3, characterized in that: The curvature dynamic coefficient gain is introduced, and the control time domain is calculated according to the prediction time domain. The calculation formula is: N c =round[k m N p (1+k n C gn )]; Among them, k m represents the time domain weight coefficient, which ranges from 0 to 0.5; k n Indicates the gain coefficient, ranging from 0 to 1; C gn represents the curvature dynamic coefficient; N p represents the prediction time domain; N c represents the control time domain.

5. The four-wheel steering robot control method according to claim 4, characterized in that: The method uses a fourth-order Runge-Kutta method to discretize the vehicle control model, including: Calculating a first state change rate at an initial moment based on the current state and the control input; Inferring the state after half the control time domain based on the first state change rate, and calculating the second state change rate at this time; Recalculating the state after half the control time domain based on the second state change rate, and calculating the third state change rate at this time; Inferring the state after the entire control time domain according to the third state change rate, and calculating the fourth state change rate at this time; The first state change rate, the second state change rate, the third state change rate and the fourth state change rate are averaged according to preset weights to obtain an average change rate, and the state at the next sampling point is calculated using the average change rate.

6. The four-wheel steering robot control method according to claim 5, characterized in that: The constraints include range constraints on the trajectory tracking error term, the heading angle error term, the yaw rate error term, the control input smoothing term, and the rear wheel steering angle smoothing constraint term. The constraints also introduce a relaxation factor to ensure the feasibility of the solution. The method uses the curvature dynamic coefficient and the path curvature index as inputs of the fuzzy control algorithm and outputs a prediction time domain for future state prediction, and also includes: defuzzifying the output using the center of gravity method, calculating the center of gravity of the synthesized fuzzy set, and obtaining the value of the prediction time domain.

7. The four-wheel steering robot control method according to claim 6, characterized in that: The method further comprises: In response to a received movement instruction, obtaining an initial position of the four-wheel steering robot; the movement instruction includes the end position; A moving path from the initial position to the end position is constructed as the target trajectory according to a preset path planning algorithm.

8. A four-wheel steering robot control device, comprising a processor, a memory, and a computer program / instruction stored in the memory, characterized in that: The processor is configured to execute the computer program / instructions. When the computer program / instructions are executed, the device implements the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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