A robot trajectory tracking method, device, storage medium and electronic equipment

Abstract

This application belongs to the field of robot motion control technology and discloses a robot trajectory tracking method, device, storage medium, and electronic device. First, the robot system is dynamically modeled; the current error state vector is calculated, and the dynamic equation of the error state is constructed; the error state is transformed into a three-dimensional z-space, and the dynamic equation of the error state is constructed in the three-dimensional z-space; a sliding mode surface is constructed in the three-dimensional z-space, and the equivalent phase space constraints corresponding to the sliding mode surface are calculated based on the optimization objective and constraints; a subspace is constructed according to the control strategy, and the subspace where the current state is located is determined through a search algorithm; the relative distances of the current state to all subspaces are calculated, and the optimal sliding mode surface is determined based on the relative distances; the relative relationship between the optimal sliding mode surface and the current error is calculated, and the relative relationship is input into the control law to determine the final control quantity. This method can significantly suppress robot jitter when approaching the equilibrium point, while improving computational efficiency and achieving optimal arrival at the target control point.

Description

Technical Field

[0001] This application relates to the field of robot motion control technology, and in particular to a robot trajectory tracking method, device, storage medium and electronic device. Background Technology

[0002] A robot is a system capable of autonomous movement towards a target and completing corresponding tasks under the action of a controller, based on its own state and sensor information. To achieve precise trajectory tracking, robot motion control primarily employs feedback-based control strategies, typically including PID control, linear state feedback control, nonlinear feedback control, and adaptive control, fuzzy control, and sliding mode control to address system uncertainties and external disturbances. Among these, sliding mode control has attracted considerable attention due to its advantages such as fast response and insensitivity to disturbances.

[0003] However, existing synovial control methods suffer from severe jitter when the robot approaches its balance point or tracks a smooth trajectory, causing fluctuations in the robot's output torque, increasing mechanical wear on the actuators, and affecting the lifespan of the robot's joints. Summary of the Invention

[0004] Therefore, embodiments of this application provide a robot trajectory tracking method, apparatus, storage medium, and electronic device. The tracking method proposed in this application can significantly suppress robot jitter when approaching the equilibrium point, while improving computational efficiency and achieving the goal of reaching the target control point in the optimal time.

[0005] Firstly, this application provides a robot trajectory tracking method.

[0006] This application is achieved through the following technical solution: A robot trajectory tracking method, comprising: Perform dynamic modeling of the robot system, including defining the robot system's state vector, reference trajectory vector, optimization objective, and constraints; The current error state vector is calculated based on the state vector and the reference trajectory vector, and the dynamic equation of the error state is constructed. The error state is transformed into a three-dimensional z-space, and the dynamic equation of the error state is constructed in the three-dimensional z-space. A sliding mode surface is constructed in three-dimensional z-space, and the phase space equivalent constraints corresponding to the sliding mode surface are calculated based on the optimization objective and constraints. A subspace is constructed based on the control strategy, and the subspace where the current state is located is determined through a search algorithm. Calculate the relative distances of the current state to all subspaces, and determine the optimal sliding surface based on the relative distances; Calculate the relative relationship between the optimal sliding surface and the current error, input the relative relationship into the control law, and determine the final control quantity.

[0007] In a preferred example of this application, it may further be configured to include: The final control value is fed back to the actuators of the robot joints to update the current state.

[0008] In a preferred embodiment of this application, the step of constructing the subspace according to the control strategy may be further configured as follows: In the three-dimensional z-space, determine the endpoint equation of the state trajectory generated by the control strategy; In a fixed parameter combination, the control direction mode determines three basis vectors through the state trajectory endpoint equation. These basis vectors are used to indicate the local set structure of the control strategy. For each combination of parameters, the three basis vectors span a three-dimensional subspace.

[0009] In a preferred embodiment of this application, the step of calculating the relative distances of the current state to all subspaces and determining the optimal sliding surface based on the relative distances includes: Traverse all parameter combinations in the control sequence, calculate the relative distance from the current state to each subspace, search for the optimal parameter combination that minimizes the relative distance, and construct the optimal sliding surface based on the optimal parameter combination.

[0010] In a preferred example of this application, the search for the optimal combination of parameters that minimizes the relative distance may be further configured as follows: The three-dimensional search problem is transformed into a two-dimensional search problem, and the parameter combination that minimizes the relative distance is searched based on the binary search method.

[0011] In a preferred example of this application, the method can be further configured to search for the parameter combination that minimizes the relative distance based on a binary search, including: Dimensional reduction is performed, projecting onto a two-dimensional plane. The range of r is determined by the bisection method, and the convex hull corresponding to the current r is constructed. A local search is performed within the determined r, sorted by distance, with priority given to searching for the nearest point. The positive and negative subspaces are checked. If the point is not found within the convex hull corresponding to the current r, the search range is expanded.

[0012] Secondly, this application provides a robot trajectory tracking device.

[0013] This application is achieved through the following technical solution: A robot trajectory tracking device, used to perform the robot trajectory tracking method described in the first aspect above, includes: The modeling module is used to perform dynamic modeling of the robot system, including defining the robot system's state vector, reference trajectory vector, optimization objective, and constraints; calculating the current error state vector based on the state vector and the reference trajectory vector, and constructing the dynamic equations of the error state. The dimension transformation module is used to transform the error state into a three-dimensional z-space and construct the dynamic equation of the error state in the three-dimensional z-space. The sliding surface determination module is used to construct a sliding surface in three-dimensional z-space, and calculate the phase space equivalent constraints corresponding to the sliding surface based on the optimization objective and constraint conditions; construct a subspace according to the control strategy, determine the subspace where the current state is located through a search algorithm; calculate the relative distance between the current state and all subspaces, and determine the optimal sliding surface based on the relative distance; The control quantity determination module is used to calculate the relative relationship between the optimal sliding surface and the current error, input the relative relationship into the control law, and determine the final control quantity.

[0014] In a preferred embodiment of this application, the control quantity determination module may further be configured to: The final control value is fed back to the actuators of the robot joints to update the current state.

[0015] Thirdly, this application is achieved through the following technical solution: A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of any of the robot trajectory tracking methods described above.

[0016] Fourthly, this application provides a computer-readable storage medium.

[0017] This application is achieved through the following technical solution: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the above-described robot trajectory tracking methods.

[0018] In summary, compared with the prior art, the beneficial effects of the technical solution provided in this application include at least the following: This application performs dynamic modeling of a robot system, including defining the robot system's state vector, reference trajectory vector, optimization objective, and constraints; calculating the current error state vector based on the state vector and reference trajectory vector, and constructing the dynamic equation of the error state; transforming the error state to a three-dimensional z-space, and constructing the dynamic equation of the error state in the three-dimensional z-space; constructing a sliding mode surface in the three-dimensional z-space, and calculating the phase space equivalent constraints corresponding to the sliding mode surface based on the optimization objective and constraints; constructing a subspace according to the control strategy, and determining the subspace where the current state is located through a search algorithm; calculating the relative distance of the current state from all subspaces, and determining the optimal sliding mode surface based on the relative distance; calculating the relative relationship between the optimal sliding mode surface and the current error, and inputting the relative relationship into the control law to determine the final control quantity. This application maps the tracking error under physical constraints to the three-dimensional z-space through linear transformation, which can achieve time-optimal tracking with approximately bang-bang performance and no overshoot within the high-order constraint range, while the single-cycle settlement of the sliding mode controller has high computational efficiency. In summary, the tracking method proposed in this application can significantly suppress robot jitter when approaching the equilibrium point, while improving computational efficiency and achieving the goal of reaching the target control point in the optimal time. Attached Figure Description

[0019] Figure 1 A flowchart illustrating a robot trajectory tracking method provided in an embodiment of this application; Figure 2 This is a schematic diagram of the structure of a robot trajectory tracking device provided in an embodiment of this application. Detailed Implementation

[0020] This specific embodiment is merely an explanation of this application and is not intended to limit it. After reading this specification, those skilled in the art can make modifications to this embodiment without contributing any inventive step, but such modifications are protected by patent law as long as they fall within the scope of the claims of this application.

[0021] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] Furthermore, the term "and / or" in this application is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. Additionally, the character " / " in this application, unless otherwise specified, generally indicates that the preceding and following related objects have an "or" relationship.

[0023] In this application, the terms "first," "second," etc., are used to distinguish identical or similar items with essentially the same function. It should be understood that there is no logical or temporal dependency between "first," "second," and "nth," nor are there any restrictions on quantity or execution order.

[0024] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0025] To address the aforementioned issues, this application proposes a third-order optimal control method based on one-dimensional nonlinearity. Compared to traditional tracking methods, this method can achieve time-optimal tracking with no overshoot and near-bang-bang performance within high-order constraints. It is suitable for industrial control scenarios with high real-time requirements and strict requirements on high-order constraint boundaries, and is applicable to industrial motion control equipment and servo-related high-precision and high-speed fields.

[0026] The embodiments of this application will now be described in further detail with reference to the accompanying drawings.

[0027] See Figure 1 As shown, a first exemplary embodiment of this application provides a robot trajectory tracking method, which includes: S1: Perform dynamic modeling of the robot system, including defining the robot system's state vector, reference trajectory vector, optimization objective, and constraints.

[0028] S2: Calculate the current error state vector based on the state vector and the reference trajectory vector, and construct the dynamic equation of the error state.

[0029] S3: Transform the error state into a three-dimensional z-space and construct the dynamic equation of the error state in the three-dimensional z-space.

[0030] S4: Construct a sliding surface in three-dimensional z-space, and calculate the equivalent phase space constraints corresponding to the sliding surface based on the optimization objective and constraints.

[0031] S5: Construct a subspace based on the control strategy, and determine the subspace where the current state is located through a search algorithm.

[0032] S6: Calculate the relative distances of the current state to all subspaces, and determine the optimal sliding surface based on the relative distances.

[0033] S7: Calculate the relative relationship between the optimal sliding surface and the current error, input the relative relationship into the control law, and determine the final control quantity.

[0034] In some preferred embodiments, after determining the final control value, the method further includes: S8: Feed the final control input back to the actuators of the robot joints to update the current state.

[0035] Specifically, in step S1, dynamic modeling of the robot system is performed, including defining the robot system's state vector, reference trajectory vector, optimization objective, and constraints. This process includes the following steps: First, we model the tracking problem of the robot system and define the state vector of the robot system. and reference trajectory vector State vector Represents the actual state of the robot system, reference trajectory vector This represents the ideal path or sequence of states that the robot system is expected to follow. , , Represents the state vector. Represents a first-order state vector. Represents a second-order state vector. Represents the reference trajectory vector. Represents the first-order reference trajectory vector. Represents a second-order reference trajectory vector; It should be noted that at the initial time t=0, the corresponding reference trajectory vector , Represents the set of feasible states.

[0036] The optimization objective for robot trajectory tracking in this application is expressed as: It refers to the minimum terminal time in time for the state vector x(t). This indicates the terminal time, which is the end time of the entire control process; The constraints for robot trajectory tracking in this application, also known as the terminal time tracking conditions, are expressed as follows: Among the above constraints The reference trajectory vector representing the terminal time. The state vector representing the terminal time; Meanwhile, the state vector of the robot system The following constraints must be met: in, and Let each represent the first order of the state vector at time t. The lower bound constraint and the upper bound constraint, and Let each represent the second order of the state vector at time t. The lower bound constraint and the upper bound constraint, and The third order of the state vector at time t represents the state vector at time t. The lower bound constraint and the upper bound constraint.

[0037] Specifically, in step S2, after determining the state vector and reference trajectory vector of the robot system, the update equations for the state vector and reference trajectory vector can be obtained: , , in, Let be the transfer function matrix of the system. For control vectors: , In the matrix, T represents the discretized control period.

[0038] Define the error state vector and construct the dynamic equations for the error states: The error state vector is represented as: , Based on the system's transfer function matrix, control vector, and error state vector, the dynamic equation for the error state is determined as follows: .

[0039] In actual implementation, step S3 transforms the error state into a three-dimensional z-space, and constructs the dynamic equation of the error state in the three-dimensional z-space. The relationship between the transformation matrix and the original dynamic equation and the new dynamic equation is: zi = W ⋅ yi, where zi is the state vector in z-space, W is the transformation matrix, and yi is the error state vector in y-space. By constructing yi, a dynamic system is described, and W is used to achieve the decorrelation of the state variables with respect to time T.

[0040] Specifically, it includes: The transformation matrix is ​​represented as: , The dynamic equations for the error state in z-space are as follows: , Wherein, the transfer function matrix of the system in z-space and control vector for: , .

[0041] In step S4, the sliding surface is constructed in z-space, and the equivalent phase space constraints corresponding to the sliding surface are calculated. The specific process is as follows: Based on the sliding surface constructed with velocity and acceleration constraints, the corresponding phase space equivalent constraints are calculated.

[0042] The sliding surface is represented as: , , in, , , , and All are sliding surfaces, sliding surfaces and Ensure the speed does not exceed the limit, sliding surface and Ensure that the acceleration does not exceed the limit.

[0043] Among them, the phase space equivalence constraint is: In the above formula, and This represents the lower and upper bounds of the acceleration constraint mapping onto the z-space. and This represents the lower and upper bounds of the velocity constraint mapped to the z-space. and This represents the amount of change required to reach the acceleration boundary from the current state.

[0044] Sliding surface and sliding surface Construction: In the formula, when n takes the value of 1 and 2, it corresponds to the range of the equivalent constraint boundary in the z space under the current reference signal.

[0045] This represents the distance from the current state to the upper boundary. This represents the distance from the current state to the lower boundary, used to quantify the margin of the current state relative to the constraint boundary. This refers to limiting the distance to ensure that the control actions are within a feasible range, prevent over-control, and ensure that the system always operates within the constraint boundaries. Used to control direction, when This indicates that the control direction is negative, and a negative control variable needs to be used. This indicates that the control direction is positive, and a positive control variable needs to be used in this case. This represents the number of control steps, indicating the number of steps required to move from the current state to the endpoint.

[0046] Sliding surface It is a sliding surface obtained based on Bellman optimality discrete integration. The control quantity U can be determined according to the relative relationship between the current error and the sliding surface.

[0047] Sliding surface and Construction: ; In some preferred embodiments, step S5, which involves constructing a subspace based on a control strategy and determining the subspace where the current state z resides based on a search algorithm, specifically includes: In z-space, determine the endpoint equation of the state trajectory generated by the control strategy; By using the directional pattern in the fixed parameter combination, three basis vectors are determined through the state trajectory endpoint equation. These basis vectors are used to describe the local set structure of the control strategy. For each combination of parameters, the three basis vectors span a three-dimensional subspace.

[0048] In actual implementation, the control strategy is first determined. The control strategy includes three parameters, namely the control direction mode. Number of control steps in the first stage Number of control steps in the second stage ,in , as well as .

[0049] The control quantity sequence is represented as: , Indicates that a control quantity is applied first. continued Each time step Indicates switching to control quantity continued Each time step, a total of [number] times [time steps], through [number] times After the step, the system state returns to the origin.

[0050] In z-space, the endpoint of the state trajectory generated by the above control strategy is represented as: , It can be understood as This indicates starting from the origin and passing through the control sequence. The state point reached later.

[0051] Fixed control direction mode Three basis vectors are defined to describe the local geometry of the control strategy. The three basis vectors are: , , The three basis vectors mentioned above represent In parameter combination Derivatives or differences in different directions.

[0052] .

[0053] For each parameter combination The three basis vectors span a three-dimensional subspace. : , Iterate through all possible parameter combinations Construct a complete subspace coverage: .

[0054] In some preferred embodiments, the relative distances of the current state z from all subspaces are calculated, and the optimal sliding surface is determined based on the relative distances, specifically including: Given any current state The current state is determined by performing parameter traversal, distance measurement, and optimal parameter selection. The subspace to which it belongs.

[0055] Iterate through all possible parameter combinations Calculate the current state Distance to each subspace: , Choose the parameter combination that minimizes the distance: ; The optimal sliding surface is constructed based on the parameter combination that minimizes the distance. The parsed expression is: .

[0056] In actual implementation, step S7, based on the relative relationship between the optimal sliding surface and the current error, inputs the control law to determine the final control quantity, whereby the control law is expressed as: , Saturation function Defined as: .

[0057] The final control quantity is expressed as: .

[0058] The essence of finding the parameter combination that minimizes the distance is to traverse all parameter combinations contained in all strategies under the current constraint, calculate the sliding surface in z-space, and finally determine which parameter combination subspace the current state z falls into.

[0059] In some preferred embodiments, considering It is a combination of parameters Irrelevant variables, and for a given control direction mode Vector It is always perpendicular to the (z1,z2) plane. To accelerate the solution process, the three-dimensional search problem is transformed into a two-dimensional subspace solution problem: .

[0060] In the problem of solving two-dimensional subspaces, there exists a .

[0061] Enclose the subspaces corresponding to the same r in 𝒫⁺(h,k,η) into a larger subspace, and by proving that this space is a convex hull, transform the problem of searching which subspace z is inside into the problem of solving for the point z inside the convex hull.

[0062] In some preferred embodiments, the parameter combination that minimizes the relative distance is searched based on a binary search method, including: The dimensions are simplified and projected onto a two-dimensional plane. The range of r is determined by the bisection method, and the convex hull corresponding to the current r is constructed. A local search is performed within the determined r, sorted by distance, and the nearest point is searched first. The positive and negative subspaces are checked. If the point is not found in the convex hull of the current r, the search range is expanded.

[0063] Another embodiment of this application also provides a robot trajectory tracking device for performing the above-described method, such as... Figure 2 As shown, the device includes: The modeling module is used to perform dynamic modeling of the robot system, including defining the robot system's state vector, reference trajectory vector, optimization objective, and constraints; calculating the current error state vector based on the state vector and the reference trajectory vector, and constructing the dynamic equations of the error state. The dimension transformation module is used to establish a mapping relationship zi=W⋅yi between the z-space state vector and the y-space error state vector based on the transformation matrix W, realizing the transformation of the error state from y-space to z-space. W is used to realize the decorrelation of the state variables with respect to time T. At the same time, it is used to transform the error state to the three-dimensional z-space and construct the dynamic equation of the error state in the three-dimensional z-space. The sliding surface determination module is used to construct a sliding surface in three-dimensional z-space, and calculate the phase space equivalent constraints corresponding to the sliding surface based on the optimization objective and constraint conditions; construct a subspace according to the control strategy, determine the subspace where the current state is located through a search algorithm; calculate the relative distance between the current state and all subspaces, and determine the optimal sliding surface based on the relative distance; The control quantity determination module is used to calculate the relative relationship between the optimal sliding surface and the current error, input the relative relationship into the control law, and determine the final control quantity.

[0064] In some preferred embodiments, the control quantity determination module is further configured to: The final control value is fed back to the actuators of the robot joints to update the current state.

[0065] The specific limitations of the robot trajectory tracking device provided in this embodiment can be found in the embodiment of the robot trajectory tracking method described above, and will not be repeated here. Each module in the above-described robot trajectory tracking device can be implemented entirely or partially through software, hardware, or a combination thereof. Each module can be embedded in or independent of the processor in a computer device in hardware form, or stored in the memory of a computer device in software form, so that the processor can call and execute the operations corresponding to each module.

[0066] This application provides a computer device that may include a processor, memory, network interface, and database connected via a system bus. The processor provides computing and control capabilities. The memory includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The network interface communicates with external terminals via a network connection. When the computer program is executed by the processor, it causes the processor to perform the steps of a robot trajectory tracking method as described in any of the above embodiments.

[0067] The working process, working details, and technical effects of the computer device provided in this embodiment can be found in the embodiment of a robot trajectory tracking method described above, and will not be repeated here.

[0068] This application provides a computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the steps of a robot trajectory tracking method as described in any of the above embodiments. The computer-readable storage medium refers to a data storage medium, which may include, but is not limited to, floppy disks, optical disks, hard disks, flash memory, USB flash drives, and / or memory sticks. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable devices.

[0069] The working process, working details, and technical effects of the computer-readable storage medium provided in this embodiment can be found in the embodiment of a robot trajectory tracking method described above, and will not be repeated here.

[0070] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

[0071] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0072] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is used as an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the system described in this application can be divided into different functional units or modules to complete all or part of the functions described above.

Claims

1. A robot trajectory tracking method, characterized in that, The method includes: Perform dynamic modeling of the robot system, including defining the robot system's state vector, reference trajectory vector, optimization objective, and constraints; The current error state vector is calculated based on the state vector and the reference trajectory vector, and the dynamic equation of the error state is constructed. The error state is transformed into a three-dimensional z-space, and the dynamic equation of the error state is constructed in the three-dimensional z-space. A sliding mode surface is constructed in three-dimensional z-space, and the phase space equivalent constraints corresponding to the sliding mode surface are calculated based on the optimization objective and constraints. A subspace is constructed based on the control strategy, and the subspace where the current state is located is determined through a search algorithm. Calculate the relative distances of the current state to all subspaces, and determine the optimal sliding surface based on the relative distances; Calculate the relative relationship between the optimal sliding surface and the current error, input the relative relationship into the control law, and determine the final control quantity.

2. The robot trajectory tracking method according to claim 1, characterized in that, After determining the final control quantity, the following also includes: The final control value is fed back to the actuators of the robot joints to update the current state.

3. The robot trajectory tracking method according to claim 1, characterized in that, The construction of the subspace according to the control strategy includes: In the three-dimensional z-space, determine the endpoint equation of the state trajectory generated by the control strategy; In a fixed parameter combination, the control direction mode determines three basis vectors through the state trajectory endpoint equation. These basis vectors are used to indicate the local set structure of the control strategy. For each combination of parameters, the three basis vectors span a three-dimensional subspace.

4. The robot trajectory tracking method according to claim 1, characterized in that, The calculation of the relative distances between the current state and all subspaces, and the determination of the optimal sliding surface based on the relative distances, includes: Traverse all parameter combinations in the control sequence, calculate the relative distance from the current state to each subspace, search for the optimal parameter combination that minimizes the relative distance, and construct the optimal sliding surface based on the optimal parameter combination.

5. The robot trajectory tracking method according to any one of claims 1 to 4, characterized in that, The search for the optimal combination of parameters that minimizes the relative distance includes: The three-dimensional search problem is transformed into a two-dimensional search problem, and the parameter combination that minimizes the relative distance is searched based on the binary search method.

6. The robot trajectory tracking method according to claim 5, characterized in that, The parameter combination that minimizes the relative distance based on the binary search method includes: Dimensional reduction is performed, projecting onto a two-dimensional plane. The range of r is determined by the bisection method, and the convex hull corresponding to the current r is constructed. A local search is performed within the determined r, sorted by distance, with priority given to searching for the nearest point. The positive and negative subspaces are checked. If the point is not found within the convex hull corresponding to the current r, the search range is expanded.

7. A robot trajectory tracking device, characterized in that, The robot trajectory tracking device is used to perform the robot trajectory tracking method as described in any one of claims 1 to 6, and the robot trajectory tracking device includes: The modeling module is used to perform dynamic modeling of the robot system, including defining the robot system's state vector, reference trajectory vector, optimization objective, and constraints; calculating the current error state vector based on the state vector and the reference trajectory vector, and constructing the dynamic equations of the error state. The dimension transformation module is used to transform the error state into a three-dimensional z-space and construct the dynamic equation of the error state in the three-dimensional z-space. The sliding surface determination module is used to construct a sliding surface in three-dimensional z-space, and calculate the phase space equivalent constraints corresponding to the sliding surface based on the optimization objective and constraint conditions; construct a subspace according to the control strategy, determine the subspace where the current state is located through a search algorithm; calculate the relative distance between the current state and all subspaces, and determine the optimal sliding surface based on the relative distance; The control quantity determination module is used to calculate the relative relationship between the optimal sliding surface and the current error, input the relative relationship into the control law, and determine the final control quantity.

8. The robot trajectory tracking device according to claim 7, characterized in that, The control quantity determination module is also used for: The final control value is fed back to the actuators of the robot joints to update the current state.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method according to any one of claims 1 to 6.

10. A computer device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the method according to any one of claims 1 to 6.

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