Robot collaborative positioning method and system based on infinite dimensional parameter model

Abstract

The present invention provides a robot collaborative localization method and system based on an infinite-dimensional parameter model, relating to the field of intelligent robots. The method comprises: for a robot cluster consisting of multiple robots, each robot in the cluster obeys an infinite-dimensional ARX model; for each robot and at any given moment, a regression vector of the historical position state and historical control input is constructed; each robot uses the current estimate, information matrix, regression vector, and observed output at the next moment, combined with a recursive least squares algorithm, to calculate an intermediate estimate and intermediate information matrix for the next moment; each robot exchanges information with its neighbors in the current neighborhood topology and obtains an updated estimate and information matrix based on a convex combination of the neighbor information weights, thereby outputting estimates of the three-dimensional position state and control input. The present invention can address the problems of insufficient expressiveness and low single-unit estimation accuracy of traditional methods.

Description

Technical Field

[0001] The present invention relates to the field of intelligent robots, and in particular to a robot collaborative positioning method and system based on an infinite-dimensional parameter model. Background Art

[0002] As intelligent robot systems rapidly develop towards clustering and autonomy, multi-robot systems have been widely used in industrial automation, disaster relief, and intelligent logistics. As a basic link to ensure group collaboration, collaborative positioning technology faces core challenges such as dynamic environment perception, group behavior modeling, and real-time computing. In typical positioning scenarios such as mobile robot SLAM and drone formation control, the system dynamic characteristics often present the following characteristics: (1) High-dimensional parameter space: When using deep neural networks to model robot dynamics, the number of hidden layer nodes tends to infinity, resulting in an explosion of parameter dimensions; in online learning scenarios, the characteristic parameters generated by environmental interaction show a continuous growth characteristic, forming an infinite-dimensional dynamic characteristic. (2) Distributed coupling characteristics: In tasks such as collaborative handling and group search, the single-unit dynamic models of multi-robot systems are coupled to each other through communication topology, forming a joint parameter space whose dimension grows exponentially with the number of nodes. (3) Random dynamic time-varying: In unstructured environments such as field inspections and disaster relief, interference factors such as ground friction coefficient and air turbulence constitute random excitation sources with time-varying statistical characteristics. Traditional methods are mainly based on finite-dimensional parameter models, achieving positioning estimation by presetting the system state space dimensions. This makes it difficult to accurately characterize infinite-dimensional features such as the distribution of unstructured obstacles and non-Gaussian noise interference in dynamic environments. For example, the statistical characteristics of multimodal observation data generated by lidar in unstructured scenes are difficult to fully characterize using fixed-dimensional parameter models, resulting in accumulated positioning errors. Collaborative localization methods based on the SLAM framework require the pre-establishment of an environmental map parameter model. When unexpected structural changes occur in the scene, the parameter model needs to be rebuilt, making it difficult to achieve real-time adaptive control in a dynamic environment. Therefore, traditional robot collaborative localization methods face technical problems such as insufficient modeling of complex environments and poor adaptability. Summary of the Invention

[0003] The present invention aims to solve at least one of the technical problems existing in the prior art or related technology, and discloses a robot collaborative positioning method and system based on an infinite-dimensional parameter model, which can realize infinite-dimensional parameter modeling and distributed online estimation of dynamic interaction of robot clusters, solve the problems of insufficient expression ability and low single-unit estimation accuracy of traditional methods, and effectively improve the robustness and adaptability of the algorithm.

[0004] The first aspect of the present invention discloses a robot collaborative positioning method based on an infinite-dimensional parameter model, comprising: constructing a random dynamic system model with infinite parameters:

[0005] For a robot cluster consisting of n robots, each robot in the cluster obeys the following infinite-dimensional ARX model:

[0006] , ,

[0007] =0, ,

[0008] in, Indicates the Robots at all times The three-dimensional position state, Indicates the Robots at all times The three-dimensional position state of

[0009] Indicates the Robots at all times of Dimensional control input;

[0010] represents the disturbance noise term;

[0011] Represents the infinite-dimensional autoregressive coefficient matrix to be estimated for the robot cluster, which is used to characterize the linear influence weight of the robot's historical output on the current output;

[0012] It represents the exogenous input coefficient matrix to be estimated for the robot cluster, which is used to reflect the dynamic impact of the robot control instructions on the observed output;

[0013] definition = For the infinite-dimensional ARX model coefficients to be estimated, define For the The position states and control inputs of the robots at all historical moments in the past, where T represents the matrix transpose, then the infinite-dimensional ARX model is transformed into:

[0014] + ;

[0015] Construct a distributed infinite parameter adaptive estimation algorithm:

[0016] For each robot and at any given moment , construct the following historical position state With history control input The regression vector :

[0017] ;

[0018] Where T represents the matrix transpose, For any time Increasing positive integer function and ;

[0019] Each robot uses the current moment Estimated value of Information Matrix Regression vector as well as Observation output at time , combined with the recursive least squares algorithm to calculate the intermediate estimate of the next moment and the intermediate information matrix :

[0020] ,

[0021] ;

[0022] in, is a scalar representing the algorithm gain coefficient;

[0023] Each robot interacts with its neighbors in the current neighborhood topology and obtains an updated estimate based on the convex combination of neighbor information weights. and updated information matrix :

[0024]

[0025]

[0026] in, Represents the inverse of the matrix and outputs the estimated value .

[0027] According to the robot collaborative localization method based on the infinite-dimensional parameter model disclosed by the present invention, preferably, each robot in the cluster is only allowed to interact with neighbors within the neighborhood topology at the current moment.

[0028] According to the robot collaborative localization method based on the infinite-dimensional parameter model disclosed in the present invention, preferably, the calculation process of determining the neighbors in the neighborhood topology at the current moment includes:

[0029] definition The information exchange topology of the robots is undirected ,in Indicates this A collection of robots, Indicates the relationship between robots The communication relationship at the moment, Represents a robot Able to send data to robots Deliver information, Represents the weight of information exchange between robots, ,in Indicates the Robot To the Robot The weight of the information conveyed;

[0030] like , indicating a robot exist Time is a robot Neighbors, if Represents a robot Not a robot Neighbors;

[0031] robot The set of all neighbors is ,Due to the physical and communication constraints of the robot system, robots can only interact with each other locally, that is, robots are only allowed to interact with their topological neighbors. Exchange information.

[0032] According to the robot collaborative positioning method based on infinite dimensional parameter model disclosed in the present invention, preferably, The dimensional control input includes at least: motor speed data and inertial measurement unit data.

[0033] The second aspect of the present invention discloses a robot collaborative positioning system based on an infinite-dimensional parameter model, comprising: a memory for storing program instructions; a processor for calling the program instructions stored in the memory to implement a robot collaborative positioning method based on an infinite-dimensional parameter model as any of the above-mentioned technical solutions.

[0034] A third aspect of the present invention discloses a computer-readable storage medium storing a program code for implementing a robot collaborative positioning method based on an infinite-dimensional parameter model as described in any of the above technical solutions.

[0035] Compared with the prior art, the beneficial effects of the present invention include at least the following: the present invention realizes distributed adaptive estimation of random dynamic models with infinite parameters. First, by establishing an infinite-dimensional parameter model of the dynamic interaction of robot clusters, the bottleneck of modeling complex dynamics with traditional finite-dimensional models is broken through. Secondly, by designing a dynamic index function that characterizes the upper bound of the model order, and based on the local information fusion strategy, a distributed adaptive estimation algorithm suitable for random dynamic models with infinite parameters is constructed. Finally, a full incentive strategy for the parameter information matrix of large-scale systems is introduced, and the algorithm convergence theory without the assumption of data independence and stationarity is established using methods such as the dual-index martingale theory. Infinite-dimensional parameter modeling and distributed online estimation of dynamic interactions of robot clusters are realized, solving the problems of insufficient expression ability of traditional finite-dimensional models and low single-unit estimation accuracy, and effectively improving the robustness and adaptability of the algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A schematic diagram of an algorithm flow of a robot collaborative positioning method based on an infinite-dimensional parameter model according to an embodiment of the present invention is shown.

[0037] Figure 2 A schematic block diagram of a robot collaborative positioning system based on an infinite-dimensional parameter model according to an embodiment of the present invention is shown. DETAILED DESCRIPTION

[0038] In order to more clearly understand the above-mentioned objects, features and advantages of the present invention, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0039] In implementing the present invention, the applicant discovered that traditional ARX and state-space models rely on the finite-dimensional parameter assumption, reducing model complexity by truncating high-order terms or simplifying coupling relationships. However, in scenarios involving dynamic robot interactions, such simplifications can lead to model mismatch and degraded control performance. When a single robot independently estimates system model parameters, the observed data obtained is incomplete due to limited local observation capabilities, resulting in low estimation accuracy for stand-alone algorithms.

[0040] Furthermore, existing centralized robot control architectures require all robot observation data to be uploaded to a central node, which can easily lead to the following issues: Non-scalability of communication load: As the number of robots increases, network bandwidth becomes a bottleneck. Single point of failure risk: Failure of the central node can lead to global model collapse.

[0041] Existing distributed algorithms primarily target finite-dimensional parameter models. These algorithms struggle to adapt to the continuous expansion of the parameter space during online neural network learning, and they also cannot effectively handle the modeling of complex systems with long-range dependencies. Furthermore, traditional optimization theory struggles to guarantee the convergence of distributed algorithms in infinite-dimensional parameter spaces.

[0042] Based on the above considerations, the present invention discloses a robot collaborative positioning method based on an infinite-dimensional parameter model, comprising: S1, establishing a random dynamic system model with infinite parameters; S2, constructing a distributed infinite parameter adaptive estimation algorithm. Specifically:

[0043] S1, establish a random dynamic system model with infinite parameters:

[0044] Consider A multi-robot swarm system consists of robots, each robot obeys the following infinite-dimensional ARX model:

[0045] , ,

[0046] =0, ,

[0047] in Indicates the Robots at all times The three-dimensional position state, Indicates the Robots at all times of dimensional control inputs include motor speed, inertial measurement unit (IMU) data, represents the disturbance noise term, Represents the infinite-dimensional autoregressive coefficient matrix to be estimated for the robot cluster, which is used to characterize the linear influence weight of the robot's historical output on the current output. It represents the exogenous input coefficient matrix to be estimated for the robot cluster, and is used to reflect the dynamic impact of the robot control instructions on the observed output.

[0048] make = is the infinite-dimensional model coefficient to be estimated;

[0049] , Indicates the The states and control inputs of all the robots in the past, where Represents the matrix transpose symbol. Then the above infinite-dimensional ARX model is transformed into:

[0050] +

[0051] Assume this The information exchange topology of the robots is transformed from undirected topology to portrayal, among which Indicates this A collection of robots; Indicates the relationship between robots The communication relationship at the moment, Represents a robot Able to send data to robots Deliver information. Represents the weight of information exchange between robots, Indicates the Robot To the Robot The weight of the information transmitted. , indicating a robot exist Time is a robot Neighbors; otherwise, if Represents a robot Not a robot Neighbors. Remember the robot The set of all neighbors is Since the robot system is subject to physical and communication constraints, robots can only exchange local information. Only the topological domains with Exchange information.

[0052] S2, construct a distributed infinite parameter adaptive estimation algorithm:

[0053] First, for each robot , and at any given moment , construct the following regression vector of historical position state and historical control input:

[0054] ,

[0055] in represents the matrix transpose symbol, Over time Increasing positive integer function and .

[0056] Secondly, each robot Take advantage of the present moment Estimated value of ,Information Matrix , regression vector as well as Observation output at time , combined with the recursive least squares algorithm to calculate the intermediate estimate of the next moment and the intermediate information matrix :

[0057]

[0058]

[0059] in It is a scalar that represents the algorithm gain coefficient.

[0060] Finally, each robot interacts with its neighbors in the current neighborhood topology and obtains an updated estimate based on the convex combination of neighbor information weights. and updated information matrix :

[0061]

[0062]

[0063] in Represents the inverse of the matrix. Output estimate .

[0064] like Figure 1 As shown, in this embodiment, a distributed infinite parameter adaptive estimation method based on the ARX model is proposed to predict the three-dimensional position information and control input information of each robot in the robot cluster. The corresponding algorithm pseudo code of this method is as follows:

[0065] Initialization: For each robot , and at any given moment , construct the following regression vector:

[0066] , ;

[0067] in, For a given termination time, and given any initial estimate and any initial positive definite matrix ;

[0068] For all , every moment , each robot Perform the following operations:

[0069] Step 1: Adapt to the update process, which includes:

[0070]

[0071]

[0072]

[0073] Step 2: Information exchange process, including:

[0074]

[0075]

[0076] Output estimate: .

[0077] According to yet another embodiment of the present invention, an experiment to verify the effectiveness of the above-mentioned robot collaborative localization method based on the infinite-dimensional parameter model is also disclosed, including:

[0078] Calculate the estimated error:

[0079] ;

[0080] Among them, the symbol represents the Euclidean norm, Indicates the input and output tail items;

[0081] = To be estimated step unknown coefficient vector.

[0082] From the above estimation error formula, we can see that the noise term is needed The convergence properties of the estimation error can only be analyzed if certain conditions are met. For this purpose, it is assumed that the noise meets the following conditions:

[0083] Noise condition: Assume that is a martingale difference sequence, where Indicates non-decreasing Algebraic, and satisfies:

[0084] , as (almost everywhere), =o( ),in represents a deterministic increasing positive sequence that satisfies: ,symbol represents conditional expectation, symbol Indicates infinitesimal order.

[0085] Then, using the double-index martingale theorem, we can obtain the following convergence rate of the estimation error:

[0086] ,

[0087] in = represents the smallest eigenvalue of the matrix, Represents a network topology diagram The diameter of represents the sum of the input and output norms of the entire robot cluster at historical time, + represents the true coefficient tail term, is a constant greater than 0.

[0088] It can be seen that in special cases: (1) the input and output are bounded; (2) the noise is Gaussian independent white noise, the expression of the estimation error can be simplified to: Therefore, if there is no continuous incentive condition If is satisfied, the estimation error converges to 0, which verifies the effectiveness of the distributed infinite parameter adaptive estimation algorithm. It also shows that the distributed least squares algorithm under the finite-order model is a special case of the above-mentioned distributed infinite parameter adaptive estimation algorithm.

[0089] like Figure 2 As shown, according to another embodiment of the present invention, a robot collaborative positioning system 200 based on an infinite-dimensional parameter model is also disclosed, including: a memory 201 for storing program instructions; a processor 202 for calling the program instructions stored in the memory to implement the robot collaborative positioning method based on the infinite-dimensional parameter model as in the above embodiment.

[0090] According to yet another embodiment of the present invention, a computer-readable storage medium is disclosed. The computer-readable storage medium stores program code, and the program code is used to implement the robot collaborative positioning method based on the infinite-dimensional parameter model as in the above embodiment.

[0091] In summary, this paper proposes a distributed adaptive estimation method based on infinite-dimensional ARX model parameters, enabling infinite-dimensional parameter modeling and distributed online estimation for dynamic interactions in robot clusters. This method addresses the limited expressiveness and low individual estimation accuracy of traditional finite-dimensional models, avoids the high communication load and poor robustness of traditional centralized architectures, and effectively improves the algorithm's adaptability and accuracy. This method implements distributed adaptive estimation for stochastic dynamic models with infinite parameters. First, by establishing an infinite-dimensional parameter model for dynamic interactions in robot clusters, this method overcomes the bottleneck of traditional finite-dimensional models in modeling complex dynamics. Second, by designing a dynamic index function that characterizes the upper bound of the model order and using a local information fusion strategy, a distributed adaptive estimation algorithm suitable for infinite-parameter stochastic dynamic models is constructed. Finally, a sufficient excitation strategy for large-scale system parameter information matrices is introduced, and using methods such as the dual-index martingale theory, a convergence theory for the algorithm is established without data independence or stationarity assumptions. This method enables infinite-dimensional parameter modeling and distributed online estimation for dynamic interactions in robot clusters, addressing the limited expressiveness and low individual estimation accuracy of traditional finite-dimensional models and effectively improving the algorithm's robustness and adaptability.

[0092] All or part of the steps in the various methods of the above embodiments can be completed by controlling related hardware through a program. The program can be stored in a readable storage medium, and the storage medium includes read-only memory (ROM), random access memory (RAM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), one-time programmable read-only memory (OTPROM), electronically erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, magnetic disk storage, magnetic tape storage, or any other readable medium that can be used to carry or store data.

[0093] 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 of 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 robot collaborative positioning method based on an infinite-dimensional parameter model, characterized in that: include: Model a random dynamic system with infinite parameters: For a robot cluster consisting of n robots, each robot in the cluster obeys the following infinite-dimensional ARX model: ， ， =0， ， in, Indicates the Robots at all times The three-dimensional position state, Indicates the Robots at all times The three-dimensional position state of Indicates the Robots at all times of Dimensional control input; represents the disturbance noise term; Represents the infinite-dimensional autoregressive coefficient matrix to be estimated for the robot cluster, which is used to characterize the linear influence weight of the robot's historical output on the current output; It represents the exogenous input coefficient matrix to be estimated for the robot cluster, which is used to reflect the dynamic impact of the robot control instructions on the observed output; definition = For the infinite-dimensional ARX model coefficients to be estimated, define For the The position states and control inputs of the robots at all historical moments in the past, where T represents the matrix transpose, then the infinite-dimensional ARX model is transformed into: + ； Construct a distributed infinite parameter adaptive estimation algorithm: For each robot and at any given moment , construct the following historical position state With history control input The regression vector : ； Where T represents the matrix transpose, For any time Increasing positive integer function and ; Each robot uses the current moment Estimated value of Information Matrix Regression vector as well as Observation output at time , combined with the recursive least squares algorithm to calculate the intermediate estimate of the next moment and the intermediate information matrix : ， ； in, is a scalar representing the algorithm gain coefficient; Each robot interacts with its neighbors in the current neighborhood topology and obtains an updated estimate based on the convex combination of neighbor information weights. and updated information matrix : in, Represents the inverse of the matrix and outputs the estimated value .

2. The robot collaborative positioning method based on infinite dimensional parameter model according to claim 1, characterized in that: Each robot in the cluster is only allowed to interact with neighbors within the neighborhood topology at the current moment.

3. The robot collaborative positioning method based on infinite dimensional parameter model according to claim 2, characterized in that: The computational process for determining the neighbors within the neighborhood topology at the current moment includes: definition The information exchange topology of the robots is undirected ,in Indicates this A collection of robots, Indicates the relationship between robots The communication relationship at the moment, Represents a robot Able to send data to robots Deliver information, Represents the weight of information exchange between robots, ,in Indicates the Robot To the Robot The weight of the information conveyed; like , indicating a robot exist Time is a robot Neighbors, if Represents a robot Not a robot Neighbors; robot The set of all neighbors is ,Due to the physical and communication constraints of the robot system, robots can only interact with each other locally, that is, robots are only allowed to interact with their topological neighbors. Exchange information.

4. The robot collaborative positioning method based on an infinite-dimensional parameter model according to any one of claims 1 to 3, characterized in that: described The dimensional control input includes at least: motor speed data and inertial measurement unit data.

5. A robot collaborative positioning system based on an infinite-dimensional parameter model, characterized in that: include: a memory for storing program instructions; A processor is configured to call the program instructions stored in the memory to implement the robot collaborative positioning method based on an infinite-dimensional parameter model as described in any one of claims 1 to 4.

6. A computer-readable storage medium, characterized in that The computer-readable storage medium stores program codes, and the program codes are used to implement the robot collaborative positioning method based on an infinite-dimensional parameter model according to any one of claims 1 to 4.

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