Robot system time-varying resource allocation optimization control method, equipment and medium

Abstract

The invention relates to the field of robot intelligent control, and discloses a robot system time-varying resource allocation optimization control method and device and a medium, and the method comprises the steps: carrying out the dynamic modeling of a networked robot system, and building a time-varying resource allocation problem model of the system; based on the communication topology of the networked robot system, designing a distributed time-varying resource allocation estimator, and obtaining an estimation state converged to an optimal solution of a time-varying resource allocation problem; and designing a self-adaptive local controller based on the kinetic model to realize tracking control of the estimated state. The invention aims to efficiently allocate limited resources, reduce the operation cost of the networked robot system and improve the overall performance. According to the specific method, on the premise that the constraint condition of the total amount of system resources is met, a distributed optimization control algorithm is adopted to regulate and control the operation state of each robot agent, so that the operation cost of the whole networked robot system is minimum.

Description

Technical Field

[0001] The present invention relates to the field of robot intelligent control, and particularly to a time-varying resource allocation optimization control method for a robot system. Background Art

[0002] With the rapid development of Internet of Things, cloud computing and artificial intelligence technologies, networked robot systems have gradually become an important research direction in the field of robotics. By combining multiple robot nodes with a communication network, networked robot systems achieve distributed perception, collaborative decision-making and resource sharing, significantly improving the flexibility and intelligence level of the system. In recent years, networked robot systems have been widely applied in industrial automation, intelligent transportation, disaster rescue and smart agriculture and other fields. In the field of industrial automation, networked robots can efficiently complete complex production tasks through real-time data exchange and collaborative control.

[0003] The optimal control of resource allocation in networked robot systems refers to how to allocate limited resources, such as computing resources, communication bandwidth and energy, when each robot executes tasks, so that the total resource consumption cost is minimized or the overall performance is optimized. The parameters in the objective function and constraints of most existing research on distributed resource allocation problems are fixed values. However, in actual engineering applications, the parameters of resource allocation problems are often time-varying. Therefore, it is necessary to design efficient distributed optimization control algorithms to solve the time-varying resource allocation problem.

[0004] The dynamic model of a robot system has the characteristics of high coupling, high sensitivity and strong non-linearity. It is difficult to directly extend the resource allocation problem to the optimal control of networked robot systems. Robot systems usually work in complex and changeable environments. Factors such as sensor errors, external disturbances or changes in task requirements will affect the performance and stability of the system. Therefore, the design of the controller needs to dynamically adjust control parameters and strategies by real-time monitoring of the system state and environmental information, so as to ensure that the system can still operate efficiently and stably under uncertain conditions.

[0005] Currently, there is little research on the combination of networked robot systems and resource allocation problems. Especially when considering time-varying dynamic model parameters and time-varying cost functions and constraints, the optimal control problem will become very complex. Based on the previous discussion, this paper studies the time-varying resource allocation problem with time-varying cost functions and constraints for networked uncertain robot systems considering external disturbances and time-varying model parameters, which has important engineering significance for the combination of networked robot system control and distributed optimization problems. Summary of the Invention

[0006] The object of the present invention is to propose an optimization control method, device and medium for time-varying resource allocation of a robot system, so as to solve the technical problems of low resource allocation efficiency and high operation cost in the current robot system.

[0007] Specifically, an optimization control method for time-varying resource allocation of a robot system provided by the present invention includes the following steps:

[0008] S1: Perform dynamic modeling on the networked robot system, consider the influence of external disturbances and time-varying model parameters on the control system, and establish a time-varying resource allocation problem model of the system;

[0009] S2: Based on the communication topology of the networked robot system, design a distributed time-varying resource allocation estimator, solve the time-varying resource allocation problem model of the system, and obtain an estimated state that converges to the optimal solution of the time-varying resource allocation problem;

[0010] S3: Design a local adaptive controller according to the dynamic model of the networked robot system to realize the tracking control of the actual physical state to the estimated state obtained by the distributed time-varying resource allocation estimator.

[0011] A storage medium stores instructions and data for implementing an optimization control method for time-varying resource allocation of a robot system.

[0012] An optimization control device for time-varying resource allocation of a robot system includes: a processor and the storage medium; the processor loads and executes the instructions and data in the storage medium for implementing an optimization control method for time-varying resource allocation of a robot system.

[0013] The beneficial effects provided by the present invention are:

[0014] 1) When modeling the networked robot system, external disturbances and time-varying parameters inside the model are considered. The parameters of the objective function and constraint conditions of the solved resource allocation problem have time-varying characteristics, which is more practically significant in engineering applications.

[0015] 2) The present invention first proposes and successfully solves the time-varying resource allocation problem in the networked robot system, and provides a pioneering technical solution for this field.

[0016] 3) The designed optimization control algorithm is distributed. Neighboring agents only need to exchange their respective Lagrange multiplier information without exchanging any other sensitive information. This not only reduces the communication resource cost, but also ensures the privacy and security of each robot agent. Description of the Drawings

[0017] Figure 1 It is a simple flow schematic diagram of the method of the present invention;

[0018] Figure 2 It is a flow chart for illustrative purposes of an optimal control method for time-varying resource allocation in a networked uncertain robot system in an embodiment of the present invention;

[0019] Figure 3 It is a communication topology diagram of the networked robot system in an embodiment of the present invention;

[0020] Figure 4 It is a state error tracking diagram of each robot agent in an embodiment of the present invention;

[0021] Figure 5 It is an actual state evolution diagram of each robot agent in an embodiment of the present invention;

[0022] Figure 6 It is a graph of the total amount of resources changing in the networked robot system in an embodiment of the present invention;

[0023] Figure 7 It is a Lagrange multiplier evolution diagram of each robot agent in an embodiment of the present invention;

[0024] Figure 8 It is a schematic diagram of the operation of the hardware device in an embodiment of the present invention. Detailed implementation manners

[0025] To make the objectives, technical solutions and advantages of the present invention clearer, the embodiments of the present invention will be further described below in conjunction with the accompanying drawings.

[0026] Before formally elaborating on the present invention, the solution of the present invention will be generally described first for easy understanding.

[0027] Please refer to Figure 1 , an optimal control method for time-varying resource allocation in a robot system provided by the present invention includes:

[0028] S1: Dynamically model the networked robot system, considering the influence of external disturbances and time-varying model parameters on the control system, and establish a time-varying resource allocation problem model for the system;

[0029] As an embodiment, step S1 in the present invention specifically includes the following steps:

[0030] S101: Considering external disturbances and internal time-varying model parameters, establish the dynamic model of agent i in the networked robot system:

[0031]

[0032] In the formula respectively represent the position, velocity and acceleration vectors; M i (q i(t), t) ∈ R n×n is a symmetric and positive definite inertia matrix; represents the Coriolis - centrifuge matrix; G i (q i , t) ∈ R n represents the generalized vector of the force; F i (q i , t) ∈ R n represents the generalized vector of the loss; represents the external disturbance; τ i ∈ R n represents the control input.

[0033] Based on the proposed Euler - Lagrange system, it is usually assumed that the inertia matrix term M i (q i , t) is bounded, that is, there exist positive definite constants m1 ∈ R + and a positive definite bounded function such that the inertia matrix satisfies the following relationship:

[0034] S102: Parametric linearization of the dynamic model gives:

[0035]

[0036] where Z i ∈ R (n×d) represents the known regression matrix, where ∈ i ∈ R d represents the time - varying uncertain parameter, where ∈ di ∈ R (d-n) ; then we can obtain It is usually assumed that the time - varying uncertainty parameter ∈ i (t) and its second - order derivative are both bounded, that is, there exist positive definite constants ζ1, ζ2, ζ3 ∈ R + , such that the time - varying uncertain parameter satisfies the following relationship:

[0037] S103: In the time - varying resource allocation problem of the networked robot system, each agent collaboratively converges to the optimal state determined by the overall cost function and resource constraints. The total time - varying cost function of the system is defined as: The local time - varying resource demand of agent i is r i (t) ∈ R n , and further establish the time - varying resource allocation problem model of the networked robot system:

[0038]

[0039] It is usually assumed that for any agent \(i\in\mathcal{V}\), the local time-varying cost function \(f\) i (q i ,t) is twice continuously differentiable with respect to \(q\) i and \(t\geq t_0\) and has uniform strong convexity, and its gradient can be expressed as where and \(h\) i (t) are both time-varying parameters. Further, it is assumed that the time-varying parameters h i (t) and \(r\) i (t) have second-order derivatives that exist and are bounded, that is, there exist positive definite constants satisfying the following relationships:

[0040]

[0041] S104: For the time-varying resource allocation problem model described above, establish the following Lagrangian equation:

[0042]

[0043] where \(\lambda(t)\in\mathbb{R}\) n is the Lagrange multiplier. Based on the assumption of the uniform strong convexity of the local time-varying cost function in S103, the Lagrangian equation is also strongly convex with respect to \(q\) i and \(t\geq t_0\). Therefore, we can say that if the feasible solution satisfies the following KKT conditions, it is the unique optimal solution of the Lagrangian equation:

[0044]

[0045] where represents the partial derivative of the local time-varying cost function \(f\) i (q i ,t) with respect to \(q\) i .

[0046] S2: Based on the communication topology of the networked robot system, design a distributed time-varying resource allocation estimator to solve the time-varying resource allocation problem model of the system and obtain an estimated state that converges to the optimal solution of the time-varying resource allocation problem;

[0047] It should be noted that step S2 of the present invention proposes a distributed time-varying resource allocation estimator. Only the local Lagrange multipliers need to be exchanged between adjacent agents without the need to exchange other information that may be sensitive or private. The present invention uses the knowledge of graph theory to model the communication topology of the networked robot system and assumes that its communication topology is an undirected connected graph.

[0048] Specifically, step S2 specifically includes the following steps:

[0049] S201: Define the estimated state as Design a distributed time-varying resource allocation estimator as follows:

[0050]

[0051] In the formula and are intermediate auxiliary variables, represents the partial derivative of the time-varying function with respect to . β and γ are positive definite constants that can be selected. Combining equation (5) of the estimator, differentiating the formula yields the following relationship:

[0052]

[0053] Since equation (6) of the estimator is a standard linear exponentially stable system, it can be obtained that when t → +∞ Therefore, That is, it satisfies

[0054] Furthermore, combining equation (2) and equation (5) of the estimator, the following relationship can be obtained:

[0055]

[0056] Define two auxiliary variables as and Differentiating the above equation gives: Combining equation (6) of the estimator gives: From equation (1) and equation (4), can be obtained. Further,

[0057] Based on the assumption that the communication topology of the aforementioned networked robot system is an undirected graph, for any auxiliary vector X ∈ R N , it satisfies Therefore, the equation holds. Further, summing both sides of the above equation gives the linear exponentially stable system Therefore, when t → +∞, the relationship is satisfied:

[0058] S202: By introducing an intermediate variable Equation (2) of the estimator can be written as Its first derivative is Therefore, equation (1) of the aforementioned estimator can be rewritten in the following form:

[0059]

[0060] where Next, the upper bound of η i will be further analyzed. From the analysis in step S201, it can be seen that By solving this differential equation, the following relationship can be obtained:

[0061]

[0062] where Therefore, the upper bound of ξ i (t) when t ≥ t0 can be obtained:

[0063]

[0064] For any auxiliary function A, the relationship is satisfied. Therefore, the variable can be rewritten and its upper bound is obtained as

[0065] Define the auxiliary variable From the analysis in S201, it can be seen that Similar to the method for obtaining the upper bound of the aforementioned ξ i (t), when t ≥ t0 the upper bound of Furthermore, the upper bound of can be obtained as the following expression:

[0066]

[0067] From the assumption in S103, it can be seen that and can be rewritten as and its first derivative is obtained Therefore, the aforementioned variable η i (t) can be rewritten as where the upper bound of Combining the above and definitions, the upper bound of η i,1 is obtained as

[0068] Define two auxiliary constants as and From the definition of the auxiliary variable it can be obtained that f to further obtain the upper bound of η i as the following expression: is the following expression:

[0069]

[0070] S203: Define an intermediate variable Introduce the vector and the diagonal matrix Equation (7) of step S203 can be rewritten in the following compact form:

[0071]

[0072] Construct a positive definite Lyapunov function as follows, where ||·||1 represents the Euclidean 1-norm of the vector:

[0073]

[0074] And take the derivative of it to obtain:

[0075]

[0076] In the formula its lower bound can be obtained as where μ min (·) represents the minimum eigenvalue of the matrix; further obtain Based on the above analysis, the derivative of the Lyapunov function satisfies the following relationship:

[0077]

[0078] In the formula has been obtained in step S202. At this time, select the controller parameter γ to satisfy the condition then it can be obtained that Therefore, when t→+∞, the relationship is satisfied, or in other words, when t→+∞, for any two neighboring nodes ν i and ν j both satisfy Further obtain λ i -λ j →0 n .

[0079] Based on the analysis of the above steps S201 to S203, when t→+∞, the following relationship (1) is satisfied

[0080]

[0081] Therefore, the designed distributed time-varying resource allocation estimator can achieve that when t→+∞, the local feasible solution of agent i can converge to the unique optimal solution of the entire networked robot system

[0082] S3: Design a local adaptive controller according to the dynamic model of the networked robot system to achieve the tracking control of the actual physical state to the estimated state obtained by the distributed time-varying resource allocation estimator.

[0083] As an embodiment, step S3 is specifically as follows:

[0084] S301: Define the actual state of robot agent i as q i , and the tracking error function is:

[0085]

[0086] α1 and α2 in the formula are positive definite constants that can be selected. Combining the tracking error function and the linearized dynamic model in step S102, the following open-loop error system can be obtained:

[0087]

[0088] In the formula represents the estimated value of the regression matrix. Design the local adaptive controller as follows:

[0089]

[0090] The first equation in the above formula is the designed control input, and the second equation is the adaptive rate of the time-varying uncertain term. α3 and α4 are positive definite constants that can be selected, is the estimated value of the time-varying uncertainty term ∈ i and is bounded, that is, there exists a positive definite constant ζ4 such that The estimated value of the regression matrix and its first and second derivatives are all bounded, that is, there exists a positive definite constant such that is a positive definite gain matrix, where Θ1∈R (d-n)×(d-n) and Θ2∈R n×n are both positive definite constant matrices. Therefore, the matrix is non-negative, and the upper bound of can be obtained as

[0091] Furthermore, based on the adaptive rate in the local adaptive controller (8), the upper bound of can be obtained as

[0092] S302: Define the vector and the time-varying parameter error as well as two auxiliary variables and Based on the mean value theorem, there exists a positive definite non-decreasing function g(·): R 3n →R + , such that ||K A,i (ι i , t)||2 ≤ g(||ι i ||2)||ι i ||2. Combining the analysis of the aforementioned steps 102 and 301, we can obtain The upper bound of Derive K B,i to get Further obtain The upper bound of where

[0093] Construct a differential equation in the following form:

[0094] Define the initial value of S i (t) at t = t0 as Therefore, it can be proved that when the controller parameters α2 and α4 satisfy the condition Then, when t ≥ t0, the solution S i (t) of the above differential equation is ≥ 0.

[0095] Furthermore, define the vector Introduce three positive definite auxiliary constants respectively as:

[0096] S303: Differentiate both sides of the open-loop error system equation obtained in step S301, and the following relationship can be obtained Construct a positive definite Lyapunov function as follows:

[0097]

[0098] Further differentiate the above equation and use the Young's inequality to obtain the following relationship:

[0099]

[0100]

[0101] Select the controller parameters where Can be rewritten as where g -1 (·) represents the inverse function of the non-decreasing function g(·). The Lyapunov function satisfies the inequality relationship The relational expression can be obtained Furthermore, κ3 > g 2 (||ι i ||2) / (2α3), that is, when t > t0 Based on the definition of the aforementioned Lyapunov function, for all agents of the networked robot system, when t → +∞, the tracking error function e 2i , e 3i will asymptotically converge to 0 n .

[0102] Based on the design and analysis of the aforementioned steps S301 to S303, the closed-loop system is uniformly bounded. That is, when time t → +∞, the actual state q i (t) of each agent of the networked robot system will converge to the estimated state obtained by the distributed resource allocation estimator

[0103] This embodiment gives a specific case to illustrate the technical solution of the present invention. Refer to Figure 2 the flowchart of the example shown. Taking a two-degree-of-freedom robotic arm as an example, the time-varying dynamic model parameters of robot agent i are given as follows:

[0104]

[0105]

[0106] In the formula, the time-varying parameters are y1(t) = 4 + 0.3cos(3t), y2(t) = 0.5cos(t) + exp(-sin(t)), y3(t) = 0.2sin(5t) + 0.5, F i,1 = 0.5sin(t) + exp(-0.1t), F i,2 = 1.1 + cos(5t), As Figure 3 shown is the communication topology of a networked robot system including 6 agents. The Laplacian matrix of this undirected connected graph is:

[0107]

[0108] The local time-varying cost function and time-varying parameters of robot agent i are:

[0109]

[0110] The control parameters of the time-varying resource allocation optimization control algorithm of the foregoing design are respectively set as β = 1.2, γ = 40, α1 = 1, α2 = 1, α3 = 40, α4 = 30, Θ = I7; the initial estimated states of the foregoing distributed time-varying resource allocation estimator are respectively set as The initial Lagrange multipliers are respectively set as λ 11 = 120, λ 12 = 240, λ 21 = 320, λ 22 = 400, λ 31 = 256, λ 32 = -440, λ 41 = -304, λ 42 = -480, λ 51 = -280, λ 52 = -400, λ 61 = -480, λ 62 =

[0111] -200, and the initial values of all agents are set as 02; the initial actual states of the foregoing local adaptive controller are respectively set as q = 20, q 11 = 45, q 12 = 55, q 21 = 70, q 22 = 50, q 31 = 75, q 32 = 55, q 41 = 80, q 42 = 47.5, q 51 = 22.5, q 52 = 40, q 61 = 35, and the initial values of all agents are 62 set to zero.

[0112] Figures 4 to 7 The simulation results of the designed hierarchical control algorithm are shown. Figure 4 It shows that the state error e 1i can asymptotically converge to the neighborhood of the origin, which means that the actual physical states of the local control layer can track the estimated states obtained by the distributed time-varying resource allocation estimator; Figure 5 shows the evolution of the estimated states and actual states of the networked robot system; Figure 6 shows the change of the sum of the state variables in the distributed time-varying resource allocation estimator and the local adaptive controller, which indicates that the sum of the estimated state variables and the sum of the actual state variables of all agents in the system can asymptotically converge to the total time-varying resource demand; Figure 7 ​It shows that the local Lagrange multipliers of each agent i will tend to be consistent and asymptotically converge to the optimal value.

[0113] Please refer to Figure 8 , Figure 8 which is a schematic diagram of the operation of the hardware device according to an embodiment of the present invention. The hardware device specifically includes: a time-varying resource allocation optimization control device 401 for a robot system, a processor 402, and a storage medium 403.

[0114] A time-varying resource allocation optimization control device 401 for a robot system: The time-varying resource allocation optimization control device 401 for a robot system implements the time-varying resource allocation optimization control method for a robot system.

[0115] Processor 402: The processor 402 loads and executes the instructions and data in the storage medium 403 to implement the time-varying resource allocation optimization control method for a robot system.

[0116] Storage medium 403: The storage medium 403 stores instructions and data; the storage medium 403 is used to implement the time-varying resource allocation optimization control method for a robot system.

[0117] The beneficial effects of the present invention are:

[0118] 1) When modeling a networked robot system, external disturbances and time-varying parameters inside the model are considered. The parameters of the objective function and constraint conditions for solving the resource allocation problem have time-varying characteristics, which is more practically significant in engineering applications.

[0119] 2) The present invention first proposes and successfully solves the time-varying resource allocation problem in a networked robot system, and provides a pioneering technical solution for this field.

[0120] 3) The designed optimization control algorithm is distributed. Neighboring agents only need to exchange their respective Lagrange multiplier information without exchanging any other sensitive information. This not only reduces the communication resource cost but also ensures the privacy and security of each robot agent.

[0121] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A time-varying resource allocation optimization control method for a robot system, characterized in that: Including the following: S1: Conduct dynamic modeling on the networked robot system, consider the influence of external disturbances and time-varying model parameters on the control system, and establish a time-varying resource allocation problem model for the system; S2: Based on the communication topology of the networked robot system, design a distributed time-varying resource allocation estimator to solve the time-varying resource allocation problem model of the system, and obtain an estimated state that converges to the optimal solution of the time-varying resource allocation problem; S3: Design a local adaptive controller according to the dynamic model of the networked robot system to achieve tracking control of the actual physical state to the estimated state obtained by the distributed time-varying resource allocation estimator.

2. The time-varying resource allocation optimization control method for a robot system according to claim 1, characterized in that: The time-varying resource allocation problem model of the system described in step S1 is specifically as follows: where q i represents the position of the robot, i represents the agent number, N is the total number of general agents, t represents the time variable, and r i (t) is the local time-varying resource demand of agent i.

3. The time-varying resource allocation optimization control method for a robot system according to claim 2, characterized in that: In step S2, the distributed time-varying resource allocation estimator is specifically as follows: where is the estimated state, and are intermediate auxiliary variables defined by Eqs. (2) and (5), respectively, represents a time-varying function with respect to and β and γ are positive definite constants to be chosen. ψ in Eq. (1) ij and are both auxiliary variables defined by Eqs. (3) and (4), respectively, and a ij represents the weight coefficient of communication between agent i and agent j in the communication topology of the multi-robot system, represents the set of neighbor nodes of agent i in the communication topology.

4. The time-varying resource allocation optimization control method for a robot system according to claim 3, characterized in that: The estimated state of the optimal solution of the time-varying resource allocation problem in step S2 is specifically: The designed distributed time-varying resource allocation estimator enables the local feasible solution of agent i, which consists of the estimated state and the local Lagrange multiplier, to converge to the unique optimal solution of the entire networked robot system as t → +∞ when t → +∞ 5. The time-varying resource allocation optimization control method for a robot system according to claim 3, characterized in that: In step S, the local adaptive controller is as follows: Among them, the first equation is the designed control input, the second equation is the adaptive rate of the time-varying uncertain term, α3 and α4 are positive definite constants that can be selected. is the estimated value of the time-varying uncertainty term ∈ i and is bounded; the actual state of the robotic agent i is q i , and the tracking error function is: is a positive definite gain matrix, where Θ1 ∈ R (d-n)×(d-n) and Θ2 ∈ R n×n are both positive definite constant matrices.

6. The time-varying resource allocation optimization control method for a robot system as claimed in claim 1, characterized in that: The tracking control in step S3 specifically means that when time t → +∞, the actual state q of each agent in the networked robot system i (t) will converge to the estimated state obtained by the distributed resource allocation estimator 7. A storage medium, characterized in that: The storage medium stores instructions and data for implementing the time-varying resource allocation optimization control method for a robot system according to any one of claims 1 to 6.

8. An optimization control device for time-varying resource allocation of a robot system, characterized in that: Including: A processor and a storage medium; the processor loads and executes the instructions and data in the storage medium for implementing the time-varying resource allocation optimization control method for a robot system according to any one of claims 1 to 6.

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