A control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism

Abstract

The present invention discloses a control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism, the method comprising the following steps: step 1, establishing a dynamic model of the single-arm robot system under continuous time; step 2, based on the dynamic model of the single-arm robot system established in step 1, designing a hybrid trigger strategy including a time trigger mechanism and an event trigger mechanism under the condition of measurement loss; step 3, according to the hybrid trigger strategy described in step 2, designing a time-delay feedback controller based on the hybrid trigger strategy; step 4, based on the time-delay feedback controller designed in step 3, obtaining sufficient conditions to ensure that the controlled system achieves mean square exponential stability. The method has the advantages of being simple and easy to implement, and effectively improves the stability and overall performance of the single-arm robot system. Through the hybrid trigger mechanism, the utilization of system network resources can be effectively balanced to ensure that effective control can be achieved under various working conditions.

Description

Technical Field

[0001] The present invention belongs to the field of control technology, and relates to a feedback control based on a hybrid trigger mechanism, and specifically to a control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism. Background Art

[0002] The single-arm robot system, with its compact size and light weight, can flexibly adapt to various complex environments and has relatively little demand for operating space. It is particularly suitable for delicate tasks such as assembly, handling, packaging, and object grasping. It is worth noting that ensuring its stable operation is the key to fully exerting the system's effectiveness. Therefore, it is crucial to design a control strategy that can calm the single-arm robot system. The output feedback control strategy, whose core concept is to use the obtained output information as the basis for designing feedback control input to achieve the predetermined performance goals, is highly favored in the industry due to its significant advantages such as simple operation, high efficiency, easy application, and low cost. Therefore, in-depth research on the output feedback control problem of the single-arm robot system has practical value and practical significance.

[0003] In actual operation, the output feedback control of the single-arm robot system faces many challenges. First, the physical and technical limitations of the equipment, negligence or errors in human operation may lead to missing or inaccurate measurements in the process of obtaining the output signal. On the other hand, the network effect in the signal transmission environment should not be ignored. During peak hours, such as when the production line is busy or a large amount of data is interacting, the same network may carry multiple signals, which will increase the burden on the network and may cause signal delays, packet loss or packet conflicts. This not only affects the real-time performance of the control instructions, but also may reduce the response speed of the system. During the trough period, network resources are not fully utilized, which may lead to a waste of system performance, especially in tasks with high requirements for real-time performance and response speed. Therefore, designing an efficient network transmission mechanism to meet these challenges is a key link in improving the stability and overall performance of the single-arm robot system.

[0004] Existing output feedback methods are difficult to solve the stabilization problem of single-arm robot systems that are subject to network bandwidth constraints and measurement loss. If traditional control methods are used to control the single-arm robot system, the expected performance requirements may not be achieved. Summary of the invention

[0005] In order to cope with the problem that the single-arm robot system is difficult to operate efficiently and stably under the conditions of measurement loss and limited network bandwidth, the present invention provides a control method for stabilizing the single-arm robot system based on a hybrid trigger mechanism. The method takes into account the random occurrence of measurement loss, transmission delay, and network effects in the signal transmission environment to more realistically and objectively reflect the actual engineering situation. At the same time, the method has the advantages of being simple and easy to implement, and effectively improves the stability and overall performance of the single-arm robot system. Through the hybrid trigger mechanism, the utilization of the system network resources can be effectively balanced to ensure effective control under various working conditions.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] A control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism comprises the following steps:

[0008] Step 1: Establish a dynamic model of a single-arm robot system in continuous time. The dynamic model of the single-arm robot system is:

[0009] dx(t)=(f(x(t),x(t-τ),t)+u(t))dt+g(x(t),x(t-τ),t)dB(t)

[0010] y(t)=h(x(t))

[0011] x(t)=ξ(t),t∈[-τ,0]

[0012] In the formula, x(t) and x(t-τ) represent the state vectors of the single-arm robot system at time t and time t-τ respectively, u(t) represents the control input of the single-arm robot system at time t, y(t) represents the measured output of the single-arm robot system at time t, τ is a constant used to characterize the time lag, ξ(t) represents the initial value function of the system state, and B(t) is defined in the complete probability space The standard Brownian motion in , where t represents time, Ω, Represent sample space set, set family, filter and probability measure respectively, and the filter is right continuous and All included Empty set, d is the differential operator, f(x(t), x(t-τ), t) and g(x(t), x(t-τ), t) are the nonlinear functions of the drift part and the diffusion part related to the state of the single-arm robot system at time t and the state at time t-τ, and h(x(t)) represents the output function related to the system state x(t) at time t;

[0013] Step 2: Based on the single-arm robot system dynamic model established in step 1, a hybrid trigger strategy including time trigger mechanism and event trigger mechanism is designed in the case of measurement loss. The specific steps are as follows:

[0014] In the case of measurement loss, the measurement output obtained by sampling is:

[0015]

[0016] In the formula, represents the actual measurement output value obtained through the k-th sampling, y(kη) represents the measurement output value theoretically obtained through the k-th sampling, η represents the sampling interval, and α(kη) is a random variable that obeys the Bernoulli distribution;

[0017] In the hybrid trigger strategy, the switching between the time trigger mechanism and the event trigger mechanism is characterized by a random variable that obeys the Bernoulli distribution, that is:

[0018]

[0019] In the formula, kη represents the time of the kth sampling, T 1 represents the set of time intervals activated by the time trigger mechanism, T 2 represents the set of time intervals activated by the event trigger mechanism, β(kη) represents a random variable that obeys the Bernoulli distribution;

[0020] The transmission strategy under the time-triggered mechanism is:

[0021]

[0022] In the formula, Indicates the measurement output to be transmitted to the controller;

[0023] The time trigger sequence of the event trigger mechanism is composed of

[0024]

[0025] Generate, t σ+1 η represents the time when the signal is released by the event trigger mechanism for the σ+1th time, min represents the minimum value function, k represents the kth sampling, Indicates the latest measurement output transmitted to the controller. Indicates the time when the controller receives the latest measured output value, θ 1 ,θ 2 and θ 3 are the proportional parameter, dynamic coefficient and exponential parameter in the event triggering mechanism, and e represents a natural constant;

[0026] The transmission strategy under the event trigger mechanism is:

[0027]

[0028] Step 3: According to the hybrid triggering strategy described in step 2, a time-delay feedback controller based on the hybrid triggering strategy is designed. The specific form of the time-delay feedback controller is:

[0029]

[0030] In the formula, represents the control input nonlinear function designed according to the measured output obtained by the hybrid trigger mechanism, ω represents the transmission delay;

[0031] Step 4: Based on the time-delay feedback controller designed in step 3, a sufficient condition is obtained to ensure that the controlled system achieves mean square exponential stability. The sufficient condition to ensure that the controlled system achieves mean square exponential stability is:

[0032] There exists a scalar constant γ 1 and γ 2 , the free parameter ε 1 and ε 2 , the control input function k(y(t)) designed using the measured output y(t) can make

[0033] x T (t)(f(x(t),x(t-τ),t)+u(y(t)))+0.5g(x(t),x(t-τ),t) 2

[0034] ≤-γ 1 |x(t)| 2 +γ 2 |x(t-τ)| 2

[0035] Established, and

[0036] γ 1 -γ 2 -Δ 1 ≥Δ 2 Δ 3 (η+ω) 2 +λ

[0037]

[0038] In the formula, x T (t) represents the transpose of vector x(t), |·| 2 represents the square of the Euclidean norm of the vector ·, λ represents the exponential decay order, Δ 1 , Δ 2 and Δ 3 There are three transition parameters.

[0039] Compared with the prior art, the present invention has the following advantages:

[0040] 1. The present invention takes into account the measurement loss phenomenon, network effects and the impact on the dynamic system, and designs an output feedback control strategy based on a hybrid trigger mechanism. Compared with the traditional state feedback control strategy, the present invention uses more easily available output design control, which can greatly reduce the cost consumed in measuring and estimating state information, and the proposed output feedback control strategy based on a hybrid trigger mechanism can reduce the signal transmission frequency and make full use of network resources, solving the problem that the existing control method is difficult to simultaneously handle the output feedback control under measurement loss and limited network bandwidth.

[0041] 2. The present invention uses Lyapunov stability theorem and The formula is used to establish the judgment conditions for ensuring the stability of the controlled system's mean square significance exponential stability, and the influence of time delay, measurement loss parameters, and parameters in the hybrid trigger mechanism on the system stability is revealed. The above method realizes that the designed output feedback control strategy can still achieve good stability under the conditions of measurement loss and network resource limitation.

[0042] 3. The control method based on the hybrid trigger mechanism proposed in the present invention can effectively stabilize an unstable single-arm robot system. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 It is a flow chart of a control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism according to the present invention;

[0044] Figure 2 This is the state trajectory diagram of the single-arm robot without control. In the figure, “-”, and "-----" respectively depict the single-arm machine state x 1 (t), x 2 (t), x 3 (t) and x 4 (t) trajectory, x 1 (t), x 2 (t), x 3 (t) and x 4 (t) respectively characterizes the first component, second component, third component and fourth component of the state vector x(t) of the single-arm robot system;

[0045] Figure 3 For The triggering moment of the hybrid trigger mechanism is shown in the figure. and They respectively depict the triggering moment of the event triggering mechanism and the triggering moment of the time triggering mechanism;

[0046] Figure 4 For The trajectory diagram of the control input. In the figure, “-”, and "-----" respectively depict the control input u 1 (t),u 2 (t),u 3 (t) and u 4 (t) trajectory, u 1 (t),u 2 (t),u 3 (t) and u 4 (t) respectively characterizes the first component, second component, third component and fourth component of the control input u(t);

[0047] Figure 5 For When , the state trajectory diagram of the single-arm robot under the action of the controller, in the figure, “-”, and "-----" respectively depict the single-arm machine state x 1 (t), x 2 (t), x 3 (t) and x 4 (t) trajectory;

[0048] Figure 6 For The triggering moment of the time-confusion trigger mechanism;

[0049] Figure 7 For The trajectory diagram of the control input;

[0050] Figure 8 For When , the state trajectory diagram of the single-arm robot under the action of the controller;

[0051] Fig. 9 For The triggering moment of the time-confusion trigger mechanism;

[0052] Fig.10 For The trajectory diagram of the control input;

[0053] Fig.11 For The state trajectory diagram of the single-arm robot under the action of the controller. DETAILED DESCRIPTION

[0054] The technical solution of the present invention is further described below in conjunction with the accompanying drawings, but is not limited thereto. Any modification or equivalent replacement of the technical solution of the present invention without departing from the spirit and scope of the technical solution of the present invention should be included in the protection scope of the present invention.

[0055] The present invention provides a control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism. First, a state space model of the single-arm robot system is constructed. In the case of measurement loss, a hybrid trigger transmission strategy including a time trigger mechanism and an event trigger mechanism is designed. Secondly, a time-delay output feedback control strategy is designed using the measurement information obtained through the hybrid trigger mechanism transmission. Finally, a judgment basis is given to ensure that the controlled single-arm robot system achieves mean square exponential stability. Figure 1 As shown, the method comprises the following steps:

[0056] Step 1: Establish a dynamic model of the single-arm robot system in continuous time.

[0057] In this step, the dynamic model of the single-arm robot system is established as follows:

[0058] dx(t)=(f(x(t),x(t-τ),t)+u(t))dt+g(x(t),x(t-τ),t)dB(t)

[0059] y(t)=h(x(t))

[0060] x(t)=ξ(t),t∈[-τ,0]

[0061] Where x(t) and x(t-τ) represent the state vectors of the single-arm robot system at time t and time t-τ, respectively; u(t) represents the control input of the single-arm robot system at time t; y(t) represents the measured output of the single-arm robot system at time t; τ is a constant used to characterize the time lag; ξ(t) represents the initial value function of the system state; [-τ,0] represents an interval with -τ as the left endpoint and 0 as the right endpoint; B(t) is defined in the complete probability space The standard Brownian motion in , where t represents time, Ω, Represent sample space set, set family, filter and probability measure respectively, and the filter is right continuous and All included Empty set, d is the differential operator, f(x(t), x(t-τ), t) and g(x(t), x(t-τ), t) are nonlinear functions of the drift part and the diffusion part related to the state of the single-arm robot system at time t and the state at time t-τ, h(x(t)) represents the output function related to the system state x(t) at time t. The above-mentioned nonlinear functions satisfy the local Lipschitz condition, and:

[0062] |f(x(t),x(t-τ),t)|≤δ 1 (|x(t)|+|x(t-τ)|)

[0063] |g(x(t),x(t-τ),t)|≤δ 2 (|x(t)|+|x(t-τ)\)

[0064] |h(x(t))|≤δ 3 |x(t)|

[0065] In the formula, δ 1 , δ 2 and δ 3 are the linear growth coefficients of the nonlinear functions f(x(t),x(t-τ),t), g(x(t),x(t-τ),t) and h(x(t)), and |·| represents the Euclidean norm of the vector ·.

[0066] Step 2: Based on the single-arm robot system dynamic model established in step 1, a hybrid trigger strategy including a time trigger mechanism and an event trigger mechanism is designed in the case of measurement loss. The hybrid trigger strategy is as follows:

[0067] In the case of measurement loss, the measurement output obtained by sampling is:

[0068]

[0069] In the formula, represents the actual measured output value obtained through the k-th sampling, y(kη) represents the theoretical measured output value obtained through the k-th sampling, η represents the sampling interval, α(kη) is a random variable that obeys the Bernoulli distribution and satisfies the statistical characteristics and is the expected value of the random variable, represents the probability that α(kη) takes the value 1, represents the probability that α(kη) takes the value of 0.

[0070] In the hybrid trigger strategy, the switching between the time trigger mechanism and the event trigger mechanism is characterized by a random variable that obeys the Bernoulli distribution, that is:

[0071]

[0072] In the formula, kη represents the time of the kth sampling, T 1 represents the set of time intervals activated by the time trigger mechanism, T 2 represents the set of time intervals activated by the event trigger mechanism, and the random variable β(kη) obeying the Bernoulli distribution satisfies the statistical property and is the expected value of the random variable, represents the probability that β(kη) takes the value 1, represents the probability that β(kη) takes the value of 0. The random variables α(kη) and β(kη) are independent of each other.

[0073] The transmission strategy under the time-triggered mechanism is:

[0074]

[0075] In the formula, Indicates the measurement output to be transmitted to the controller. It represents the actual measured output value obtained through the k-th sampling.

[0076] The time trigger sequence of the event trigger mechanism is composed of

[0077]

[0078] Generate, t σ+1 η represents the time when the signal is released by the event trigger mechanism for the σ+1th time, min represents the minimum value function, k represents the kth sampling, Indicates the latest measurement output transmitted to the controller. Indicates the time when the controller receives the latest measured output value, θ 1 ,θ 2 and θ 3 are the proportional parameter, dynamic coefficient and exponential parameter in the event trigger mechanism, e represents the natural constant, and time Select t σ η and The maximum value, t σ η represents the time when the signal is released by the event trigger mechanism for the σth time, It indicates the time when the measured value is transmitted to the controller by the time trigger mechanism before the σ+1th event trigger mechanism releases the signal.

[0079] The transmission strategy under the event trigger mechanism is:

[0080]

[0081] Step 3: According to the hybrid triggering strategy described in step 2, a time-delay feedback controller based on the hybrid triggering strategy is designed. The specific form of the time-delay feedback controller is:

[0082]

[0083] In the formula, represents the control input nonlinear function designed based on the measured output obtained by the hybrid trigger mechanism, ω represents the transmission delay, and the nonlinear function satisfy:

[0084]

[0085] In the formula, δ 4 is a nonlinear function The linear growth coefficient of .

[0086] Step 4: Based on the time-delay feedback controller designed in step 3, obtain sufficient conditions to ensure that the controlled system achieves mean square exponential stability.

[0087] The sufficient condition to ensure the controlled system achieves mean square exponential stability is that there exists a scalar constant γ 1 and γ 2 , the free parameter ε 1 and ε 2 , the control input function k(y(t)) designed using the measured output y(t) can make

[0088] x T (t)(f(x(t),x(t-τ),t)+u(y(t)))+0.5g(x(t),x(t-τ),t) 2

[0089] ≤-γ 1 |x(t)| 2 +γ 2 |x(t-τ)| 2

[0090] Established, and

[0091] γ 1 -γ 2 -Δ 1 ≥Δ 2 Δ 3 (η+ω) 2 +λ

[0092]

[0093] In the formula, x T (t) represents the transpose of vector x(t), |·| 2 represents the square of the Euclidean norm of the vector ·, λ represents the exponential decay order, Δ 1 , Δ 2 and Δ 3 are three transition parameters, which are defined as:

[0094]

[0095] Example:

[0096] This embodiment takes a single-arm robot system as an example and uses the method of the present invention to perform simulation:

[0097] The correlation coefficient of the single-arm robot system is set as follows:

[0098]

[0099] g(x(t),x(t-τ),t)=0.2x(t)+0.1x(t-τ)

[0100] h(x(t))=0.4x(t), k(y(t))=2y(t), ξ(t)=[2 2 -2 -2] T

[0101] The values ​​of other simulation parameters are selected as follows: The probability of no measurement loss is The switching probability in the hybrid trigger mechanism is Free parameter ε 1 =1.1,ε 2 =0.1, exponential decay order λ=0.1, sampling interval η=0.001, transmission delay ω=0.002.

[0102] The effect of output feedback controller based on hybrid trigger mechanism:

[0103] Depend on Figure 3 , Figure 6 , Fig. 9 It can be seen that for the single-arm robot system under the condition of measurement loss and network resource limitation, different switching parameters in the hybrid trigger mechanism have an important impact on the output feedback control performance designed by the present invention. Specifically, as the probability of the event trigger mechanism increases, the convergence speed of the system will decrease. Figure 2 , Figure 4-5 , Figure 7-Figure 8 , Figure 10-11 It can be seen that for the single-arm robot system under the condition of measurement loss and network resource limitation, the measurement loss probability has an important impact on the output feedback control performance designed by the present invention. The output feedback controller based on the hybrid trigger mechanism designed by the present invention can effectively stabilize the unstable system.

Claims

1. A control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism, characterized in that The method comprises the following steps: Step 1: Establish a dynamic model of a single-arm robot system in continuous time. The dynamic model of the single-arm robot system is: dx(t)=(f(x(t),x(t-τ),t)+u(t))dt+g(x(t),x(t-τ),t)dB(t) y(t)=h(x(t)) x(t)=ξ(t),t∈[-τ,0] In the formula, x(t) and x(t-τ) represent the state vectors of the single-arm robot system at time t and time t-τ respectively, u(t) represents the control input of the single-arm robot system at time t, y(t) represents the measured output of the single-arm robot system at time t, τ is a constant used to characterize the time lag, ξ(t) represents the initial value function of the system state, and B(t) is defined in the complete probability space The standard Brownian motion in , where t represents time, Ω, Represent sample space set, set family, filter and probability measure respectively, and the filter is right continuous and All included Empty set, d is the differential operator, f(x(t), x(t-τ), t) and g(x(t), x(t-τ), t) are the nonlinear functions of the drift part and the diffusion part related to the state of the single-arm robot system at time t and the state at time t-τ, and h(x(t)) represents the output function related to the system state x(t) at time t; Step 2: Based on the single-arm robot system dynamic model established in step 1, a hybrid trigger strategy including time trigger mechanism and event trigger mechanism is designed in the case of measurement loss. The specific steps are as follows: In the case of measurement loss, the measurement output obtained by sampling is: In the formula, represents the actual measurement output value obtained through the k-th sampling, y(kη) represents the theoretical measurement output value obtained through the k-th sampling, η represents the sampling interval, and α(kη) is a random variable obeying the Bernoulli distribution1; In the hybrid trigger strategy, the switching between the time trigger mechanism and the event trigger mechanism is characterized by a random variable that obeys the Bernoulli distribution, that is: Where kη represents the kth sampling moment, T1 represents the set of time intervals activated by the time trigger mechanism, T2 represents the set of time intervals activated by the event trigger mechanism, and β(kη) represents the random variable 2 that obeys the Bernoulli distribution; The transmission strategy under the time-triggered mechanism is: In the formula, Indicates the measurement output to be transmitted to the controller; The time trigger sequence of the event trigger mechanism is composed of Generate, t σ+1 η represents the time when the signal is released by the event trigger mechanism for the σ+1th time, min represents the minimum value function, k represents the kth sampling, Indicates the latest measurement output transmitted to the controller. represents the time when the latest measured output value is received in the controller, θ1, θ2 and θ3 are the proportional parameters, dynamic coefficients and exponential parameters in the event trigger mechanism, and e represents a natural constant; The transmission strategy under the event trigger mechanism is: Step 3: According to the hybrid triggering strategy described in step 2, a time-delay feedback controller based on the hybrid triggering strategy is designed. The specific form of the time-delay feedback controller is: In the formula, represents the control input nonlinear function designed according to the measured output obtained by the hybrid trigger mechanism, ω represents the transmission delay; Step 4: Based on the time-delay feedback controller designed in step 3, a sufficient condition is obtained to ensure that the controlled system achieves mean square exponential stability. The sufficient condition to ensure that the controlled system achieves mean square exponential stability is: There are scalar constants γ1 and γ2, free parameters ε1 and ε2, and the control input function k(y(t)) designed using the measured output y(t) can make x T (t)(f(x(t),x(t-τ),t)+u(y(t)))+0.5g(x(t),x(t-τ),t) 2 ≤-γ1x(t) 2 +γ2x(t-τ) 2 Established, and γ1-γ2-Δ1≥Δ2Δ3(η+ω) 2 +λ In the formula, x T (t) represents the transpose of the vector x(t), |g 2 represents the square of the Euclidean norm of the vector ·, λ represents the exponential decay order, and Δ1, Δ2 and Δ3 are three transition parameters.

2. The control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism according to claim 1 is characterized in that In step 1, f(x(t), x(t-τ), t) and g(x(t), x(t-τ), t) satisfy the local Lipschitz condition, and: |f(x(t),x(t-τ),t)|≤δ1(x(t)+x(t-τ)) |g(x(t),x(t-τ),t)|≤δ2(x(t)+x(t-τ)) |h(x(t))|≤δ3x(t)| Where δ1, δ2 and δ3 are the linear growth coefficients of the nonlinear functions f(x(t), x(t-τ), t), g(x(t), x(t-τ), t) and h(x(t)), and |g| represents the Euclidean norm of the vector ·.

3. The control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism according to claim 1 is characterized in that In step 2, α(kη) satisfies the statistical characteristics and is the expected value of the random variable, represents the probability that α(kη) takes the value 1, represents the probability that α(kη) takes the value of 0.

4. The control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism according to claim 1 is characterized in that In step 2, β(kη) satisfies the statistical characteristics and is the expected value of the random variable, represents the probability that β(kη) takes the value 1, represents the probability that β(kη) takes the value of 0. The random variables α(kη) and β(kη) are independent of each other.

5. The control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism according to claim 1 is characterized in that In the step 2, Select t σ η and The maximum value, t σ η represents the time when the signal is released by the event trigger mechanism for the σth time, It indicates the time when the measured value is transmitted to the controller by the time trigger mechanism before the σ+1th event trigger mechanism releases the signal.

6. The control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism according to claim 1 is characterized in that In step 3, the nonlinear function satisfy: In the formula, δ4 is a nonlinear function The linear growth coefficient of .

7. The control method for stabilizing a single-arm robot system based on a hybrid trigger mechanism according to claim 1 is characterized in that In step 4, Δ1, Δ2 and Δ3 are defined as: In the formula, is the expected value of the random variable, is the expected value of the random variable, δ3 is the linear growth coefficient of the nonlinear function h(x(t)), and δ4 is the nonlinear function is the linear growth coefficient of , and ε1 and ε2 are free parameters.

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