A dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction

Abstract

The application discloses a dynamic event trigger logarithmic sliding mode control method for digital human-computer interaction. The method is based on a preset event driving condition, and optimal trigger control quantity at a key moment is screened out from a continuous-time logarithmic sliding mode track tracking control quantity to control the mechanical arm, so that the switching energy consumption of system control input is reduced, the large amount of information interaction data in the digital human-computer interaction process is avoided, the overall digital interaction dynamics calculation burden is reduced, and the steady-state accuracy and dynamic response performance can be ensured.

Description

Technical Field

[0001] This invention belongs to the field of digital collaborative interaction technology between humans and robots, and specifically relates to a dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction. Background Technology

[0002] Physical human-computer interaction involves introducing human operational behaviors into a computer through devices such as robotic arms. By calculating the impact of the data corresponding to the operational behaviors on the dynamics of the controlled system, the desired tracking trajectory of the control system is actively adjusted, thereby completing the robotic arm's movement behavior under the active intervention of the operator.

[0003] With the development of the digital economy, and addressing the challenges of evaluating the effects of human-machine collaboration in industrial scenarios—namely, the difficulty in intuitively assessing results and confirming accuracy—digital-assisted physical human-machine interaction (HMI) technology, or digital HMI for short, overlays digital models onto actual physical systems to enhance operators' understanding and experience of the operational process. In digital HMI, the information representation of the model is computer-simulated, offering high flexibility. A key difference from traditional physical HMI lies in the fact that the HMI process relies on computer computation and presentation; therefore, the dynamic model needs to be transformed from a continuous-time dynamic description to a discrete-time dynamic description. Discrete-time dynamic models are typically based on the Euler discretization method, obtaining a sequential sequence describing the iterative dynamic process. Some state updates depend on measurement data, while other essential states are obtained through iterative calculations. This also presents challenges for controller design. Unlike continuous-time control systems, discrete-time controller design requires ensuring the strict monotonical decrease of the discrete-time Lyapunov function of the sequence. Furthermore, the large data throughput and frequent information exchange in digital HMI processes can easily lead to system instability.

[0004] Therefore, a discrete-time control method needs to be proposed to solve the technical problem of how to effectively reduce the control command update frequency of the control system while ensuring system stability, so as to achieve low power consumption and high efficiency control. Summary of the Invention

[0005] The purpose of this invention is to provide a dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction, which effectively reduces the frequency of control command updates in the control system while ensuring system stability, thereby reducing the frequency of system information exchange and saving control power.

[0006] The present invention adopts the following technical solution:

[0007] Embodiment 1 of the present invention provides a dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction, comprising:

[0008] Step S101: Based on the logarithmic sliding mode trajectory tracking control model of continuous-time digital human-machine interaction, calculate the first trigger control quantity of the control force at the current moment according to the sliding surface vector of the end of the robotic arm at the current moment, the velocity of the reference trajectory at the current moment and the velocity of the reference trajectory at the next moment, the tracking error at the current moment and the tracking error at the next moment.

[0009] Step S102: Calculate the time from time 0 to kT according to the method in step S101. c The first trigger control variable at any given time;

[0010] Step S103: From time 0 to kT c Filter out k from all the first trigger control values ​​at time 1. i T c The second trigger control quantity when the sliding surface vector at time t satisfies the preset event-driven condition is used as (k) i +1)T c The third trigger control quantity at time k, where the third trigger control quantity is the actual trigger control quantity of the robotic arm's control force to control the robotic arm, k i T c The time is the earliest time that meets the preset conditions.

[0011] Optionally, step S101: Based on the logarithmic sliding mode trajectory tracking control model of continuous-time digital human-machine interaction, the first trigger control quantity of the control force at the current moment is calculated according to the sliding surface vector of the end effector of the robotic arm at the current moment, the velocity of the reference trajectory at the current moment and the velocity of the reference trajectory at the next moment, the tracking error at the current moment and the tracking error at the next moment, including:

[0012] Using the sliding surface vector at the current moment, the velocity of the reference trajectory at the current moment, the velocity of the reference trajectory at the next moment, the tracking error at the current moment, and the tracking error at the next moment as inputs to the following continuous-time digital human-computer interaction logarithmic sliding mode trajectory tracking control model, the first trigger control quantity of the control force at the current moment is obtained:

[0013]

[0014] Where the current time is kT c At time k, the next time step is (k+1)T. c At that moment, u l (k) is kT c The first trigger control quantity at time t, s(k) is kT c The sliding surface vector at time Δx r (k) is kT c The velocity of the reference trajectory at time Δx r(k+1) is (k+1)T c The velocity of the reference trajectory at time k, e(k) is kT c The tracking error at time step (k+1) is (k+1)T. c Tracking error at any time, This represents a column vector where all elements are 1. It is the gain matrix of the first sliding surface. It is the gain matrix of the second sliding surface. It's kT c The expression relating the Coriolis force and gravity term at the end effector of the robotic arm at any given moment. It's kT c Expressions related to the inertia matrix of the robotic arm's end effector at any given time.

[0015] Optionally, the sliding mode surface quantity is calculated as follows:

[0016] s(k)=Δe(k)+βdiag(sgn(e(k)))ln(α|e(k)|+1 c ),

[0017] Where Δe(k) is kT c Tracking speed error at any given moment.

[0018] Alternatively, Δe(k) can be calculated as follows:

[0019] Δe(k)=Δx(k)-Δx r (k),

[0020] Indicates time kT c The speed of the robotic arm's end effector is collected in real time. It's kT c The speed of the reference trajectory at all times.

[0021] Optionally, the default event-driven condition is:

[0022]

[0023] Δθ(k)=-θ(k)+s(k) T η(η-2)s(k) / 2-ρΛ(k),

[0024] Λ(k)=|δ(k) T η(2-η)s(k)+δ(k) T δ(k)|,

[0025] in, It's kT c Auxiliary parameters of time, It is the rate of change of θ(k). To preset the first constant value, As a preset second constant, Λ(k) represents kT c The deviation value of the sliding mode surface vector at any given time. Indicates kT c Real-time digital input deviation, u l (k i ) is k i T c The trigger control quantity at any given time, u l (k) is kT c The trigger control quantity at any given time.

[0026] The beneficial effects of this invention are as follows: This invention proposes a dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction. Based on preset event-driven conditions, this method selects the optimal trigger control quantity at key moments from the logarithmic sliding mode trajectory tracking control quantities over continuous time to control the robotic arm, thereby reducing the energy consumption of switching system control inputs, avoiding large amounts of information exchange data during digital human-computer interaction, reducing the overall digital interaction dynamics calculation burden, and ensuring steady-state accuracy and dynamic response performance. Attached Figure Description

[0027] Figure 1 This is a flowchart of a dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction provided in Embodiment 1 of the present invention;

[0028] Figure 2 This is a simulation result of the reference trajectory tracking of the robotic arm in the x-dimensional of the Cartesian coordinate system provided in Embodiment 1 of the present invention.

[0029] Figure 3 This is a simulation result of the reference trajectory tracking of the robotic arm in the y-dimensional of the Cartesian coordinate system provided in Embodiment 1 of the present invention.

[0030] Figure 4 This is a simulation result of the reference trajectory tracking of the robotic arm in the z-dimensional of the Cartesian coordinate system provided in Embodiment 1 of the present invention.

[0031] Figure 5 This is a schematic diagram illustrating the relationship between trigger time and time interval, provided in Embodiment 1 of the present invention. Detailed Implementation

[0032] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0033] Combination Figure 1 Embodiment 1 of the present invention provides a dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction, comprising:

[0034] Step S101: Based on the logarithmic sliding mode trajectory tracking control model of continuous-time digital human-machine interaction, calculate the first trigger control quantity of the control force at the current moment according to the sliding surface vector of the end of the robotic arm at the current moment, the velocity of the reference trajectory at the current moment and the velocity of the reference trajectory at the next moment, the tracking error at the current moment and the tracking error at the next moment.

[0035] Optionally, the sliding surface vector at the current moment, the velocity of the reference trajectory at the current moment, the velocity of the reference trajectory at the next moment, the tracking error at the current moment, and the tracking error at the next moment are used as inputs to the following continuous-time digital human-machine interaction logarithmic sliding mode trajectory tracking control model to obtain the first trigger control quantity of the control force at the current moment:

[0036]

[0037] Where the current time is kT c At time k, the next time step is (k+1)T. c At that moment, u l (k) is kT c The first trigger control quantity at time t, s(k) is kT c The sliding surface vector at time Δx r (k) is kT c The velocity of the reference trajectory at time Δx r (k+1) is (k+1)T c The velocity of the reference trajectory at time k, e(k) is kT c The tracking error at time step (k+1) is (k+1)T. c Tracking error at any time, This represents a column vector where all elements are 1. It is the gain matrix of the first sliding surface. It is the gain matrix of the second sliding surface. It's kT c The expression relating the Coriolis force and gravity term at the end effector of the robotic arm at any given moment. It's kT c Expressions related to the inertia matrix of the robotic arm's end effector at any given time.

[0038] In one embodiment, the dynamic system update for digital human-computer interaction can be described by the following discrete-time mathematical model:

[0039]

[0040] Among them, T c This refers to the sampling time of the digital human-computer interaction process, where k represents the sampling time number, kT c At the current time, (k+1)Tc For the next moment, Represents time (k+1)T c The trajectory of the digital robotic arm's end effector in real time. Indicates time kT c The trajectory of the robotic arm's end effector at all times. Indicates time kT c The speed of the robotic arm's end effector at all times. This indicates that (k+1)T is calculated based on the Euler forward difference. c The speed of the robotic arm's end effector at all times. It describes kT c The expression relating the Coriolis force and gravity term at the end effector of the robotic arm at any given moment. It's kT c The expression related to the inertia matrix of the robotic arm's end effector at time kT, u(k) is kT c The control force input to the system at any given moment. It should be noted that, based on this model, the motion states of the robotic arm's end effector in the Cartesian coordinate system along the x, y, and z axes during digital human-computer interaction can be calculated and generated.

[0041] By collecting the trajectory and velocity of the robotic arm end effector at the current moment, and participating in the iterative calculation of the above formula (1), the trajectory and velocity of the robotic arm end effector at the next moment can be obtained.

[0042] Secondly, under discrete-time conditions, the reference trajectory x of the robotic arm's end effector is generated using the following second-order discrete system. r :

[0043]

[0044] in, It is (k+1)T c The speed of the reference trajectory at the end of the robotic arm at all times. It's kT c The speed of the reference trajectory at the end of the robotic arm at all times. It is the mass matrix of the desired impedance structure of the reference trajectory. It is the damping matrix of the desired impedance structure of the reference trajectory. It is the elastic matrix of the desired impedance structure of the reference trajectory. It's kT c Given the known operating force of the operator, the reference trajectory x of the robotic arm's end effector can be obtained through numerical iteration based on formula (2). r .

[0045] kT obtained based on the above process cThe trajectory x(k) and kT of the robotic arm end effector at time points c Reference trajectory x at the end of the robotic arm at any given moment r (k), calculate the difference between the two to obtain the tracking error: e(k)=x(k)-x r (k).

[0046] and the above process to obtain kT c The speed of the trajectory at the end of the robotic arm at all times and kT c The speed of the reference trajectory at the end of the robotic arm at all times kT is obtained through calculation using formula (4). c Sliding surface vector at time:

[0047] s(k)=Δe(k)+βdiag(sgn(e(k)))ln(α|e(k)|+1 c (3)

[0048] Where, Δe(k)=Δx(k)-Δx r (k) represents time kT c Tracking speed error It is time kT c The sliding mode surface vector at time is used as the system input to induce and stabilize the sliding mode, ensuring system control. Furthermore, (k+1)T can be obtained using the finite difference method. c Velocity of the reference trajectory at time: Δx r (k+1), (k+1)T c The tracking error at time step e(k+1).

[0049] Will e(k)=x(k)-x r (k), e(k+1) The logarithmic sliding mode trajectory tracking control model for continuous-time digital human-computer interaction, as described in formula (3), calculates the trajectory at kT. c The first trigger control quantity u at time 1 l (k):

[0050]

[0051] Where, e(k+1)=x(k+1)-x r (k+1) represents (k+1)T c The tracking error at time step (k+1) is (k+1)T. c The trajectory of the end effector of the robotic arm, x r (k+1) is (k+1)T c The reference trajectory of the robotic arm's end effector at any given moment. It is the sliding mode control gain matrix. For example, the sliding mode control gain matrix is ​​a diagonal matrix, and the elements η on the diagonal are... 1，1 η 2，2 η 3，3 Satisfying η 1，1 ∈(0,2),η 2，2 ∈(0,2),η 3，3 ∈(0,2). It is the gain matrix of the first sliding surface. This is the gain matrix of the second sliding surface. For example: For a diagonal matrix, the elements α on the diagonal are... 1，1 α 2，2 α 3，3 and Given a diagonal matrix, the elements β on the diagonal are... 1，1 ,β 2，2 ,β 3，3 The first and second sliding surface gain matrices must simultaneously satisfy T. c α 1，1 β 1，1 <2,T c α 2，2 β 2，2 <2, and T c α 3，3 β 3，3 <2 conditions must be met simultaneously, This represents a column vector where all elements are 1. This represents time (k+1)T c The sign of the tracking error, similarly, This represents time kT c The sign of the tracking error. This indicates taking (k+1)T c The tracking error e(k+1) at time step e is a diagonal matrix composed of the elements on the diagonal. Take kT c The tracking error e(k) at time step e is a diagonal matrix composed of the elements on the diagonal.

[0052] Step S102: Calculate the time from time 0 to kT according to the method in step S101. c The first trigger control variable at any given time;

[0053] In one embodiment, based on step S101, the time from time 0 to kT can be calculated. c The first trigger control quantity at each sampling time constitutes a data set stored in the memory.

[0054] Step S103: From time 0 to kT c Filter out k from all the first trigger control values ​​at time 1.i T c The second trigger control quantity when the sliding surface vector at time t satisfies the preset event-driven condition is used as (k) i +1)T c The third trigger control quantity at time k, where the third trigger control quantity is the actual trigger control quantity of the robotic arm's control force to control the robotic arm, k i T c The time is the earliest time that meets the preset conditions.

[0055] Optionally, the default event-driven condition is:

[0056]

[0057] Δθ(k)=-θ(k)+s(k) T η(η-2)s(k) / 2-ρΛ(k),

[0058] Λ(k)=|δ(k) T η(2-η)s(k)+δ(k) T δ(k)|,

[0059] in, It's kT c Auxiliary parameters of time, It is the rate of change of θ(k). To preset the first constant value, As a preset second constant, Λ(k) represents kT c The deviation value of the sliding mode surface vector at any given time. Indicates kT c Real-time digital input deviation, u l (k i ) is k i T c The trigger control quantity at any given time, u l (k) is kT c The trigger control quantity at any given time.

[0060] In one embodiment, from the set of the first trigger control quantities described above, based on the judgment from time 0 to kT... c Does the sliding surface vector at each time step satisfy the following conditions? This condition is used to filter out the trigger control quantity at the earliest moment under the composite condition, denoted as u. l (k i ), representing k i T c The trigger control quantity at time k is used as the next time step (k) i +1)T c The third trigger control quantity at time k i Tc The time is the earliest time that meets the preset conditions. It should be noted that the third trigger control quantity is the actual trigger control quantity of the robotic arm's control force to control the robotic arm, and it is an optimal trigger control quantity that can ensure both system stability and human-computer interaction experience.

[0061] Specifically, the judgment is based on the following preset event-driven conditions:

[0062]

[0063] Δθ(k)=-θ(k)+s(k) T η(η-2)s(k) / 2-ρΛ(k),

[0064] Λ(k)=|δ(k) T η(2-η)s(k)+δ(k) T δ(k)|,

[0065] in, It's kT c Auxiliary parameters of time, It is the rate of change of θ(k). To preset the first constant value, As a preset second constant, Λ(k) represents kT c The deviation value of the sliding mode surface vector at any given time. Indicates kT c Real-time digital input deviation, u l (k i ) is k i T c The trigger control quantity at any given time, u l (k) is kT c The trigger control quantity at any given time.

[0066] In practice, the event-driven logarithmic sliding mode trajectory tracking control algorithm used in digital human-computer interaction is not triggered continuously; it is chosen to be triggered at time k. i T c Trigger control quantity u at time l (k i ) as the next moment (k) i +1)T c Actual trigger control quantity at any given time:

[0067]

[0068] Where, k i k represents the sampling time number at the i-th trigger. i+1 This represents the sampling time sequence number of the (i+1)th trigger, where i represents the number of triggers, and the numbers are accumulated starting from 0. Indicates the trigger time k i T c The trigger control quantity is calculated as follows:

[0069]

[0070] In the above expression, It is k i T c The expression related to the inertia matrix of the robotic arm's end effector at any given time. It describes k i T c The expression relating the Coriolis force and gravity term at the end effector of the robotic arm at any given moment. It is time k i T c The sliding surface vector at that time, It means (k) i +1)T c The tracking error at time t, where, This represents time (k) i +1)T c The sign of the tracking error. Indicates taking (k) i +1)T c Tracking error e(k) at time step i +1) A diagonal matrix formed by the elements on the diagonal. It is (k) i +1)T c The speed of the trajectory is constantly referenced. It is k i T c The speed of the trajectory is constantly referenced. This represents time k. i T c The sign of the tracking error at any given moment. Take k i T c Time tracking error e(k) i A diagonal matrix composed of the elements on the diagonal.

[0071] It should be noted that after step S103, the algorithm returns to step S101 to complete the closed-loop iteration, which ensures the stability of the digital human-computer interaction process under actual event triggering conditions. In addition, the algorithm provided by this invention can also effectively reduce system data throughput, improve data exchange efficiency, enhance the effectiveness of human-computer interaction, and reduce system energy consumption.

[0072] Based on the dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction according to Embodiment 1 of the present invention, a simulation of the motion state in the three dimensions of x-axis, y-axis, and z-axis in Cartesian coordinate system was performed. The simulation results are as follows: Figures 2-4 As shown, Figure 2 This is a simulation result of the reference trajectory tracking of the robotic arm in the x-dimensional of the Cartesian coordinate system provided in Embodiment 1 of the present invention. Figure 3 This is a simulation result of the reference trajectory tracking of the robotic arm in the y-dimensional of the Cartesian coordinate system provided in Embodiment 1 of the present invention. Figure 4 The simulation effect of the reference trajectory tracking of the robot arm in the z-dimensional of the Cartesian coordinate system provided in Embodiment 1 of the present invention.

[0073] from Figures 2-4 In trajectory tracking, it's evident that it takes approximately 6 seconds for the reference and desired trajectories to completely overlap from the initial state. During this process, the robotic arm's end effector can track the reference trajectory with high precision, providing operators with a smooth interactive experience.

[0074] from Figure 5 As can be easily seen from the figure, taking the trigger control quantity at the 5th to 6th trigger time as an example, the time interval between the 5th and 16th trigger time and the 5th trigger time in this interval is 0.16. There are no other trigger control quantities generated between the 5th and 16th trigger time and the 5th trigger time. It can be seen that the method proposed in this invention can ensure the tracking performance of the system under the condition of limited trigger input frequency. The steady-state error and dynamic response of the tracking process can meet the requirements of general human-computer interaction process.

Claims

1. A dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction, characterized in that, include: Step S101: Based on the logarithmic sliding mode trajectory tracking control model of continuous-time digital human-machine interaction, calculate the first trigger control quantity of the control force at the current moment according to the sliding surface vector of the end of the robotic arm at the current moment, the velocity of the reference trajectory at the current moment and the velocity of the reference trajectory at the next moment, the tracking error at the current moment and the tracking error at the next moment. Step S102: Calculate the time from time 0 to... according to the method in step S101. The first trigger control quantity at all trigger times; Step S103: From time 0 to Filter out all the trigger control quantities at any given time. The second trigger control quantity when the sliding surface vector at a given time satisfies the preset event-driven conditions is used as... The third trigger control quantity at a given time, wherein the third trigger control quantity is the actual trigger control quantity of the control force of the robotic arm to control the robotic arm, the... The time is the earliest time that satisfies the preset event-driven condition; Step S101: Based on the logarithmic sliding mode trajectory tracking control model of continuous-time digital human-machine interaction, the first trigger control quantity of the control force at the current moment is calculated according to the sliding surface vector of the robotic arm end effector at the current moment, the velocity of the reference trajectory at the current moment and the velocity of the reference trajectory at the next moment, the tracking error at the current moment and the tracking error at the next moment, including: Using the sliding surface vector at the current moment, the velocity of the reference trajectory at the current moment, the velocity of the reference trajectory at the next moment, the tracking error at the current moment, and the tracking error at the next moment as inputs to the logarithmic sliding mode trajectory tracking control model of continuous-time digital human-computer interaction as described below, the first trigger control quantity of the control force at the current moment is obtained: ， Wherein, the current time is The next moment is... time, for The first trigger control quantity at time [time]. for The sliding surface vector at time t, for The velocity of the reference trajectory at any given moment. for The velocity of the reference trajectory at any given moment. for Tracking error at any time, for Tracking error at any time, This represents a column vector where all elements are 1. It is the gain matrix of the first sliding surface. It is the gain matrix of the second sliding surface. yes The expression relating the Coriolis force and gravity term at the end of the robotic arm at that moment is given. yes The expression related to the inertia matrix of the robotic arm's end effector at any given time. It is the sliding mode control gain matrix.

2. The dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction as described in claim 1, characterized in that, The calculation method for the sliding mode surface quantity is as follows: ， in, for Tracking speed error at any given moment.

3. The dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction as described in claim 2, characterized in that, The The calculation method is as follows: ， Indicates time The speed of the robotic arm's end effector is collected in real time. yes The speed of the reference trajectory at all times.

4. The dynamic event-triggered logarithmic sliding mode control method for digital human-computer interaction as described in claim 3, characterized in that, The preset event-driven condition is: , , , in, yes Auxiliary parameters of time, It is the aforementioned The rate of change To preset the first constant value, To preset a second constant value, It means The deviation value of the sliding mode surface vector at any given time. express Constant digital input deviation for The trigger control quantity at any given time. for The trigger control quantity at any given time.

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