Modular robotic arm control method

Abstract

The application discloses a kind of modular mechanical arm control methods, it is related to mechanical arm control field.The application constructs the system dynamic model of modular mechanical arm, and then obtains system state equation;The uncertainty in the dynamic model is observed by adaptive observation model;Establish the uncertain performance index function, and obtain the optimal control law of event triggering according to the uncertain performance index function is by judging neural network to obtain the derivative of approximate performance index function and the derivative of approximate performance index function is substituted into the optimal control law of event triggeringThe amplitude and frequency of the control torque can be reduced by the application, the control precision of modular mechanical arm is improved, and the service life of the system is prolonged.

Description

Technical Field

[0001] This invention relates to the field of robotic arm control, and more particularly to a modular robotic arm control method. Background Technology

[0002] The replacement of humans by robots is an inevitable trend in the current development of intelligence and automation. With the continuous progress of industrial development, modular robotic arms, due to their configuration advantages, have been widely studied in fields such as aerospace and intelligent manufacturing. Traditional time-triggered control mainly involves fixed sampling periods and periodic data transmission. Whenever large amounts of data are transmitted, the system control performance is affected. Therefore, for modular robotic arm systems with limited resources, it is necessary to conserve resources and extend their service life.

[0003] Modular robotic arm control typically employs time-triggered control, which results in a significant computational burden on the system. In resource- and energy-constrained environments, the control performance of modular robotic arm systems cannot be optimized, increasing energy consumption. Summary of the Invention

[0004] In view of the above-mentioned deficiencies of the prior art, the present invention provides a modular robotic arm control method, comprising the following steps:

[0005] S1. Construct a system dynamic model of the modular robotic arm, and then obtain the system state equation as follows:

[0006]

[0007] Among them, state variables q i and These represent the joint positions and joint velocities of each subsystem in the robotic arm system, B. i Uncertainties in the representative model, frictional torque, and cross-linking coupling torque;

[0008] S2. Observe the uncertainties in the dynamic model through an adaptive observation model;

[0009] S3. Establish an uncertain energy index function, and obtain the optimal control law for event triggering based on the uncertain energy index function.

[0010] S4. Obtain the derivative of the approximate performance index function through the evaluation neural network. And the derivative of the approximate performance index function Substituting into the optimal control law for the event triggering described above

[0011] Furthermore, the system dynamic model is as follows:

[0012]

[0013] Where i represents the i-th subsystem, I vi Represented as the inertial quantity in the actuator, γ i Indicating the harmonic speed ratio, q in the subsystem, These represent angular position, velocity, and acceleration, respectively. This represents the sum of friction terms between subsystems. τ represents the cross-linking coupling term between subsystems. si The torque τ is measured by the torque sensor of the subsystem. ai To control the torque.

[0014] Furthermore, the adaptive observer is:

[0015]

[0016] in, For the observed values, and To tune the observation gain; Representing uncertainty B i The estimated value is:

[0017] Furthermore, the method for obtaining the event-triggered optimal control law includes:

[0018] S31. Construct an uncertainty energy index function J. i (v i (x i )):

[0019]

[0020] Among them, v i (x i ) = v i This is the fusion error function;

[0021] S32. The time-triggered HJB equation is constructed as follows:

[0022]

[0023] S33. Optimal performance index function under optimal conditions for:

[0024]

[0025] By solving the HJB equation, the optimal control law under time triggering is obtained:

[0026]

[0027] S34. Convert time-triggered mode into event-triggered mode to obtain the optimal control law for event-triggered mode.

[0028] Furthermore, the method for obtaining the derivative of the approximate performance index function from the evaluation neural network includes:

[0029] S41. Establish an approximate performance index function.

[0030] Among them, W Fi The weight vector representing the neural network. On behalf of W Fi The table estimates, Represents the activation function;

[0031] S42. Partial derivatives of the approximate performance index function for:

[0032] partial derivatives Replace the optimal control law triggered by the event

[0033] Compared with the prior art, the present invention has the following technical effects:

[0034] 1. The input of the modular robotic arm system of this invention is constrained by a hyperbolic tangent function. This not only solves the problem of a sharp increase in system control torque during the initial learning phase of the controller, making it difficult to implement in engineering applications, but also limits the system input and extends the service life of the motor. The uncertainty of the model is observed by an adaptive observer. With the introduction of an event-triggered mechanism, the ADP control algorithm is adopted to better control the system and save communication resources between the operating system and the controller. The Lyapunov function ensures the stability of the closed-loop system.

[0035] 2. The event-triggered optimization control method adopted in this invention can reduce the computational burden of the system, decrease the transmission of control signals beyond the maximum tolerance range, and reduce the number of control law updates. Simultaneously, it optimizes the control performance and energy consumption of the modular robotic arm system operating in resource- and energy-constrained environments, thereby improving the resource utilization rate of the modular robotic arm.

[0036] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0037] Figure 1 This is a position tracking curve of joint 1 in a specific embodiment of the present invention;

[0038] Figure 2 This is a position tracking curve of joint 2 in a specific embodiment of the present invention;

[0039] Figure 3 This is a trajectory tracking error curve of joint 1 in a specific embodiment of the present invention;

[0040] Figure 4 This is a trajectory tracking error curve of joint 2 in a specific embodiment of the present invention;

[0041] Figure 5 This is a specific embodiment of the present invention, showing the triggering conditions and triggering threshold curves for joint 1;

[0042] Figure 6 This is a specific embodiment of the present invention, showing the triggering conditions and triggering threshold curves for joint 2;

[0043] Figure 7 This is a torque curve under time-triggered optimized control of joint 1 in a specific embodiment of the present invention;

[0044] Figure 8 This is a torque curve under time-triggered optimized control of joint 2 in a specific embodiment of the present invention;

[0045] Figure 9 This is a torque curve under event-triggered optimized control of joint 1 in a specific embodiment of the present invention;

[0046] Figure 10 This is a torque curve of joint 2 under event-triggered optimized control in a specific embodiment of the present invention. Detailed Implementation

[0047] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content presented in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that, unless otherwise specified, the following embodiments and features described therein can be combined with each other.

[0048] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the illustrations only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0049] Some exemplary embodiments of the invention have been described for illustrative purposes. It should be understood that the invention may be implemented in other ways not specifically shown in the accompanying drawings.

[0050] In one specific embodiment, a modular robotic arm control method is provided, comprising the following steps:

[0051] S1. Construct a system dynamic model of the modular robotic arm, and then obtain the system state equation.

[0052] In this embodiment, based on existing JTF technology, the dynamic model of the i-th subsystem of the modular robotic arm is as follows:

[0053]

[0054] Where i represents the i-th subsystem, I vi Represented as the inertial quantity in the actuator, γ i Indicating the harmonic speed ratio, q in the subsystem, These represent angular position, velocity, and acceleration, respectively. This represents the sum of friction terms between subsystems. τ represents the cross-linking coupling term between subsystems. si The torque τ is measured by the torque sensor of the subsystem. ai To control the torque.

[0055] Based on the subsystem dynamic model described in equation (1), the system state equation is obtained as shown in equation (2).

[0056]

[0057] Among them, state variables C i =(I vi γ i ) -1 ∈R + ;q i and These represent the position and velocity of each joint in the robotic arm system; B i Uncertainties representing the model, frictional torque, and cross-linking coupling torque include, u i (x i ) represents control torque, which is n and ξ are positive constants.

[0058] S2. Observe the uncertainties in the dynamic model through an adaptive observation model.

[0059] Joint friction torque This reflects the friction of the motor and harmonic reducer, which is less affected by temperature and lubrication in practical applications, and the dynamic coupling torque generated in the system has a relatively small impact. Therefore, the frictional torque and the interconnected dynamic coupling torque are always constant and bounded, and we can observe the uncertainties in the model by establishing an adaptive observer.

[0060] For the uncertainties in the subsystem model shown in equation (2), an adaptive observer is involved in a specific embodiment:

[0061]

[0062] in, For the observed values, and To tune the observation gain; Representing uncertainty B i The estimated value is:

[0063]

[0064] Where η is a positive definite constant.

[0065] Model observation error is Combining (2) and (3), we get:

[0066]

[0067] Among them, e B Reporting nonlinear term B i The observation error is:

[0068] The Lyapunov candidate function is defined as follows:

[0069]

[0070] Calculate the time derivative of equation (6) and obtain:

[0071]

[0072] visible, hour, It is explained that for the modular robotic arm subsystem shown in equation (2), the uncertainty in the model can be estimated by the adaptive update law (4) and the adaptive observer (3), and the model observation error is guaranteed to be UUB.

[0073] S3. Establish an uncertain energy index function, and obtain the optimal control law for event triggering based on the uncertain energy index function, specifically including:

[0074] S31. Constructing the uncertainty index function Ji (v i (x i )).

[0075] For the state equation (2) of the modular robotic arm, the tracking error e is defined. ai and for:

[0076] e ai =x 1i -q di (8)

[0077]

[0078] in, e represents the tracking error of the joint velocity of the i-th subsystem; ai q represents the joint position tracking error of the i-th subsystem; di and Represent the desired position and desired velocity of the joint in the i-th subsystem, respectively; define the fusion error function v. i (x i )for:

[0079]

[0080] Where, α i Represents a positive constant. Among them, v i (x i Satisfying v i (x i (0))=v i (0), its time derivative is:

[0081]

[0082] Based on equation (2), the improved uncertainty energy exponential function is defined as follows:

[0083]

[0084] Where, θ i Represents a positive constant; This represents the uncertainty estimate of the adaptive model, where Q is a positive definite matrix; Represents the inverse function of the hyperbolic tangent, q = [q i1 ,q i2 ,...,q in ] T .

[0085] S32. Construct time-triggered HJB equations.

[0086] The solution for the non-quadratic utility function is:

[0087]

[0088] R i R represents a positive definite diagonal matrix. i =diag(r) i 1, r i 2, ..., r in )>0, R i ∈R n×n , R represents a row vector whose elements consist of a diagonal matrix. i ,for Then, the time-triggered HJB function is constructed as shown in (14):

[0089]

[0090] Where, the partial derivative is

[0091] S33. Optimal performance index function under optimal conditions for:

[0092]

[0093] Substituting equation (15) into equation (14), we get:

[0094]

[0095] Therefore, the optimal control law under time triggering is obtained:

[0096]

[0097] S34. Convert time-triggered mode into event-triggered mode to obtain the optimal control law for event-triggered mode.

[0098] definition We obtain the following from equations (16) and (17):

[0099]

[0100] Considering the aperiodic approach, incremental sequences From the trigger time t j Composition, 0 <t j <t j+1 , The system's sampled state equation is:

[0101] v ij (xij ) = v i (x i (t j ))=v ij (19)

[0102] v ij (x ij ) is time t∈[t j , t j+1 For the sampled data components within a given range, in order to obtain appropriate event triggering conditions, a gap function is defined as the difference between the actual state and the sampled state. The gap function is:

[0103] e ij (t)=v ij (x ij )-v i (x i (20)

[0104] In this embodiment, the triggering condition is obtained through a gap function. When the triggering condition is activated, the state of the subsystem is sampled and updated again, and the time-triggered state error e is recorded. ij (t) is reset to zero. In this case, through the sampled state mapping of the zero-order hold, the distributed tracking control is converted into piecewise continuous-time input signals, and the control strategy is updated to... In the time region t∈[t j , t j+1 ), j∈N, combined with the time-triggered optimal control law shown in equation (17), the event-triggered distributed optimal tracking control law is:

[0105]

[0106] because These are continuously updated discrete values. In this embodiment, a zero-order hold is introduced to solve this problem. The definition is... Substituting equation (21) into equation (14), the non-periodic HJB equation is constructed as follows:

[0107]

[0108] In this embodiment, for each state v ij v ij ∈Ω, the optimal tracking control law of the subsystem under distributed control It is Lipschitz continuous and has a positive constant β, as shown in the following formula:

[0109]

[0110] S4. Obtain the derivative of the approximate performance index function through the evaluation neural network. And the derivative of the approximate performance index function Substituting into the optimal control law for the event triggering described above Specifically, it includes:

[0111] S41. Based on the event-triggered mechanism, an approximate performance index function is established to solve the HJB function.

[0112] Among them, W Fi ∈R c This represents the weight vector of the neural network, where c represents the total number of neurons. It is W Fi The estimated value, Represents the activation function, which satisfies ε is a positive constant. Fi For the approximation error, ε Fimax It is a positive constant and satisfies ||ε Fi (v ij )||≤ε Fimax .

[0113] Taking the partial derivative of equation (24), we get:

[0114]

[0115] in It is Lipschitz continuous. Substituting equation (25) into equation (21) shows the event-triggered optimized tracking notification:

[0116]

[0117] Combining equations (22) and (26), the HJB equation for the expected event triggering is obtained as follows:

[0118]

[0119] in, e is the approximate residual of the neural network (NN). FSi Satisfy ||e FSi ||≤e FSimax , where e FSimax It is a positive number.

[0120] S42. Establish the partial derivatives of the approximate performance index function.

[0121] Because in an ideal neural network, the weight vector W Fi Since it is unknown, an approximate performance index function is established as follows:

[0122]

[0123] Among them, J i (v ij ) and W Fi The estimated values ​​are respectively and right partial derivatives for:

[0124]

[0125] According to equations (21) and (29), the partial derivatives Replace the optimal control law triggered by the event The approximately aperiodic update optimal control law is obtained as follows:

[0126]

[0127] Combining (22) and (30), the approximate event-triggered HJB equation is:

[0128]

[0129] According to equation (31), we define:

[0130]

[0131] μ i M is a positive constant that satisfies ||μ i ||≤μ iM Define the objective function. To minimize the gradient descent algorithm, Update using the following formula:

[0132]

[0133] To assess the approximate error, It is a positive integer and satisfies The update pattern obtained using gradient descent is as follows:

[0134]

[0135] The Lyapunov candidate function is selected as follows:

[0136]

[0137] Considering (35), the time derivative of V2(t) can be obtained as:

[0138]

[0139] in, It is the smallest eigenvalue of the matrix. When satisfied At that time, the approximation error of the evaluation neural network is UUB. When the triggering condition shown in equation (37) is met, the relevant control law will be increased, and the weights of the critical NN will also be updated, which can guarantee the weights of the neural network. The approximation error is UUB.

[0140] The optimal controller is updated in an aperiodic manner by violating the condition shown in (37).

[0141]

[0142] Where β represents the sampling frequency parameter, and 0 < β < 1.

[0143] Based on the continuous-time modular robotic arm system as shown in Equation (2), and the time-triggered optimal approximate distributed control law updating weights as shown in Equation (30), it is shown that the closed-loop control system of the present invention is uniformly eventually bounded. Since the modular robotic arm system is a nonlinear continuous-time system, a minimum time interval Δt is defined. min satisfy: This demonstrates that the robotic arm system can eliminate Zeno's behavior and possesses stability.

[0144] In one specific embodiment, the modular robotic arm comprises a monitoring screen, a host computer, an emergency stop button, a linear power amplifier, a QPIDE data acquisition board, joint torque sensors, a DC motor, an encoder, two joint modules, and connecting rods. Each joint module consists of a DC motor, a joint torque sensor, an absolute encoder, and a reducer. The DC motor has a rated voltage of 48V and a rated torque of 0.2Nm. The reducer in the DC motor has a transmission ratio of 100:1, and the torque sensor at the joint is responsible for measuring the torque of the joint. The signals programmed by the host computer are sent to the modular robotic arm through the linear power amplifier. Within the internal structure of each joint, the DC motor drives the modular robotic arm to move as expected. Finally, all collected data is transmitted through the QPIDE data acquisition board. If an accident occurs during system operation, pressing the emergency stop button will stop the system, thereby reducing further damage to the motors.

[0145] In this embodiment, we designed a trajectory tracking control task using a modular robotic arm experimental platform, verifying the efficiency of the event-triggered optimization control method based on constraint input. The expected trajectory of each joint was designed as follows:

[0146]

[0147] For the modular robotic arm subsystem, we define the neural network weights as follows: The initial value of joint 1 is The initial value of joint 2 is The neural network used is a 151-critical neural network with one input layer, five hidden layers, and one output layer, and its activation function is: Where b j =1.5, j = 1, 2, 3, 4, 5; and given initial values ​​c1 and c2, where c1 = [-1, -0.5, 0, 0.5, 1] T c2 = [-2, -1, 0, 1, 2] T In this embodiment, the specific values ​​of other parameters are shown in Table 1.

[0148] Table 1: Control Parameters

[0149]

[0150] Figure 1 and Figure 2 The figures show the trajectory tracking curves of each joint of a modular robotic arm using an input constraint-based control method. The red solid line and blue dashed line represent the expected trajectory curve and the actual trajectory curve during system operation, respectively. As can be seen from the figures, the actual trajectory of each joint tracks the expected trajectory very well, demonstrating good tracking performance. The motion trajectory errors of the two joints are shown below. Figure 3 and Figure 4 As shown in the curve, the trajectory tracking error shows that in the initial state, the system requires a certain learning time, resulting in a large error. However, the error gradually decreases and remains within an acceptable range.

[0151] The triggering conditions and triggering thresholds for each joint are as follows: Figure 5 and Figure 6 As shown in the diagram, the red asterisk line represents the system's trigger threshold, and the blue dashed line represents the trigger condition. In the enlarged sub-diagram, when the trigger condition intersects with the trigger threshold, the pre-set trigger condition is met, the event is triggered, the system samples, and the controller's state is updated. Otherwise, the system maintains the sampling state from the previous moment until the next trigger condition coincides with the trigger threshold. This control method reduces the number of samples taken by the modular robotic arm and saves communication resources between systems.

[0152] Figure 7 and Figure 8 These are the optimal control torque curves for two joints of a modular robotic arm using traditional methods. Figure 9 and Figure 10This represents the optimal control torque curve for the joint using the control algorithm proposed in this paper. It can be seen that, using the control method proposed in this embodiment, the control torque change of each joint follows a non-periodic pattern, and the control torque can persist for a period of time. When there is no trigger, the control torque of the two joints will remain unchanged until the next trigger occurs. Therefore, the control method used in this embodiment reduces the number of times the control strategy in the controller is updated, shortens the information exchange time between the control system and the motor, and extends the service life of the motor. Figure 9 and Figure 10 As can be seen from the enlarged sub-figures, the control method used in this embodiment limits the input torque of the modular robotic arm system to within 0.15 Nm, and the trajectory tracking error of the modular robotic arm system remains within the allowable range. The control method used in this embodiment can avoid motor damage caused by large torque generated during the initial learning process of the controller, thus improving the practicality and reliability of the modular robotic arm control system. It is evident that the control method used in this embodiment reduces the amplitude and frequency of the control torque, improves the control accuracy of the modular robotic arm, and extends the service life of the system.

[0153] This invention can solve the trajectory tracking control law of a modular robotic arm under actuator saturation conditions. First, based on JTF technology, a dynamic model is established using a measurable model, and an adaptive observer is used to observe model uncertainties in the system. Constraints are introduced into the performance index function to control the actuator saturation. Under an event-triggered mechanism, the optimal distributed control law can be obtained by constructing a critical neural network to solve the HJB equations.

[0154] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. Any person skilled in the art can modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in the present invention should still be covered by the claims of the present invention.

Claims

1. A modular robotic arm control method, characterized in that, Includes the following steps: S1. Construct the system dynamic model of the modular robotic arm as follows: ； Where i represents the i-th subsystem, Represented as the inertial quantity in the actuator, Expressed as harmonic speed ratio, in the subsystem These represent angular position, velocity, and acceleration, respectively. This represents the sum of friction terms between subsystems. This indicates the cross-linking and coupling terms between the subsystems. For the torque of the subsystem, To control the torque; The system state equation is then obtained as follows: ； Among them, state variables , and B represents the angular position and velocity of each joint in the robotic arm system. i This represents the uncertainty of the model, friction torque, and cross-linking coupling torque; Represents control torque; S2. Observe the uncertainties in the dynamic model through an adaptive observation model; S3. Establish an uncertain energy index function, and obtain the optimal control law for event triggering based on the uncertain energy index function, specifically including: S31. Construct the uncertainty energy index function as follows: : ； Among them, v i (x i ) = v i This is the fusion error function; Represents a positive constant; This represents the uncertainty estimate of the adaptive model, Q=Q T It is a positive definite matrix; , Represents the inverse function of the hyperbolic tangent. ;R i R represents a positive definite diagonal matrix. i =diag(r i1 r i2 , ..., r in )>0, ξ i It is a positive number; S32. Optimal performance index function under optimal conditions for: ； S33. The time-triggered HJB equation is constructed as follows: ； By solving the HJB equation, the optimal control law under time triggering is obtained: ； S34. Convert time-triggered mode into event-triggered mode to obtain the optimal control law for event-triggered mode. for: ； S4. Obtain the derivative of the approximate performance index function through the evaluation neural network. And the derivative of the approximate performance index function Substituting into the optimal control law for the event triggering described above .

2. The modular robotic arm control method according to claim 1, characterized in that, The adaptive observation model is as follows: ； in, For the observed values, and For tuning the observation gain; uncertainty B i The estimated value The estimation method is as follows: , where 𝜂 is a positive definite constant.

3. The modular robotic arm control method according to claim 1, characterized in that, The method for obtaining the derivative of the approximate performance index function by the evaluation neural network includes: S41. Establish an approximate performance index function. : ; in, The weight vector representing the neural network. for The estimated value, Represents the activation function; S42. Partial derivatives of the approximate performance index function for: ; partial derivatives Replace the optimal control law triggered by the event .

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