Modularized mechanical arm control method

Abstract

The invention discloses a modular mechanical arm control method, and relates to the field of mechanical arm control. According to the method, a system dynamic model of the modular mechanical arm is constructed, and then a system state equation is obtained; the uncertainty in the dynamic model is observed through a self-adaptive observation model; establishing an uncertainty performance index function; and obtaining an optimal control law # imgabs0 # triggered by an event according to the uncertainty performance index function, obtaining a derivative # imgabs1 # of the approximate performance index function by evaluating a neural network, and substituting the derivative # imgabs2 # of the approximate performance index function into # imgabs3 # in the optimal control law triggered by the event. The control precision of the modular mechanical arm is improved, and the service life of the system is prolonged.

Description

Technical Field

[0001] The present invention relates to the field of robot arm control, and in particular to a modular robot arm control method. Background Art

[0002] Robots replacing humans is an inevitable trend in the development of intelligence and automation at this stage. With the continuous progress of industrial development, modular robotic arms have been widely studied in aerospace, intelligent manufacturing and other fields due to their configuration advantages. Traditional time-triggered control mainly involves fixed sampling cycles and periodic data transmission. Whenever a large amount of data is transmitted, the system control performance will be affected. Therefore, for modular robotic arm systems with limited resources, it is necessary to save resources and extend their service life.

[0003] Modular robotic arm control usually adopts time-triggered control, which leads to a heavy computational burden on the system. In an environment with limited resources and energy, the control performance of the modular robotic arm system cannot be optimized, which increases the energy consumption burden. Summary of the invention

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

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

[0006]

[0007] Among them, the state variable q i and are the joint positions and joint velocities of each subsystem in the robotic arm system, respectively. i represents the uncertainty of the model, friction torque and cross-link coupling torque;

[0008] S2. observing the uncertainty in the dynamic model through an adaptive observation model;

[0009] S3, establish an uncertain performance index function, and obtain the optimal control law triggered by the event according to the uncertain performance index function:

[0010] S4. Obtain the derivative of the approximate performance index function by judging the neural network And the derivative of the approximate performance index function Substitute into the optimal control law triggered by the event

[0011] Furthermore, the system dynamic model is:

[0012]

[0013] Where i represents the i-th subsystem, I vi Expressed as the inertia in the actuator, γ i represents the harmonic speed ratio, q in the subsystem, denote angular position, velocity and acceleration respectively, represents the sum of friction terms between subsystems, represents the cross-coupling term between subsystems, τ si is the torque measured by the subsystem torque sensor, τ ai To control the torque.

[0014] Furthermore, the adaptive observer is:

[0015]

[0016] in, is the observed value, and is the setting observation gain; Represents uncertainty B i The estimated value of is:

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

[0018] S31. Constructing the uncertain performance index function as J i (v i (x i )):

[0019]

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

[0021] S32. The HJB equation for constructing time trigger is:

[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 the time trigger into an event trigger mode to obtain the optimal control law of the event trigger

[0028] Furthermore, the method for evaluating the neural network to obtain the derivative of the approximate performance index function includes:

[0029] S41. Establishing approximate performance index function

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

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

[0032] The partial derivative 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 manipulator system of the present invention is constrained by the hyperbolic tangent function, which not only solves the problem that the system control torque will increase sharply in the initial learning stage of the controller, making it difficult to achieve engineering applications, but also limits the system input and prolongs the service life of the motor. The uncertainty of the model is observed by an adaptive observer. Under the premise of introducing an event trigger 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 by the present invention can reduce the computational burden of the system, reduce the transmission of control signals beyond the maximum tolerance range and the number of updates of the control law. At the same time, it realizes the optimization of the control performance and energy consumption of the modular manipulator system working in a resource and energy-constrained environment, and improves the resource utilization of the modular manipulator.

[0036] The concept, specific structure and technical effects of the present invention will be further described below in conjunction with the accompanying drawings to fully understand the purpose, characteristics and effects of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

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

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

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

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

[0041] Figure 5 is a trigger condition and a trigger threshold curve of joint 1 in a specific embodiment of the present invention;

[0042] Figure 6 is a trigger condition and a trigger threshold curve of joint 2 in a specific embodiment of the present invention;

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

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

[0045] Fig. 9 is a torque curve of joint 1 under event-triggered optimization control in a specific embodiment of the present invention;

[0046] Fig.10 It is a torque curve under event-triggered optimization control of joint 2 in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0047] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents presented in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0048] It should be noted that the illustrations provided in the following embodiments are only used to illustrate the basic concept of the present invention in a schematic manner, and thus the illustrations only show components related to the present invention rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed arbitrarily, and the component layout may also be more complicated.

[0049] While some exemplary embodiments of the present invention have been described for the purpose of illustration, it should be understood that the present invention may be implemented in other ways not specifically shown in the drawings.

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

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

[0052] In this embodiment, based on the existing JTF technology, the dynamic model of the ith subsystem of the modular robotic arm is:

[0053]

[0054] Where i represents the i-th subsystem, I vi Expressed as the inertia in the actuator, γ i represents the harmonic speed ratio, q in the subsystem, denote angular position, velocity and acceleration respectively, represents the sum of friction terms between subsystems, represents the cross-coupling term between subsystems, τ si is the torque measured by the subsystem torque sensor, τ ai To control the torque.

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

[0056]

[0057] Among them, the state variable C i =(I vi γ i ) -1 ∈R + ;q i and are the position and velocity of each joint in the robotic arm system; B i Represents the uncertainty in the model, friction torque and cross-link coupling torque, including, u i (x i ) represents the control torque, which is n,ξ is a positive constant.

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

[0059] Joint friction torque It reflects the friction between the motor and the harmonic reducer, which is less affected by temperature and lubrication in practical applications, and the dynamic coupling torque generated in the system is less affected. Therefore, the friction torque and the interconnected dynamic coupling torque are always constant and bounded, and we can observe the uncertainty in the model by establishing an adaptive observer.

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

[0061]

[0062] in, is the observed value, and is the setting observation gain; Represents uncertainty B i The estimated value of is:

[0063]

[0064] Where η is a positive definite constant.

[0065] The model observation error is Combining (2) with (3), we obtain:

[0066]

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

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

[0069]

[0070] Calculating the time derivative of equation (6) yields:

[0071]

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

[0073] S3, establishing an uncertain performance indicator function, and obtaining an optimal control law triggered by an event according to the uncertain performance indicator function, specifically including:

[0074] S31. Constructing uncertain performance index function Ji (v i (x i )).

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

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

[0077]

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

[0079]

[0080] Among them, α i represents a normal number, Among them, v i (x i ) satisfies v i (x i (0)) = v i (0), its time derivative is:

[0081]

[0082] Based on formula (2), the improved uncertainty performance index function is defined as:

[0083]

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

[0085] S32. Construct the time-triggered HJB equation.

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

[0087]

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

[0089]

[0090] Among them, the partial derivative is

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

[0092]

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

[0094]

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

[0096]

[0097] S34, convert the time trigger into an event trigger mode to obtain the optimal control law of the event trigger

[0098] definition Through equation (16) and equation (17), we can get:

[0099]

[0100] Considering the non-periodic mode, the increment sequence By the triggering time t j Composition, 0 <t j <t j+1 , The sampling state equation of the system is:

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

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

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

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

[0105]

[0106] because is a discrete value that is continuously updated. In this embodiment, a zero-order holder is introduced to solve this problem. Define Substituting equation (21) into equation (14), the HJB equation for non-periodic update is constructed as follows:

[0107]

[0108] In this embodiment, for each state v ij , v ij ∈Ω, optimal tracking control law of the subsystem under decentralized control It is Lipschitz continuous, and there exists a positive constant β. The specific formula is as follows:

[0109]

[0110] S4. Obtain the derivative of the approximate performance index function by judging the neural network And the derivative of the approximate performance index function Substitute into the optimal control law triggered by the event Specifically include:

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

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

[0113] Taking partial derivative of formula (24) we get:

[0114]

[0115] in is Lipschitz continuous. Substituting equation (25) into the event-triggered optimization tracking notification shown in equation (21) yields:

[0116]

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

[0118]

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

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

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

[0122]

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

[0124]

[0125] According to equations (21) and (29), the partial derivative Replace the optimal control law triggered by the event The approximate non-periodic update optimal control law is obtained as:

[0126]

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

[0128]

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

[0130]

[0131] μ i M is a positive constant, satisfying ||μ i ||≤μ iM . Define the objective function is the minimization of the gradient descent algorithm, Update it with the following formula:

[0132]

[0133] is the approximate error of the evaluation, is a positive number and satisfies The update rule obtained using the gradient descent method is:

[0134]

[0135] The Lyapunov candidate function is selected as:

[0136]

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

[0138]

[0139] in, is the smallest eigenvalue of the matrix, When satisfied When the trigger condition shown in equation (37) is met, the relevant control law will be adjusted upward, and the weight of the critical NN will also be updated, which can ensure that the weight of the neural network The approximate error is UUB.

[0140] The optimal controller is updated in a non-periodic manner by violating the condition shown in (37).

[0141]

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

[0143] Based on the continuous-time modular manipulator system shown in equation (2), the time-triggered optimal approximate decentralized control law updates the weights as shown in equation (30), indicating that the closed-loop control system of the present invention is uniformly ultimately bounded. Since the modular manipulator system is a nonlinear continuous-time system, the minimum time interval Δt is defined as min satisfy: This shows that the robotic arm system can eliminate Zeno behavior and is stable.

[0144] In a specific embodiment, the modular robot arm is composed of a monitoring screen, a host, an emergency stop button, a linear power amplifier, a QPIDE data acquisition board, a joint torque sensor, a DC motor, an encoder, two joint modules and a connecting rod. Each joint module is composed of a DC motor, a joint torque sensor, an absolute encoder and a reducer. The rated voltage of the DC motor is 48V, the rated torque is 0.2Nm, the transmission ratio of the reducer in the DC motor is 100:1, and the torque sensor of the joint is responsible for measuring the torque of the joint. The signal programmed by the host computer is sent to the modular robot arm through the linear power amplifier, and in the internal structure of each joint, the DC motor will drive the modular robot arm to move as expected. Finally, all the collected data will be transmitted through the QPIDE data acquisition board. If an accident occurs during the operation of the system, the emergency stop button is pressed and the system will stop running, thereby reducing more serious damage to the motor.

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

[0146]

[0147] For the modular robotic arm subsystem, we define the neural network weights as: 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 give an initial value c1 and c2, respectively c1=[-1,-0.5,0,0.5,1] T , c2=[-2,-1,0,1,2] T In this embodiment, specific values ​​of other parameters are shown in Table 1.

[0148] Table 1: Control parameters

[0149]

[0150] Figure 1 and Figure 2 The following are the trajectory tracking curves of each joint of the modular manipulator using the control method based on input constraints. The red solid line and the blue dotted line represent the expected trajectory curve and the actual trajectory curve when the system is running. It can be seen from the figure that the actual trajectory of each joint can track the expected trajectory well, with good tracking effect. The motion trajectory errors of the two joints are shown in Figure 3 and Figure 4 As shown in the figure, it can be seen from the trajectory tracking error curve that in the initial state, since the system needs a certain amount of learning time, a large error will occur, but then the error will gradually decrease and remain within an acceptable range.

[0151] The trigger conditions and trigger thresholds of each joint are as follows: Figure 5 and Figure 6 As shown. The red asterisk line indicates the trigger threshold of the system, and the blue dotted line indicates the trigger condition. In the enlarged sub-graph, when the trigger condition intersects the trigger threshold, the pre-set trigger condition is reached, the event is triggered, the system will sample, and the controller state is also updated at this time. Otherwise, the system will maintain the sampling state of the previous moment until the next trigger condition coincides with the trigger threshold again. This control method reduces the sampling times of the modular robot arm and saves communication resources between systems.

[0152] Figure 7 and Figure 8 They are the optimal control torque curves of the two joints of the modular robot arm using the traditional method. Fig. 9 and Fig.10This is the optimal control torque curve of the joint using the control algorithm proposed in this article. It can be seen that using the control method proposed in this embodiment, the control torque change of each joint follows a non-periodicity, and the control torque can last 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 adopted in this embodiment reduces the number of updates of the control strategy in the controller, shortens the information exchange time between the control system and the motor, and extends the service life of the motor. Fig. 9 and Fig.10 It can be seen from the partially enlarged sub-figure that the control method adopted in this embodiment limits the input torque of the modular robot arm system to within 0.15Nm, and the trajectory tracking error of the modular robot arm system is still within the allowable range. The control method adopted in the embodiment can avoid the large torque generated by the controller during the initial learning process from causing damage to the motor, and improve the practicality and reliability of the modular robot arm control system. It can be seen that the control method adopted in this embodiment reduces the amplitude and frequency of the control torque, improves the control accuracy of the modular robot arm, and extends the service life of the system.

[0153] The present invention can solve the trajectory tracking control law of the modular manipulator under the actuator saturation state. Firstly, based on the JTF technology, a dynamic model is established using a measurable model, and the model uncertainty in the system is observed using an adaptive observer. Constraints are introduced into the performance index function to control the saturation of the actuator. Under the event trigger mechanism, the optimal decentralized control law can be obtained by constructing a critical neural network to solve the HJB equation.

[0154] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may 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 a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. A modular robotic arm control method, characterized in that: The steps include: S1. Build a system dynamic model of the modular robotic arm, and then get the system state equation as follows: Among them, the state variable q i and are the angular position and velocity of each joint in the robotic arm system, B i Represents the uncertainty of the model, friction torque and cross-link coupling torque; S2. observing the uncertainty in the dynamic model through an adaptive observation model; S3, establish an uncertain performance index function, and obtain the optimal control law triggered by the event according to the uncertain performance index function: S4. Obtain the derivative of the approximate performance index function by judging the neural network And the derivative of the approximate performance index function Substitute into the optimal control law triggered by the event 2. A modular robotic arm control method according to claim 1, characterized in that: The system dynamic model is: Where i represents the i-th subroutine, I vi Expressed as the inertia in the actuator, γ i Expressed as harmonic speed ratio, q in the subroutine, denote angular position, velocity and acceleration respectively, represents the sum of friction terms between subroutines, represents the cross-coupling term between subsystems, τ si is the torque measured by the torque sensor of the subroutine, τ ai To control the torque.

3. A modular robotic arm control method according to claim 1, characterized in that: The adaptive observer is: in, is the observed value, and is the setting observation gain; Represents uncertainty B i The estimated value of is:

4. A modular robotic arm control method according to claim 1, characterized in that: The method for obtaining the event-triggered optimal control law includes: S31. Constructing the uncertain performance index function as J i (v i (x i )): Among them, v i (x i )=v i is the fusion error function; S32. The HJB equation for constructing time trigger is: S33. Optimal performance index function under optimal conditions for: By solving the HJB equation, the optimal control law under time triggering is obtained: S34, convert the time trigger into an event trigger mode to obtain the optimal control law of the event trigger 5. A modular robotic arm control method according to claim 4, characterized in that: The method for evaluating the derivative of the neural network to obtain the approximate performance index function includes: S41. Establishing approximate performance index function Among them, W Fi represents the weight vector of the neural network, W Fi The estimated value of represents the activation function; S42. Partial derivatives of approximate performance index functions for: The partial derivative Replace the optimal control law triggered by the event

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