Mechanical arm trajectory tracking control method and device, electronic equipment and medium

Abstract

The invention provides a mechanical arm trajectory tracking control method and device, electronic equipment and a medium, and relates to the field of mechanical arm control. The method comprises the steps that an expected track and an actual track of the mechanical arm are obtained; according to the expected track and the actual track of the mechanical arm, a non-singular fast terminal sliding mode surface and a switching control law of the non-singular fast terminal sliding mode surface are determined; inputting the expected trajectory, the actual trajectory and the nonsingular fast terminal sliding mode surface into an equivalent control law output model to obtain an equivalent control law; and according to the equivalent control law and the switching control law, the mechanical arm is controlled, and a target track is obtained. The trajectory tracking precision of the mechanical arm is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of robotic arm control, and more specifically, to a robotic arm trajectory tracking control method, device, electronic equipment, and medium. Background Art

[0002] A robotic arm is an advanced automated mechanical device that integrates a mechanical structure, drive system, control system, and sensors. It features multiple inputs and outputs, high nonlinearity, and strong coupling, making it widely used in various fields, including industry, healthcare, and aerospace. Most tasks require the robotic arm to track the desired trajectory with high precision. However, model errors and parameter uncertainties in the dynamics of the robotic arm make it difficult to achieve high-precision tracking. Summary of the Invention

[0003] In view of this, the present invention provides a robot arm trajectory tracking control method, device, electronic equipment and medium capable of improving the robot arm trajectory tracking accuracy.

[0004] One aspect of the present invention provides a robot arm trajectory tracking control method, including: obtaining the expected trajectory and actual trajectory of the robot arm; determining the non-singular fast terminal synovial surface and the switching control law of the non-singular fast terminal synovial surface based on the expected trajectory and actual trajectory of the robot arm; inputting the expected trajectory, the actual trajectory and the non-singular fast terminal synovial surface into an equivalent control law output model to obtain an equivalent control law; controlling the robot arm according to the equivalent control law and the switching control law to obtain a target trajectory.

[0005] According to an embodiment of the present invention, the function of the non-singular fast terminal synovial surface is: Among them, S represents the sliding surface function, e is the joint error, p and k are both positive odd numbers, and c is a constant. is the joint angular velocity error, ν is a constant less than 0, and μ is a constant greater than 0.

[0006] According to an embodiment of the present invention, the function of the switching control law is: sw =k1*S+k2*tanh(S); where τ sw represents the switching control law; S represents the sliding surface function; tanh(S) function is the hyperbolic tangent function; k1 and k2 are both constants greater than 0.

[0007] According to an embodiment of the present invention, the above-mentioned robotic arm is controlled according to the above-mentioned equivalent control law and the above-mentioned switching control law to obtain a target trajectory, including: obtaining a total control law by adding the above-mentioned equivalent control law and the above-mentioned switching control law; constructing a dynamic model of the robotic arm; inputting the above-mentioned total control law into the above-mentioned dynamic model to obtain the target angle, target angular velocity and target angular acceleration of each joint of the above-mentioned robotic arm.

[0008] According to an embodiment of the present invention, the dynamic model of the robotic arm is constructed using the Lagrangian method.

[0009] According to an embodiment of the present invention, the dynamic model of the above-mentioned robotic arm is: Among them, M(q) is the positive definite symmetric inertia matrix of the robot arm; q is the angle of each joint of the robot arm, is the angular velocity of each joint of the robotic arm, is the angular acceleration of each joint of the robotic arm, is the Coriolis force and centrifugal force matrix of the robot arm; G(q) is the gravity matrix of the robot arm; F is the sum of the model error and parameter uncertainty factors of the robot arm; τ is the control law input of the robot arm.

[0010] According to an embodiment of the present invention, the above-mentioned equivalent control law output model adopts a radial basis function neural network model.

[0011] Another aspect of the present invention provides a robot arm trajectory tracking control device, including: an acquisition module for acquiring the expected trajectory and actual trajectory of the robot arm; a synovial surface construction module for determining the non-singular fast terminal synovial surface and the switching control law of the non-singular fast terminal synovial surface based on the expected trajectory and actual trajectory of the above-mentioned robot arm; a control law determination module for inputting the above-mentioned expected trajectory, the above-mentioned actual trajectory and the above-mentioned non-singular fast terminal synovial surface into an equivalent control law output model to obtain an equivalent control law; a control module for controlling the above-mentioned robot arm according to the above-mentioned equivalent control law and the above-mentioned switching control law to obtain the target trajectory.

[0012] Another aspect of the present invention provides an electronic device, comprising: one or more processors; and a memory for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the above-mentioned method.

[0013] Another aspect of the present invention provides a computer-readable storage medium storing computer-executable instructions, which are used to implement the above method when executed.

[0014] According to an embodiment of the present invention, in order to improve the trajectory tracking accuracy of a six-degree-of-freedom robotic arm, a dynamic model of the robotic arm is constructed, and a non-singular fast terminal sliding mode surface is designed to improve the convergence speed of trajectory tracking and solve the singularity problem of sliding mode control; an equivalent control law output model is used to comprehensively approximate and compensate for parameter uncertainty factors, thereby achieving the effect of improving the trajectory tracking accuracy of the six-degree-of-freedom robotic arm. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] The above and other objects, features and advantages of the present invention will become more apparent through the following description of the embodiments of the present invention with reference to the accompanying drawings, in which:

[0016] Figure 1 The flowchart of the robot arm trajectory tracking control method according to an embodiment of the present invention is schematically shown.

[0017] Figure 2 The figure schematically shows the overall structure of a robotic arm according to an embodiment of the present invention.

[0018] Figure 3 The figure schematically shows the joint coordinates of a robotic arm according to an embodiment of the present invention.

[0019] Figure 4 The structure of a radial basis function neural network according to an embodiment of the present invention is schematically shown.

[0020] Figure 5 The figure schematically shows an overall principle block diagram of a collaborative controller according to an embodiment of the present invention.

[0021] Figure 6 A schematic diagram of the tracking change curves of the first three joint angles of a six-degree-of-freedom robotic arm trajectory tracking according to an embodiment of the present invention is shown schematically.

[0022] Figure 7 A schematic diagram of a tracking error variation curve of the first three joints of a six-degree-of-freedom robotic arm trajectory tracking according to an embodiment of the present invention is shown schematically.

[0023] Figure 8 A schematic diagram of actual operating angular velocity curves of the first three joints of a six-degree-of-freedom robotic arm trajectory tracking according to an embodiment of the present invention is shown.

[0024] Figure 9 A schematic diagram of the angular velocity tracking error curves of the first three joints of a six-degree-of-freedom robotic arm trajectory tracking according to an embodiment of the present invention is shown schematically.

[0025] Figure 10 A schematic diagram of the tracking effect of the end flange of a six-degree-of-freedom robotic arm according to an embodiment of the present invention is shown schematically.

[0026] Figure 11A block diagram schematically shows a robot arm trajectory tracking control device according to an embodiment of the present invention.

[0027] Figure 12 A block diagram of an electronic device suitable for implementing a robot arm trajectory tracking control method according to an embodiment of the present invention is schematically shown. DETAILED DESCRIPTION

[0028] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings. However, it should be understood that these descriptions are exemplary only and are not intended to limit the scope of the present invention. In the following detailed description, for ease of explanation, many specific details are set forth to provide a comprehensive understanding of embodiments of the present invention. However, it is apparent that one or more embodiments may also be implemented without these specific details. In addition, in the following description, descriptions of known structures and technologies are omitted to avoid unnecessary confusion of the concept of the present invention.

[0029] The terms used herein are only for describing specific embodiments and are not intended to limit the present invention. The terms "comprise", "include", etc. used herein indicate the presence of the features, steps, operations and / or components, but do not exclude the presence or addition of one or more other features, steps, operations or components.

[0030] All terms used herein (including technical and scientific terms) have the meanings commonly understood by those skilled in the art unless otherwise defined. It should be noted that the terms used herein should be interpreted as having a meaning consistent with the context of this specification and should not be interpreted in an idealized or overly rigid manner.

[0031] When expressions such as "at least one of A, B and C, etc." are used, they should generally be interpreted in accordance with the meaning of the expression commonly understood by those skilled in the art (for example, "a system having at least one of A, B and C" should include but is not limited to a system having A alone, B alone, C alone, A and B, A and C, B and C, and / or A, B, C, etc.).

[0032] To address the low trajectory tracking accuracy of six-degree-of-freedom manipulators, various manipulator control methods have been proposed, including fuzzy control, disturbance observer control, robust control, and sliding mode control. To address the low trajectory tracking accuracy of multi-degree-of-freedom manipulators, a control method based on a radial basis function neural network combined with a terminal sliding mode control scheme was proposed. This method achieves model-free control and achieves a maximum average steady-state error of 0.005 rad. However, its computational complexity is high, making it difficult to implement real-time control. To address model uncertainty and external disturbances and improve manipulator trajectory tracking accuracy, a block approximation neural network based on a dynamic model and terminal sliding mode control was proposed. This method enables model reconstruction and achieves a maximum average steady-state error of 0.0073 rad. However, its design is complex, and insufficient coordination between subnetworks can easily lead to systematic errors. To address the impact of model errors and uncertain disturbances on manipulator tracking accuracy, a novel adaptive neural network sliding mode control strategy was proposed. This method avoids excessive system jitter and ensures tracking accuracy, achieving a maximum average steady-state error of 0.0372 rad. However, the nominal model cannot be accurately determined. To achieve more stable trajectory tracking for the robot arm, a fuzzy sliding mode switching gain control was proposed. This method effectively improved tracking stability, but fuzzy control relies too much on experience. To improve the tracking accuracy of the robot arm, a fractional-order PID algorithm was designed, which effectively improved tracking accuracy, with a maximum average steady-state error of 0.0088 rad. However, this method is prone to falling into local optimality.

[0033] In summary, various controllers have been designed to improve the trajectory tracking accuracy of robotic arms, and all have been validated on six-DOF robotic arms. However, these methods generally increase computational complexity and present a high level of design difficulty. Therefore, using a six-DOF robotic arm as the control target, a controller combining an RBF neural network with a nonsingular fast terminal sliding mode control is designed. This controller achieves an overall approximation and compensation for nonlinear terms, and improves trajectory tracking accuracy. The main points are as follows:

[0034] 1. Construct a dynamic model of the robotic arm and design a symmetrical non-singular fast terminal sliding surface that includes even-order nonlinear terms and terminal terms, showing consistent convergence characteristics for errors in the positive and negative directions of the robotic arm joints.

[0035] The 2RBF neural network adopts symmetrically distributed center values ​​and uniform width to approximate the positive and negative nonlinear terms of the robotic arm as a whole.

[0036] 3. Construct the Lyapunov function to verify the overall stability of the system.

[0037] 4. Through simulation and actual verification, and comparison with neural network combined with traditional sliding film control and sliding mode algorithm.

[0038] Figure 1The following schematically shows a flow chart of a robot arm trajectory tracking control method according to an embodiment of the present invention. Figure 1 As shown, the method includes operations S110 to S140.

[0039] In operation S110 , an expected trajectory and an actual trajectory of the robot arm are acquired.

[0040] In operation S120 , a non-singular fast terminal sliding surface and a switching control law of the non-singular fast terminal sliding surface are determined according to the expected trajectory and the actual trajectory of the robot arm.

[0041] In operation S130, the expected trajectory, actual trajectory, and non-singular fast terminal sliding surface are input into an equivalent control law output model to obtain an equivalent control law. The equivalent control law output model uses a radial basis function neural network model. The equivalent control law output model is obtained by applying a holistic approximation to the radial basis function neural network model.

[0042] In operation S140 , the robotic arm is controlled according to the equivalent control law and the switching control law to obtain a target trajectory.

[0043] Among them, operation S140 includes: adding the equivalent control law and the switching control law to obtain a total control law; constructing a dynamic model of the robotic arm; inputting the total control law into the dynamic model to obtain the target angle, target angular velocity and target angular acceleration of each joint of the robotic arm.

[0044] Figure 2 The figure schematically shows the overall structure of a robotic arm according to an embodiment of the present invention. Figure 3 Schematically shows a schematic diagram of the joint coordinates of a robotic arm according to an embodiment of the present invention. Figure 2 and Figure 3 As shown in the figure, taking the Jieka collaborative robot arm as an example of the control object, this robot arm is a six-degree-of-freedom industrial robot arm with high flexibility.

[0045] There are many methods for building a dynamic model of a robotic arm, such as the Newton-Euler method, the Lagrangian method, the Kane method, and the principle of virtual work. The Lagrangian method uses energy to model, which can avoid the appearance of internal force terms in the equation and is suitable for dynamic analysis of multi-degree-of-freedom systems. In the present invention, the process of building a dynamic model of the six-degree-of-freedom robotic arm is as follows:

[0046]

[0047] In formula (1), L represents the Lagrangian function; K represents the kinetic energy of the system; P represents the potential energy of the system; i = 1, 2....., n; τ i Expressed as the torque of the i-th joint; Expressed as the angular velocity of the i-th joint; qi Expressed as the i-th joint angle. According to formula (1), the dynamic equation of the robot arm is as follows:

[0048]

[0049] In formula (2), M(q)∈R 6×6 is the positive symmetric inertia matrix of the manipulator; q∈[q1,q2,q3,q4,q5,q6] T Represents the angle of each joint of the robot arm. Unit: rad; Indicates the angular velocity of each joint of the robotic arm. Unit: rad / s; Expressed as the angular acceleration of each joint of the robotic arm. Unit: rad / s^2; Represented as the Coriolis force and centrifugal force matrix of the manipulator; G(q)∈R 6×1 Represented as the gravity matrix of the manipulator; F∈R 6×1 Expressed as the sum of the model error and parameter uncertainty factors of the robot arm; τ∈R 6×1 Represented as the control input of the robotic arm.

[0050] Specifically, the dynamic model of the robotic arm has the following two properties:

[0051] (1) The inertia matrix M(q) is symmetric and positive definite. There exist positive numbers m1 and m2 that satisfy the inequality: m1||x|| 2 ≤x T M(q)x≤m2||x|| 2 (3)

[0052] (2) is a skew-symmetric matrix, and any real number x can satisfy:

[0053]

[0054] In the design process of the non-singular fast terminal sliding mode controller, the expected angle of each joint of the manipulator is q d =[q 1d ,q 2d ,q 3d ,q 4d ,q 5d ,q 6d ] T , the actual joint angle is q=[q1,q2,q3,q4,q5,q6] T , the joint angle error e and joint angular velocity error are The joint angular acceleration error is as follows:

[0055]

[0056] In order to improve the tracking speed of the robot arm and solve the singularity problem in the traditional terminal sliding mode, a non-singular fast terminal sliding mode surface is designed:

[0057]

[0058] In formula (6), S represents the sliding surface function; υ<0; μ>0; 1<p / k≤2, p and k are both positive odd numbers; c is a constant. If the joint error e is particularly large, the nonlinear term is the dominant term, which makes the system state quickly approach the equilibrium state; when e is small, the nonlinear term can be ignored At this time, the linear term It plays a leading role and ensures that the system state quickly converges to the equilibrium point.

[0059] Based on the non-singular fast terminal sliding film surface, the control law is designed. The time derivative of the sliding film surface S can be obtained:

[0060]

[0061] From formula (2), we can get:

[0062] Combining formula (5), we can get The expression is:

[0063]

[0064] make The equivalent control law τ of the equivalent control term can be obtained eq The expression is as follows:

[0065]

[0066] In formula (10), I represents the 6x6 identity matrix; It is represented by a vector The elements of are diagonal elements to generate a diagonal matrix.

[0067] In sliding film control systems, switching control terms play a crucial role in the sliding film control process. The primary purpose of designing switching control terms is to rapidly guide the system state back to the sliding surface through a discrete control action when the system state deviates from the sliding surface. The reaching law, a key component of the switching control law, defines how the system state approaches the sliding surface and directly influences the speed and quality with which the system reaches a stable state. Common reaching laws include the constant velocity reaching law, the exponential reaching law, and the power reaching law.

[0068] Among them, the isokinetic reaching law:

[0069] In formula (11), ε>0, the constant speed reaching law is: The larger the value of ε is, the faster the synovial control system reaches the switching surface, but the jitter caused is also greater.

[0070] Exponential reaching law:

[0071] In formula (12), ε>0, k>0, the exponential reaching law is suitable for solving the corresponding control problem of large steps. Increasing k while reducing ε can accelerate the approach and weaken the chattering.

[0072] Power reaching law:

[0073] In formula (13), k>0, 1>α>0 can be adjusted to ensure that the system state approaches the sliding surface at a higher speed when the distance is far away, and approaches at a lower speed when the distance is close, while reducing chattering.

[0074] In order to accelerate the convergence speed and improve the robustness of the system, the switching control law designed in the present invention is:

[0075] τ sw =k1*S+k2*tanh(S) (14)

[0076] The tanh(S) function in formula (14) is a hyperbolic tangent function, which is continuously differentiable and helps to reduce the chattering generated by the system and can balance the requirements of control accuracy and chattering suppression.

[0077] In summary, the control law of the controller can be designed as: τ = τ eq +τ sw (15)

[0078] Construct the Lyapunov function as:

[0079] Taking the derivative with respect to time:

[0080] Combining equations (7), (10), (14), and (15), we can obtain:

[0081]

[0082] In formula (18), k1>0; k2>0; it can be guaranteed When S=0,

[0083] According to the stability of the Lyapunov function, the system is stable. However, in reality, the parameters in the equivalent control law are difficult to obtain for a six-degree-of-freedom manipulator, so further transformation of the control law is required.

[0084] Figure 4The structure of the radial basis function neural network according to an embodiment of the present invention is schematically shown. Figure 4 As shown in Figure 1, the radial basis function neural network (RBFNN) has a simple structure, fast training speed, and strong ability to approximate nonlinear functions. Therefore, in order to solve the actual controller parameter problem, the RBF neural network is used to approximate the nonlinear function as a whole. The RBF neural network consists of: input layer, hidden layer, and output layer.

[0085] Figure 4 The RBF neural network structure consists of n input layer neuron nodes, m hidden layer neuron nodes and one output layer neuron node. n Represents the output signal of the neural network input layer. In practical applications, this signal is the angle, angular velocity, joint angle error, etc.; h1, h2, h3....h m Represents the output signal of the hidden layer; f represents the output signal of the output layer, which is the result of the overall approximation; the output signal of the hidden layer is calculated using the radial basis function, and the formula is as follows:

[0086]

[0087] In formula (19), c m represents the center vector of the Gaussian basis function of the mth neuron node; b m Represents the width of the Gaussian basis function of the mth neuron node.

[0088] Define f as the ideal output of the RBF neural network's overall approximation of the equivalent control law, which can be expressed as:

[0089]

[0090] In formula (20), W = [W1, W2…Wm] Τ is the weight value of the RBF neural network.

[0091] The adaptive law for setting the neural network weights is:

[0092] In formula (21), Fai is a 6x6 positive definite diagonal learning law matrix.

[0093] The modified overall control law is: τ 总 =f+k1*S+k2*tanh(S) (22)

[0094] In formula (22), k1*S can prompt the system state of the manipulator to converge quickly to the sliding mode surface, thereby improving the convergence speed; k2*tanh(S) can make the control input smoother, thereby improving the robustness and stability of the system.

[0095] The stability of the control system composed of the modified overall control law is proved below.

[0096] Construct the Lyapunov function as:

[0097]

[0098] In formula (23), tr(·) represents the trace of the matrix; W represents the current weight, W* represents the ideal weight; Fai and Θ represent the positive definite diagonal matrix and the positive definite symmetric matrix respectively; the function is introduced Used to enhance the description of the dynamic characteristics of the system.

[0099] Taking the time derivative of formula (23), we can get:

[0100]

[0101] According to the RBF neural network, the dynamic terms of the robot arm need to be approximated as a whole so that the system can reach the ideal sliding mode and ensure system stability. There is the following relationship:

[0102]

[0103] W T h+k1S+k2 tanh(S)=τ (27)

[0104] Substituting equations (26) and (27) into (25), we obtain:

[0105]

[0106] Substituting (29) into (28) and selecting appropriate ν, c, and μ parameters, we can obtain:

[0107]

[0108] Due to the synovial surface design It is the linear feedback of the error derivative. According to the sliding surface arrival condition S=0, it can be made It cancels out the error derivative in the system. Finally, we get:

[0109]

[0110] Since M is a positive definite inertia matrix, and c and ν are both designed parameters, we can It is considered as a positive definite gain and does not affect the negative definiteness of the final equal sign.

[0111] In summary, we can get:

[0112] according to Simplifying equation (24) with equation (32) yields:

[0113]

[0114] In formula (33), λ min (Θ)>0 is the minimum eigenvalue of the Θ positive symmetric matrix; k1>0; k2>0, it can be concluded that choosing a suitable k1 value can ensure Make the system stable.

[0115] Figure 5 The figure schematically shows an overall principle block diagram of a collaborative controller according to an embodiment of the present invention. Figure 5 The method mainly consists of two parts: the RBF neural network overall approximation term and the switching control term. The expected joint angle samples, angular velocity samples, angular acceleration samples and the actual joint angle samples, angular velocity samples and angular acceleration samples of the robot arm are used as the input signals of the RBF neural network. After each input of the expected joint angle samples, angular velocity samples, angular acceleration samples and the actual joint angle samples, angular velocity samples and angular acceleration samples of the robot arm to the RBF neural network, the joint angles, angular velocities and angular accelerations of the robot arm in the current situation output by the dynamic model of the robot arm are obtained. According to the difference between the joint angles, angular velocities and angular accelerations of the robot arm in the current situation output by the dynamic model of the robot arm and the expected joint angle samples, angular velocity samples and angular acceleration samples, the overall approximation degree described by the RBF neural network is judged. When the overall approximation degree meets the requirements, the parameters of the RBF neural network in the current situation are used as the final parameters of the RBF neural network, that is, the equivalent control law output model. When the overall approximation does not meet the requirements, the parameters of the current RBF neural network are adjusted and the overall approximation of the RBF neural network is continuously obtained until the overall approximation meets the requirements. In addition, in the process of determining the parameters of the RBF neural network through the overall approximation, the error dynamics are constrained by a non-singular fast terminal sliding surface to improve robustness.

[0116] like Figure 5As shown in FIG, the expected trajectory includes the expected joint angles, angular velocities, and angular accelerations of the manipulator. The expected joint angles, angular velocities, and angular accelerations of the manipulator and the actual joint angles, angular velocities, and angular accelerations of the manipulator are approximated by the equivalent control law using the RBF neural network as a whole. The expected joint angles, angular velocities, and angular accelerations of the manipulator are subtracted from the actual joint angles, angular velocities, and angular accelerations to obtain the errors of the joint angles, angular velocities, and angular accelerations of the manipulator. The errors of the joint angles, angular velocities, and angular accelerations of the manipulator are input into the non-singular fast terminal synovium to obtain To the sliding surface, the equivalent control law is obtained by using the derivative of the sliding surface equal to zero. However, the robot arm has many parameters and the equivalent control law is not easy to obtain. A switching control law is designed, and the output result f of the RBF neural network approximating the equivalent control law as a whole is used to replace the equivalent control law and the switching control law. After adding the total control law, the total control law is input into the robot arm model to obtain the target angle, target angular velocity, and target angular acceleration of each joint of the robot arm. The target angle, target angular velocity, and target angular acceleration of each joint of the robot arm are used as the actual joint angle, angular velocity, and angular acceleration of the robot arm to continue to control the robot arm.

[0117] To verify the effectiveness and feasibility of the designed control algorithm, a robot arm trajectory tracking control model was constructed in a simulation environment using a Jieka six-degree-of-freedom collaborative robot as the control object. The robot arm model was constructed using the robot arm's URDF (Unified Robot Description Format) file. While the simulation process validated all joints of the six-degree-of-freedom robot arm, the trajectory tracking results for the last three joints are similar to those for the first three, so trajectory tracking data was collected only for the first three joints.

[0118] The simulation parameter settings are as follows: the expected trajectories of the six joints are set to qd1=qd2=qd3=qd4=qd5=qd6=sin(t); the sliding surface parameters are set to: v=-0.3; c=10; μ=0.3; p=5; k=3; the parameters in the neural network are set to: the hidden layer nodes are set to 10; the radial basis function center value of the neural network is center=[-1.0, -0.7778, -05556, -0.3333, -0.1111, -0.1111, 0.3333, 0.5556, 0.7778, 1.0]; the width b of the radial basis function is set to 10; the parameter Fai in the weight adaptation law of the neural network is Fai=50*eye(6); the parameter settings in the switching control law are: k1=150*eye(6); k2=150*eye(6); the simulation time t is set to 10s.

[0119] Figure 6The schematic diagram of the tracking curve of the three joint angles before the trajectory tracking of the six-degree-of-freedom manipulator according to an embodiment of the present invention is shown. Figure 6 As shown in the figure, the RBF neural network and non-singular fast terminal sliding mode control algorithm proposed in the present invention are simulated and compared with the RBF neural network and traditional sliding mode collaborative control method and non-singular fast terminal sliding mode control method also applied to the six-degree-of-freedom manipulator trajectory tracking. Figure 6 It can be seen that since the first three joints are close to the base and the load is large, although they can track the expected trajectory, there are some error fluctuations.

[0120] Figure 7 The following schematically shows the curve diagram of the tracking error variation of the first three joints of the six-degree-of-freedom robot arm trajectory tracking according to an embodiment of the present invention. Figure 7 As shown in the figure, when the neural network is combined with the traditional sliding mode control and NFTSM control algorithm, the robot arm joint tracking error is large, and the robot arm trajectory tracking error under the neural network, traditional synovial control and NFTSM control shows large fluctuations. The maximum tracking error of the designed control method is about 0.05rad, the maximum tracking error of the neural network and traditional synovial collaborative control is about 0.1rad, and the maximum tracking error of NFTSM control is about 0.15rad. It can be concluded that the control effect of the method designed by the present invention is better than that of the neural network combined with the sliding mode control method and the NFTSM control method. The average absolute error of the first three joints is shown in Table 1.

[0121] Table 1 Statistics of the average absolute error of the first three joints of the robotic arm

[0122]

[0123] Table 1 shows that the maximum average absolute angle tracking error between the neural network and traditional synovial membrane control is 0.04 rad, the maximum average absolute angle tracking error between the NFTSM control and the controller designed in this invention is 0.05 rad, and the maximum average absolute angle tracking error between the two is 0.03 rad. The robot arm trajectory tracking accuracy under RBFNN-NFTSM control is good, demonstrating the effectiveness of this controller in controlling complex joint motions.

[0124] Figure 8 The following schematically shows the actual running angular velocity curve of the first three joints of the six-degree-of-freedom robot trajectory tracking according to an embodiment of the present invention. Figure 8 As shown, the expected joint angular velocity of each robot arm is set to The angular velocity of the robot arm controlled by the neural network and traditional sliding mode is too fast at the beginning, and deviates greatly from the expected angular velocity. The NFTSM control effect can be seen from the figure. Although it can track the expected angular velocity well, the fluctuation is large. Compared with the designed controller, it tracks the expected trajectory well.

[0125] Figure 9 The following schematically shows the angular velocity tracking error curves of the first three joints of a six-degree-of-freedom robot arm according to an embodiment of the present invention. Figure 9 As shown, the maximum angular velocity error between the neural network and traditional sliding mode control in the first three joints is 0.5 rad / s. The maximum tracking angular velocity error of the NFTSM control is 0.18 rad / s, and the maximum angular velocity error of the controller designed by the present invention is 0.03 rad / s, further verifying the superiority of the designed controller.

[0126] To verify the effectiveness of the proposed RBFNN-NFTSM control method, an experimental verification was conducted using a six-degree-of-freedom robotic arm experimental platform. The robotic arm was set to move from an initial joint angle of [0, 90, 90, 180, 90, 0]° to a final joint angle of [90, 45, 30, 60, 36, -30]°, with the motion path planned using quintic polynomial interpolation. The present invention used the spatial coordinates of the robotic arm's end flange as the tracking object and compared the proposed RBFNN-NFTSM control method with the RBFNN-SMC and NFTSM algorithms to determine the tracking effectiveness.

[0127] Figure 10 The following schematically shows the tracking effect of the flange at the end of a six-degree-of-freedom robotic arm according to an embodiment of the present invention. Figure 10 As shown in the figure, the tracking effect of the values ​​on the X, Y, and Z axes of the spatial coordinates of the flange at the end of the six-degree-of-freedom robotic arm is that the three control methods can track the expected trajectory, but the tracking effect of the control method of the present invention is better than the other two methods, which also verifies the authenticity and effectiveness of the proposed control method.

[0128] This paper addresses the problem of low robot arm trajectory tracking accuracy. Taking a six-degree-of-freedom robot arm as the research object, a RBF neural network and non-singular fast terminal sliding mode collaborative control method is proposed. The main achievements are as follows:

[0129] (1)1. Construct a dynamic model of the manipulator and design a symmetrical non-singular fast terminal sliding surface, which includes even-order nonlinear terms and terminal terms and exhibits consistent convergence characteristics for errors in the positive and negative directions of the manipulator joints.

[0130] (2) The RBF neural network adopts symmetrically distributed center values ​​and uniform width to approximate the positive and negative nonlinear terms of the robotic arm as a whole.

[0131] (3) Construct the Lyapunov function to verify the overall stability of the system.

[0132] (4) Through simulation and actual verification, it is compared with the traditional sliding mode control algorithm combined with the neural network and the terminal sliding mode algorithm.

[0133] According to an embodiment of the present invention, to improve the trajectory tracking accuracy of a six-degree-of-freedom (6DOF) manipulator, a trajectory tracking control method for the manipulator is provided, which utilizes the synergistic effects of a radial basis function neural network (RBFNN) and a nonsingular fast terminal sliding mode (NFTSM). First, the Lagrangian method is used to construct a dynamic model of the manipulator and a nonsingular fast terminal sliding mode surface is designed. By introducing nonlinear and fast terminal terms, the convergence rate of trajectory tracking is improved and the singularity problem of sliding mode control is resolved. Second, an RBF neural network is used to comprehensively approximate and compensate for the model and parameter uncertainties of the manipulator. Then, Lyapunov stability theory is applied to construct a Lyapunov function to demonstrate the overall stability of the control system. Finally, simulations and experiments are conducted using a six-degree-of-freedom (6DOF) manipulator as the control object. Results show that compared with the nonsingular fast terminal sliding mode (NFTSM) and RBF neural network combined with traditional sliding mode control (RBFNN-SMC), the proposed method improves the trajectory tracking accuracy of the six-degree-of-freedom (6DOF) manipulator, providing an effective and feasible theoretical approach for trajectory tracking control of the manipulator.

[0134] Figure 11 A block diagram schematically shows a robot arm trajectory tracking control device according to an embodiment of the present invention.

[0135] like Figure 11 As shown, the robot arm trajectory tracking control device 1100 includes an acquisition module 1110 , a sliding surface construction module 1120 , a control law determination module 1130 and a control module 1140 .

[0136] The acquisition module 1110 is used to acquire the expected trajectory and actual trajectory of the robotic arm.

[0137] The sliding surface construction module 1120 is used to determine the non-singular fast terminal sliding surface and the switching control law of the non-singular fast terminal sliding surface according to the expected trajectory and the actual trajectory of the robot arm.

[0138] The control law determination module 1130 is used to input the expected trajectory, the actual trajectory and the non-singular fast terminal sliding membrane surface into the equivalent control law output model to obtain the equivalent control law.

[0139] The control module 1140 is used to control the robotic arm according to the equivalent control law and the switching control law to obtain the target trajectory.

[0140] According to the embodiments of the present invention, any number of modules, submodules, units, and subunits, or at least part of the functions of any number of them can be implemented in one module. According to the embodiments of the present invention, any one or more of the modules, submodules, units, and subunits can be split into multiple modules for implementation. According to the embodiments of the present invention, any one or more of the modules, submodules, units, and subunits can be at least partially implemented as a hardware circuit, such as a field programmable gate array (FPGA), a programmable logic array (PLA), a system on a chip, a system on a substrate, a system on a package, an application specific integrated circuit (ASIC), or can be implemented by hardware or firmware of any other reasonable way of integrating or packaging the circuit, or implemented in any one of the three implementation modes of software, hardware, and firmware, or in an appropriate combination of any of them. Alternatively, according to the embodiments of the present invention, one or more of the modules, submodules, units, and subunits can be at least partially implemented as a computer program module, which can perform the corresponding function when the computer program module is run.

[0141] For example, any multiple of the acquisition module 1110, the sliding surface construction module 1120, the control law determination module 1130, and the control module 1140 can be combined into a single module / unit / subunit, or any one of the modules / units / subunits can be split into multiple modules / units / subunits. Alternatively, at least part of the functionality of one or more of these modules / units / subunits can be combined with at least part of the functionality of other modules / units / subunits and implemented in a single module / unit / subunit. According to an embodiment of the present invention, at least one of the acquisition module 1110, the sliding surface construction module 1120, the control law determination module 1130, and the control module 1140 can be at least partially implemented as a hardware circuit, such as a field programmable gate array (FPGA), a programmable logic array (PLA), a system on a chip, a system on a substrate, a system on a package, an application specific integrated circuit (ASIC), or can be implemented in hardware or firmware by any other reasonable method of integrating or packaging circuits, or can be implemented in any one of the three implementation methods of software, hardware, and firmware, or in any appropriate combination of any of them. Alternatively, at least one of the acquisition module 1110 , the sliding surface construction module 1120 , the control law determination module 1130 and the control module 1140 may be at least partially implemented as a computer program module, which may perform corresponding functions when executed.

[0142] It should be noted that the data processing system part in the embodiment of the present invention corresponds to the data processing method part in the embodiment of the present invention. The description of the data processing system part specifically refers to the data processing method part and will not be repeated here.

[0143] Figure 12 A block diagram of an electronic device suitable for implementing a robot arm trajectory tracking control method according to an embodiment of the present invention is schematically shown. Figure 12 The electronic device shown is only an example and should not limit the functions and scope of use of the embodiments of the present invention.

[0144] like Figure 12 As shown, the electronic device 1200 according to an embodiment of the present invention includes a processor 1201, which can perform various appropriate actions and processes according to a program stored in a read-only memory (ROM) 1202 or a program loaded from a storage part 1208 into a random access memory (RAM) 1203. The processor 1201 may, for example, include a general-purpose microprocessor (e.g., a CPU), an instruction set processor and / or a related chipset and / or a special-purpose microprocessor (e.g., an application-specific integrated circuit (ASIC)), and the like. The processor 1201 may also include an onboard memory for caching purposes. The processor 1201 may include a single processing unit or multiple processing units for performing different actions of the method flow according to an embodiment of the present invention.

[0145] RAM 1203 stores various programs and data required for the operation of electronic device 1200. Processor 1201, ROM 1202, and RAM 1203 are interconnected via bus 1204. Processor 1201 executes the programs in ROM 1202 and / or RAM 1203 to perform various operations according to the method flow of the embodiment of the present invention. It should be noted that the programs may also be stored in one or more memories other than ROM 1202 and RAM 1203. Processor 1201 may also execute the programs stored in the one or more memories to perform various operations according to the method flow of the embodiment of the present invention.

[0146] According to an embodiment of the present invention, electronic device 1200 may further include an input / output (I / O) interface 1205, which is also connected to bus 1204. Electronic device 1200 may further include one or more of the following components connected to I / O interface 1205: an input section 1206 including a keyboard, mouse, etc.; an output section 1207 including devices such as a cathode ray tube (CRT), liquid crystal display (LCD), and speakers; a storage section 1208 including a hard disk; and a communication section 1209 including a network interface card such as a LAN card or modem. Communication section 1209 performs communication processing via a network such as the Internet. A drive 1210 is also connected to I / O interface 1205 as needed. Removable media 1211, such as a magnetic disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed in drive 1210 as needed, so that computer programs read from the removable media can be installed into storage section 1208 as needed.

[0147] According to an embodiment of the present invention, the method flow according to an embodiment of the present invention can be implemented as a computer software program. For example, an embodiment of the present invention includes a computer program product, which includes a computer program carried on a computer-readable storage medium, and the computer program includes a program code for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from the network through the communication part 1209, and / or installed from the removable medium 1211. When the computer program is executed by the processor 1201, the above-mentioned functions defined in the system of the embodiment of the present invention are performed. According to an embodiment of the present invention, the system, device, apparatus, module, unit, etc. described above can be implemented by a computer program module.

[0148] The present invention also provides a computer-readable storage medium, which may be included in the device / apparatus / system described in the above embodiments, or may exist independently and not incorporated into the device / apparatus / system. The computer-readable storage medium carries one or more programs, which, when executed, implement the method according to the embodiments of the present invention.

[0149] According to an embodiment of the present invention, a computer-readable storage medium may be a non-volatile computer-readable storage medium. For example, it may include, but is not limited to: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination thereof. In the present invention, a computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device.

[0150] For example, according to an embodiment of the present invention, the computer-readable storage medium may include the ROM 1202 and / or the RAM 1203 described above and / or one or more memories other than the ROM 1202 and the RAM 1203 .

[0151] An embodiment of the present invention also includes a computer program product, which includes a computer program, which contains program code for executing the method provided by the embodiment of the present invention. When the computer program product is run on an electronic device, the program code is used to enable the electronic device to implement the robotic arm trajectory tracking control method provided by the embodiment of the present invention.

[0152] When the computer program is executed by the processor 1201, the above functions defined in the system / device of the embodiment of the present invention are performed. According to the embodiment of the present invention, the above-described systems, devices, modules, units, etc. can be implemented by computer program modules.

[0153] In one embodiment, the computer program may be stored on a tangible storage medium such as an optical storage device or a magnetic storage device. In another embodiment, the computer program may be transmitted and distributed in the form of a signal on a network medium, downloaded and installed via the communication portion 1209, and / or installed from the removable medium 1211. The program code contained in the computer program may be transmitted using any appropriate network medium, including but not limited to wireless, wired, or any suitable combination thereof.

[0154] According to an embodiment of the present invention, the program code for executing the computer program provided by the embodiment of the present invention can be written in any combination of one or more programming languages. Specifically, these computing programs can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. Programming languages ​​include, but are not limited to, Java, C++, Python, "C" language or similar programming languages. The program code can be executed entirely on the user computing device, partially on the user device, partially on a remote computing device, or entirely on a remote computing device or server. In the case of a remote computing device, the remote computing device can be connected to the user computing device through any type of network, including a local area network (LAN) or a wide area network (WAN), or can be connected to an external computing device (e.g., using an Internet service provider to connect via the Internet).

[0155] The flowcharts and block diagrams in the accompanying drawings illustrate the possible architectures, functions, and operations of the systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each box in the flowchart or block diagram may represent a module, program segment, or portion of code, which contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the boxes may occur in an order different from that marked in the accompanying drawings. For example, two boxes shown in succession may actually be executed substantially in parallel, or they may sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram or flowchart, as well as the combination of boxes in the block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or may be implemented using a combination of dedicated hardware and computer instructions. It will be understood by those skilled in the art that the features described in the various embodiments of the present invention may be combined and / or coupled in various ways, even if such combinations or couplings are not explicitly described in the present invention. In particular, the features described in the various embodiments of the present invention may be combined and / or coupled in various ways without departing from the spirit and teachings of the present invention. All such combinations and / or combinations fall within the scope of the present invention.

[0156] The above describes embodiments of the present invention. However, these embodiments are for illustrative purposes only and are not intended to limit the scope of the present invention. Although each embodiment has been described separately above, this does not mean that the measures in each embodiment cannot be advantageously used in combination. Without departing from the scope of the present invention, those skilled in the art may make various substitutions and modifications, which should all fall within the scope of the present invention.

Claims

1. A robot arm trajectory tracking control method, characterized in that: The method comprises: Obtain the expected trajectory and actual trajectory of the robotic arm; Determining a non-singular fast terminal synovial surface and a switching control law of the non-singular fast terminal synovial surface according to the expected trajectory and the actual trajectory of the robotic arm; Inputting the expected trajectory, the actual trajectory and the non-singular fast terminal sliding membrane surface into an equivalent control law output model to obtain an equivalent control law; The robotic arm is controlled according to the equivalent control law and the switching control law to obtain a target trajectory.

2. The robot arm trajectory tracking control method according to claim 1, characterized in that: The function of the non-singular fast terminal synovial surface is: Among them, S represents the sliding surface function, e is the joint error, p and k are both positive odd numbers, and c is a constant. is the joint angular velocity error, ν is a constant less than 0, and μ is a constant greater than 0.

3. The robot arm trajectory tracking control method according to claim 2, characterized in that: The function of the switching control law is: τ sw =k1*S+k2*tanh(S); Among them, τ sw represents the switching control law; S represents the sliding surface function; tanh(S) function is the hyperbolic tangent function; k1 and k2 are both constants greater than 0.

4. The robot arm trajectory tracking control method according to claim 1, characterized in that: The controlling the robotic arm according to the equivalent control law and the switching control law to obtain a target trajectory includes: The total control law is obtained by adding the equivalent control law and the switching control law; Construct a dynamic model of the robotic arm; The overall control law is input into the dynamic model to obtain the target angle, target angular velocity and target angular acceleration of each joint of the robotic arm.

5. The robot arm trajectory tracking control method according to claim 4, characterized in that: The dynamic model of the robotic arm is constructed using the Lagrangian method.

6. The robot arm trajectory tracking control method according to claim 5, characterized in that: The dynamic model of the robotic arm is: Among them, M(q) is the positive definite symmetric inertia matrix of the robot arm; q is the angle of each joint of the robot arm, is the angular velocity of each joint of the robotic arm, is the angular acceleration of each joint of the robotic arm, is the Coriolis force and centrifugal force matrix of the robot arm; G(q) is the gravity matrix of the robot arm; F is the sum of the model error and parameter uncertainty factors of the robot arm; τ is the control law input of the robot arm.

7. The robot arm trajectory tracking control method according to claim 1, characterized in that: The equivalent control law output model adopts a radial basis function neural network model.

8. A robot arm trajectory tracking control device, characterized in that: The device comprises: The acquisition module is used to obtain the expected trajectory and actual trajectory of the robot arm; a synovial surface construction module, configured to determine a non-singular fast terminal synovial surface and a switching control law of the non-singular fast terminal synovial surface according to an expected trajectory and an actual trajectory of the manipulator; a control law determination module, configured to input the expected trajectory, the actual trajectory, and the non-singular fast terminal synovial surface into an equivalent control law output model to obtain an equivalent control law; A control module is used to control the robotic arm according to the equivalent control law and the switching control law to obtain a target trajectory.

9. An electronic device comprising: one or more processors; a memory for storing one or more programs, When the one or more programs are executed by the one or more processors, the one or more processors are enabled to implement the method according to any one of claims 1 to 7.

10. A computer-readable storage medium having executable instructions stored thereon, which, when executed by a processor, causes the processor to implement the method according to any one of claims 1 to 7.

Images