Continuum robot model-free shape control method, system, device and medium

Abstract

The present invention discloses a method, system, device, and medium for model-free shape control of a continuum robot. The method includes: applying a zeroing neural network model to a shape feature parameter error function, deriving an actuator update formula based on a first design formula, and calculating the actuator change based on an estimated Jacobian matrix; applying a zeroing neural network model to a parameter velocity error function, deriving a Jacobian matrix update formula based on a second design formula, and calculating an estimated Jacobian matrix change based on the acceleration value of the actual shape feature parameter fed back by a sensor and the estimated actuator acceleration; learning the actuator control input and the estimated Jacobian matrix for the continuum robot at the next moment based on the actuator change and the estimated Jacobian matrix change, and performing shape control on the continuum robot at the next moment. The present invention improves the efficiency and accuracy of model-free shape control of a continuum robot and can be applied to the field of robot control technology.

Description

Technical Field

[0001] The present invention relates to the field of robot control technology, and in particular to a model-free shape control method, system, device and medium for a continuum robot. Background Art

[0002] Robots have broad application prospects in various fields. Traditional robots, due to their very limited degrees of freedom, suffer from poor flexibility, safety, and adaptability. They perform poorly in unstructured or confined environments with unstable and changing surroundings, making it difficult to achieve ideal control. In contrast, continuum robots, due to their safe interactions and high flexibility and agility, can interact more safely with their environment, reducing the risk of harm to themselves and the environment. Consequently, they are finding widespread application in these complex, unstructured or confined environments. Consequently, continuum robot control has recently become a hot topic in the field of robotics.

[0003] However, in situations where collision avoidance or full-arm path planning are crucial (e.g., minimally invasive surgery on humans), global control of the robot's shape is necessary. Shape control for continuum robots typically involves moving the arm from an initial shape to a specified shape, thereby avoiding collisions with the environment.

[0004] Continuum robots are similar to human arms, and their arms are usually made of materials with a Young's modulus close to or lower than that of biological skin. There are also many ways to drive continuum robots, including rope-driven robots, pneumatic robots, concentric tube robots, etc. The mathematical model of a robot can be divided into kinematic models and dynamic models. The kinematic model describes the mapping relationship between the angles of each joint of the arm and the position of a module on the arm (such as the end of the arm) in the task space, while the dynamic model describes the mapping relationship between the force, torque and joint angle applied by each joint of the arm. The control of the arm can generally be divided into inverse kinematic control and inverse dynamics control. Inverse kinematic control refers to the calculation of the required joint angles based on the desired posture of the arm, while inverse dynamics control refers to the calculation of the required joint torque based on the desired joint angles.

[0005] The control method of continuum robots in the prior art has the following disadvantages:

[0006] 1) They are highly dependent on the robot's mathematical model. Existing technical solutions are essentially model-based control schemes. However, the relationship between actuators and shape characteristic parameters varies for robots with different drives and models. Since researchers cannot know the mathematical models of all continuum robots in advance, the application scenarios of these methods are relatively limited.

[0007] 2) Model-free control methods require network pre-training, which requires large datasets. Furthermore, since these methods require pre-training, they essentially require pre-learning the robot's mathematical model. If the robot being used for shape control is changed, pre-training must be repeated, which is time-consuming. Creating datasets is also cumbersome and resource-intensive. Consequently, these methods are still relatively inapplicable and cannot be applied to a wider range of robots. Therefore, it is necessary to develop a shape control method with a wider range of applications, lower resource consumption, and higher efficiency.

[0008] 3) Current model-free control methods, due to the lack of a model, are not ideal, with relative errors exceeding 1% in controlled shapes. While a 1% relative error is not significant in shape control tasks, it can introduce unnecessary risks in tasks requiring high precision. Therefore, a more accurate model-free shape control method is needed. Summary of the Invention

[0009] The purpose of the present invention is to solve one of the technical problems existing in the prior art to at least a certain extent.

[0010] Therefore, an object of an embodiment of the present invention is to provide a model-free shape control method for a continuum robot, which improves the efficiency and accuracy of the model-free shape control of the continuum robot.

[0011] Another object of an embodiment of the present invention is to provide a model-free shape control system for a continuum robot.

[0012] In order to achieve the above technical objectives, the technical solutions adopted by the embodiments of the present invention include:

[0013] In a first aspect, an embodiment of the present invention provides a model-free shape control method for a continuum robot, comprising the following steps:

[0014] Initialize the actuators of the continuum robot arm, control system related parameters, the initial value of the Jacobian matrix of the robot system itself, and control task related parameters;

[0015] defining a shape characteristic parameter error function for the continuum robot system, applying a zeroing neural network model to the shape characteristic parameter error function, deriving an actuator update formula based on the first design formula, and then calculating an actuator change based on an estimated value of the Jacobian matrix;

[0016] defining a parametric velocity error function for the continuum robot system, applying a zeroing neural network model to the parametric velocity error function, deriving an update formula for the Jacobian matrix based on a second design formula, and calculating an estimated change in the Jacobian matrix based on actual acceleration values ​​of shape characteristic parameters fed back by sensors and estimated actuator accelerations;

[0017] According to the variation of the actuator and the estimated variation of the Jacobian matrix, the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment are learned, and the shape of the continuum robot at the next moment is controlled according to the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment.

[0018] Furthermore, in one embodiment of the present invention, the control system related parameters include the convergence parameters of the zeroing neural network model, the control task related parameters include the control task duration and the shape characteristic parameters corresponding to the expected shape, the shape characteristic parameter error function is a function of the error between the expected shape characteristic parameters and the actual shape characteristic parameters fed back by the sensor with respect to time, and the parameter speed error function is a function of the error between the derivative value of the actual shape characteristic parameter fed back by the sensor and the product of the estimated value of the Jacobian matrix at the previous moment and the change in the actuator with respect to time.

[0019] Furthermore, in one embodiment of the present invention, the shape feature parameter error function is:

[0020] e(t)=x d (t)-x a (t)

[0021] Among them, e(t) represents the shape feature parameter error at time t, x d (t) represents the expected shape characteristic parameters at time t, x a (t) represents the actual shape characteristic parameters fed back by the sensor at time t;

[0022] The first design formula of the zeroing neural network model is:

[0023]

[0024] in, represents the derivative value of the shape feature parameter error function at time t, γ1>0 is the convergence parameter of the shape feature parameter error function, and Φ(·) represents the activation function of the error.

[0025] Furthermore, in one embodiment of the present invention, the updating formula of the actuator is:

[0026]

[0027] in, Indicates the change of the actuator, represents the estimate of the Jacobian matrix, express Moore-Penrose generalized inverse, x d represents the expected shape characteristic parameter, x a Represents the actual shape characteristic parameters of the robot.

[0028] Furthermore, in one embodiment of the present invention, the parameter speed error function is:

[0029]

[0030] Among them, ∈(t) represents the parameter speed error at time t, Represents the derivative value of the actual shape characteristic parameter fed back by the sensor at time t, represents the estimated value of the Jacobian matrix at time t, Indicates the change of the actuator at time t;

[0031] The second design formula of the zeroing neural network model is:

[0032]

[0033] in, represents the derivative value of the parameter velocity error function at time t, γ2>0 is the convergence parameter of the parameter velocity error function, and Φ(·) represents the activation function of the error.

[0034] Furthermore, in one embodiment of the present invention, the updating formula of the Jacobian matrix is:

[0035]

[0036] in, represents the estimated change in the Jacobian matrix, Represents the derivative value of the actual shape characteristic parameter fed back by the sensor, represents the estimate of the Jacobian matrix, Indicates the change of the actuator, The acceleration value representing the actual shape characteristic parameter fed back by the sensor, represents the estimated actuator acceleration, express Moore-Penrose generalized inverse.

[0037] Furthermore, in one embodiment of the present invention, the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment are calculated by the following formula:

[0038]

[0039] Among them, q(t n+1 ) represents t n+1 The actuator control input of the continuum robot at time q(t n ) represents t n The actuator control input of the moment continuum robot, Indicates t n The change of the actuator at a moment, Indicates t n+1 The estimated value of the Jacobian matrix at time t, Indicates t n The estimated value of the Jacobian matrix at time t, Indicates t n The estimated change in the Jacobian matrix at time t, where Δt represents the preset time step.

[0040] In a second aspect, an embodiment of the present invention provides a model-free shape control system for a continuum robot, comprising:

[0041] Parameter initialization module, used to initialize the actuators of the continuum robot arm, control system related parameters, the initial value of the Jacobian matrix of the robot system itself, and control task related parameters;

[0042] an actuator change calculation module, configured to define a shape characteristic parameter error function for the continuum robot system, apply a zeroing neural network model to the shape characteristic parameter error function, derive an actuator update formula based on the first design formula, and then calculate an actuator change based on an estimated value of the Jacobian matrix;

[0043] a Jacobian matrix change calculation module, configured to define a parameter velocity error function for the continuum robot system, apply a zeroing neural network model to the parameter velocity error function, derive an update formula for the Jacobian matrix based on a second design formula, and then calculate an estimated change in the Jacobian matrix based on the acceleration values ​​of the actual shape feature parameters fed back by the sensor and the estimated actuator acceleration;

[0044] The shape control module is used to learn the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment based on the change of the actuator and the estimated change of the Jacobian matrix, and to perform shape control on the continuum robot at the next moment based on the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment.

[0045] In a third aspect, an embodiment of the present invention provides a model-free shape control device for a continuum robot, comprising:

[0046] at least one processor;

[0047] at least one memory for storing at least one program;

[0048] When the at least one program is executed by the at least one processor, the at least one processor implements the above-mentioned model-free shape control method for a continuum robot.

[0049] In a fourth aspect, an embodiment of the present invention further provides a computer-readable storage medium storing a program executable by a processor, wherein the program executable by the processor is used to execute the above-mentioned method for model-free shape control of a continuum robot when executed by the processor.

[0050] The advantages and benefits of the present invention will be described in part in the following description and will become apparent from the following description or learned through practice of the present invention:

[0051] The embodiment of the present invention can control the shape of the arm of a continuum robot system when the model is unknown, thereby solving the challenges brought by model uncertainty or unknown models, avoiding the complex process of modeling the robot arm, and the control scheme has good portability for continuum robots of different types and structures; the embodiment of the present invention only needs to use the parameters and their derivative data fed back by the sensor to complete the shape control of the continuum robot in real time, avoiding the large amount of pre-training process in other model-free methods, and greatly reducing the resources consumed to complete the task; the embodiment of the present invention can achieve precise shape control of the continuum robot, and the control effect is comparable to or even exceeds the model-based shape control method, thereby expanding the application scenarios of the continuum robot. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following introduction is made to the drawings required for use in the embodiments of the present invention. It should be understood that the drawings introduced below are only for the convenience of clearly describing some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative work.

[0053] Figure 1 A flowchart of the steps of a model-free shape control method for a continuum robot provided by an embodiment of the present invention;

[0054] Figure 2 Schematic diagram of a piecewise constant curvature model in the prior art;

[0055] Figure 3 Schematic diagram of shape parameters under the piecewise constant curvature model in the prior art;

[0056] Figure 4A schematic diagram of the principle of model-free shape control of a continuum robot based on an annihilation neural network according to an embodiment of the present invention;

[0057] Figure 5 A schematic diagram of a flow chart of model-free shape control of a continuum robot based on an annihilation neural network according to an embodiment of the present invention;

[0058] Figure 6 A schematic diagram of the shape and posture of a continuum robot provided by an embodiment of the present invention with model-free shape control;

[0059] Figure 7 A shape error variation diagram of the model-free shape control of a continuum robot provided by an embodiment of the present invention;

[0060] Figure 8 A graph showing the error and evaluation index variation of shape feature parameters in a shape control task of a rope-driven robot provided by an embodiment of the present invention;

[0061] Figure 9 A diagram showing changes in actuators during a shape control task for a rope-driven robot according to an embodiment of the present invention;

[0062] Figure 10 A structural block diagram of a model-free shape control system for a continuum robot provided by an embodiment of the present invention;

[0063] Figure 11 This is a structural block diagram of a model-free shape control device for a continuum robot provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0064] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention and are not to be construed as limiting the present invention. The step numbers in the following embodiments are provided for ease of explanation only and do not limit the order of the steps. The order of execution of the steps in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0065] In the description of the present invention, "a plurality" means two or more. The terms "first" and "second" are used solely to distinguish technical features and are not to be construed as indicating or implying relative importance, or as implicitly indicating the number of the indicated technical features, or as implicitly indicating the order of the indicated technical features. Furthermore, unless otherwise defined, all technical and scientific terms used herein have the same meanings as commonly understood by those skilled in the art.

[0066] Because different robots are driven in different ways, their mathematical models are likely to be different. Therefore, to unify the control representation of robots, the term "actuator" is used to represent the control input consisting of their kinematic parameters. In robots with different drives, the actuator may include parameters such as the length of the robot's control rope, the rope's deviation angle, and the rotation angle of the control motor. Generally speaking, the kinematic model of a robot can be expressed by the following formula:

[0067] f(q(t))=x(t) (1)

[0068] in represents the value of the control actuator of the arm at time t, (·) T Represents the transpose operator. Represents the position of the arm in space. Specifically, in the robot's trajectory tracking task, x(t) represents the position of the end effector, and in the robot's shape control task, x(t) represents the robot's shape posture. is a nonlinear mapping function that describes the kinematics of the robot arm. The kinematic model of the robot can usually also be described at the velocity level. By taking the derivative of both sides of formula (1) with respect to time t, we can obtain:

[0069]

[0070] in represents the partial derivative of the function f(·) with respect to the actuator q(t), i.e. the Jacobian matrix of the robot arm, and the column vector Represents the change speed of the actuator, column vector Indicates the speed of change of the arm posture, which is expressed as the speed of change of the robot's shape posture in the shape control task. The shape control problem of the robot is to obtain the corresponding required actuator value q(t) based on the specified expected shape posture, that is:

[0071]

[0072] The obtained actuator value q(t) is then used to control the robot's arm so that it moves in the target shape and posture x d (t) Transformation, i.e., the actual shape and posture of the arm x a (t) tends to the target shape pose x d (t). The function that represents the robot shape and posture to the actuator is the inverse function of f(·), which is the inverse kinematic mapping. Since the kinematic mapping function f(·) is nonlinear in continuum robots, it is difficult to directly obtain it through mathematical derivation. At the same time, due to the different kinematic models of different robots, their inverse mapping The shapes of the robots are also different, so it is difficult to use a unified control method to control the shape of the robot.

[0073] The piecewise constant curvature model is a commonly used model in continuum robot modeling. This model divides the flexible arm of the continuum robot into multiple segments, each of which is composed of a series of mutually tangent arcs with constant curvature. Under this assumption, the curvature of each arc segment is constant in space but variable in time. The advantage of this model is that a complex continuum robot with almost infinite degrees of freedom can be regarded as multiple simple arc segments, and the robot's posture can be determined by knowing the geometric characteristics of each arc segment. The schematic diagram of the piecewise constant curvature model is shown in the figure below. Figure 2 As shown, S represents the endpoint of the arm segment, O represents the center of the arm segment, k represents the curvature of the arm segment, and l represents the length of the arm segment.

[0074] Under the assumption of the piecewise constant curvature model, the shape of the arm can be represented by some shape characteristic parameters of the arc corresponding to the arm. Common shape characteristic parameters include curvature k, rotation angle θ, deflection angle The arm length l, etc. The deflection angle is the angle between the plane passing through each arc segment and the xz coordinate plane of the starting point of the segment. The rotation angle θ represents the central angle of the arc segment. Figure 3 is a schematic diagram of these shape parameter characteristics, {S i}-{x i ,y i ,z i} represents the local coordinate system of the arm segment. When the selected shape characteristic parameters can uniquely determine the arm shape, the shape control problem of the continuum robot can be transformed into the control of the arm shape characteristic parameters. In this case, x in formulas (1) to (3) represents the value of the corresponding shape characteristic parameter.

[0075] The existing continuum robot shape control methods are as follows:

[0076] First, this method is based on the piecewise constant curvature assumption, and the shape characteristic parameters are selected as curvature k, torque τ, deflection angle The shape control problem of a continuum robot arm is transformed into the control of the arm's curvature, torque, and deflection angle. In the task space, curvature, torque, and deflection angle uniquely determine the arm's shape. This method uses a rope-driven robot as the control object, with the arm driven by four ropes. The relationship between the shape parameters of each driving rope can be obtained based on the robot's parameters:

[0077]

[0078] Where l represents the centerline length of the arm under initial conditions, d is the parameter of the robot itself, β1 = 0, β2 = π / 2, β3 = π, β4 = 3π / 2. By differentiating formula (4) with respect to the three shape characteristic parameters, we can obtain the velocity-level relationship:

[0079]

[0080] in is the Jacobian matrix of the robot shape control, and x still represents the shape feature parameters. Since shape control requires controlling the arm shape to the expected posture x d , so formula (5) can be rewritten as:

[0081]

[0082] where x d -x represents the expected change in the shape parameter, and Indicates the change value of the driving rope in the rope-driven robot, K p Represents the proportional gain, which can control the convergence speed.

[0083] Formula (6) can calculate the expected change value of the actuator at the next moment through the error between the robot shape characteristic parameters and the expected shape parameters, thus completing the shape control of the continuum robot.

[0084] As can be seen from Equations (4) and (5), this method requires prior knowledge of the mathematical model of the continuum robot. In fact, most current shape control methods also require knowledge of the robot's mathematical model. For example, the PID method, methods based on artificial potential fields, and methods based on adaptive visual servoing are all currently effective methods for shape control.

[0085] In addition to these methods, there are a few continuum robot shape control methods that can complete the shape control task without knowing the robot model in advance. Since the robot model is unknown, these methods are essentially to predict the mathematical model of the robot and then complete the shape control task. For example, the mathematical model of the continuum robot is predicted by a neural network, and the neural network is used to learn [q i ,x d ,x]→q i+1 The mapping relationship is then used to complete the shape control of the robot.

[0086] From the above, it can be seen that the control method of the continuum robot in the prior art has the following disadvantages:

[0087] 1) They are highly dependent on the robot's mathematical model. Existing technical solutions are essentially model-based control schemes. However, the relationship between actuators and shape characteristic parameters varies for robots with different drives and models. Since researchers cannot know the mathematical models of all continuum robots in advance, the application scenarios of these methods are relatively limited.

[0088] 2) Model-free control methods require network pre-training, which requires large datasets. Furthermore, since these methods require pre-training, they essentially require pre-learning the robot's mathematical model. If the robot being used for shape control is changed, pre-training must be repeated, which is time-consuming. Creating datasets is also cumbersome and resource-intensive. Consequently, these methods are still relatively inapplicable and cannot be applied to a wider range of robots. Therefore, it is necessary to develop a shape control method with a wider range of applications, lower resource consumption, and higher efficiency.

[0089] 3) Current model-free control methods, due to the lack of a model, are not ideal, with relative errors exceeding 1% in controlled shapes. While a 1% relative error is not significant in shape control tasks, it can introduce unnecessary risks in tasks requiring high precision. Therefore, a more accurate model-free shape control method is needed.

[0090] In view of the deficiencies in the prior art, the present invention has the following objectives:

[0091] First, the present invention aims to design a more versatile solution for shape control of continuum robots, one that is not restricted by the robot model. To this end, the present invention designs a model-free shape control method for continuum robots, which can control the continuum robot without knowing the robot's mathematical model.

[0092] A second objective of the present invention is to address the resource-intensive nature of existing model-free shape control methods, which require pre-training. To this end, the control method designed in this invention utilizes only sensor data transmitted back to the robot to achieve real-time shape control of the continuum robot, eliminating the need for pre-training and significantly reducing the resources required to complete the shape control task.

[0093] Finally, the third objective of the present invention is to address the unsatisfactory control effects of current shape control methods. To this end, the present invention defines shape errors based on a zeroing neural network design formula. This method estimates the Jacobian matrix of the continuum robot based on shape data transmitted by sensors, allowing the system to autonomously learn the robot's mathematical model. This results in a shape control method with improved control effects, surpassing model-based control methods.

[0094] Reference Figure 1 The embodiment of the present invention provides a model-free shape control method for a continuum robot, which specifically includes the following steps:

[0095] S101, initializing the actuators of the continuum robot arm, control system related parameters, the initial value of the Jacobian matrix of the robot system itself, and control task related parameters;

[0096] S102, defining a shape feature parameter error function for the continuum robot system, applying a zeroing neural network model to the shape feature parameter error function, deriving an actuator update formula based on the first design formula, and then calculating the actuator change based on the estimated value of the Jacobian matrix;

[0097] S103. Define a parameter velocity error function for the continuum robot system, apply a zeroing neural network model to the parameter velocity error function, derive an update formula for the Jacobian matrix based on the second design formula, and then calculate an estimated change in the Jacobian matrix based on the acceleration values ​​of the actual shape feature parameters fed back by the sensor and the estimated actuator acceleration;

[0098] S104. According to the variation of the actuator and the estimated variation of the Jacobian matrix, the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment are learned, and the shape of the continuum robot at the next moment is controlled according to the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment.

[0099] Further as an optional implementation, the control system related parameters include the convergence parameters of the zeroing neural network model, the control task related parameters include the control task duration, the shape feature parameters corresponding to the expected shape, the shape feature parameter error function is a function of the error between the expected shape feature parameters and the actual shape feature parameters fed back by the sensor with respect to time, and the parameter speed error function is a function of the error between the derivative value of the actual shape feature parameters fed back by the sensor and the product of the estimated value of the Jacobian matrix at the previous moment and the change in the actuator with respect to time.

[0100] like Figure 4 Figure 1 shows a schematic diagram of the principle behind model-free shape control for a continuum robot based on a zeroing neural network, according to an embodiment of the present invention. The control system input is the user-defined desired shape characteristic parameters, and the control system output, q, is used to control the shape and posture of the continuum robot at the next moment. ZNN stands for zeroing neural network.

[0101] like Figure 5 The figure shows a flow chart of the model-free shape control of a continuum robot based on an annihilation neural network according to an embodiment of the present invention, which is as follows:

[0102] A. Initialize the actuator q(t0) of the continuum robot arm at t0 = 0, the control system parameters (mainly the convergence parameters γ1, γ2 of the zeroing neural network), and the initial value of the Jacobian matrix of the robot system itself Control task related parameters (including control task duration T d , shape feature parameters x corresponding to the expected shape d )

[0103] B. Define the nth moment (t n )’s shape characteristic parameter error e(t n ), the error function is the error between the expected shape characteristic parameters and the actual shape characteristic parameters of the robot. The zeroing neural network model is applied to the parameter error, and the actuator update formula is obtained according to the design formula. Then, t=t is calculated based on the estimated Jacobian matrix value. n The change of the actuator at the moment

[0104] C. Define the velocity error of the parameters of the continuum robot system at the nth moment ∈(t n ), the error function is the derivative value of the shape characteristic parameter fed back by the sensor The error between the Jacobian matrix estimated at the previous moment and the derivative value of the actuator is formed. The zeroing neural network model is applied to the speed error, and the update formula of the Jacobian matrix is ​​obtained according to the design formula, and then the acceleration value of the shape characteristic parameter fed back by the sensor is obtained. and the estimated actuator acceleration Calculation shows that t = t n The estimated change in the Jacobian matrix at time

[0105] D. t = t obtained from steps B and C n The change of the actuator at the moment and the estimated change in the Jacobian matrix Learn to get the next moment t=t n+1 The actuator control input q(t n+1 ) and the value of the Jacobian matrix

[0106] After completing step D, repeat steps B to D until the entire shape control task is completed.

[0107] In the simulation experiment, a three-segment continuum robot based on the piecewise constant curvature hypothesis (i.e., a continuum arm composed of three constant curvature curves, with smooth joints and the same tangents) is taken as an example. Here, each segment of the robot arm is controlled by three different cables, so the three-segment continuum robot is controlled by a total of nine cables. First, initialize the actuator of the continuum robot arm q(t0) = [0.20, 0.21, 0.19, 0.20, 0.21, 0.19, 0.20, 0.21, 0.19] when t0 = 0. T m, where the actuator represents the length of the rope that controls the corresponding segment. The convergence parameters of the zeroing neural network in the initial control system are γ1 = 1, γ2 = 5. The above parameters will be defined in the further technical solution. In order to initialize the Jacobian matrix of the arm, it is necessary to give the angle of the j-th actuator (j = 1, 2, ..., 9) a sufficiently small increment Δq j , thereby changing the state of the control rope and measuring the characteristic parameter change vector Δx of the arm shape. The (i, j)th element of the Jacobian matrix of the arm is initialized as follows:

[0108]

[0109] Where Δx i The i-th element (i=1, 2, ..., 9) of the shape characteristic parameter change Δx is represented. Therefore, according to all elements of the shape characteristic parameter change Δx and the change Δq of the j-th actuator j , we can determine all the elements in the jth column of the initial value of the Jacobian matrix. Similarly, repeat the above process for all actuators of the arm (j=1,2,…,9) to determine the values ​​of all elements of the Jacobian matrix J(t0). After determining the initial value of the Jacobian matrix, initialize the characteristic parameters corresponding to the expected shape in, Represent the curvature, deflection angle and length of the i-th arm, respectively, and their units are m -1 , rad, m. Define the total duration T of the control task d =20 seconds.

[0110] Based on the above technical solution, the continuum robot system is controlled to complete the shape control task. The mathematical operations in the above process can be completed by MATLAB software in the host computer, and the input control signal obtained by the solution is then transmitted to the continuum robot. Here, the root mean squared error (RMSE) of the shape feature parameters and the Cartesian distance error (Car_err) of the shape are used to evaluate the effect of the continuum robot's shape control. The definition of RMSE is as follows:

[0111]

[0112] where x d (t) and x a (t) represents the shape feature parameters corresponding to the expected shape posture and the current shape posture of the robot. The Cartesian coordinate error is defined as follows:

[0113]

[0114] The arm is divided into m segments according to the principle of equal spacing, p d (t,i) and p a (t,i) represents the 3D position of the i-th endpoint of the expected shape and the current shape, respectively. The Cartesian coordinate error indicates how well the expected and current poses fit in space.

[0115] Figure 6 and Figure 7 The shape posture result diagram and error change diagram of the continuum robot using the annihilation neural network to complete the above shape control task are respectively shown. d = 20 seconds of control, the mean square error RMSE of the shape feature parameters is 1.12×10 -9 , the Cartesian coordinate error Car_err is 7.18×10 -11 m. It can be seen that the arm's posture has already coincided with the expected shape and posture halfway through the task time, making it difficult to distinguish with the naked eye. Furthermore, the mean square error of the shape feature parameters and the Cartesian coordinate error of the shape converge rapidly.

[0116] In addition, in order to demonstrate the superiority of the control performance of the present invention, the shape control task with the same parameter settings is applied to the model-based shape control method with better control effect. Table 1 shows the shape control effects of different control algorithms. The computational cost refers to the computational time it takes for the computer to complete the shape control task. It can be found that, except for the PID method, the control error of the present invention is much smaller than that of other model-based control algorithms, and the control effect is much better than that of other model-based shape control algorithms. At the same time, the computational cost of the present invention is much smaller than the duration T of the shape control task. d , indicating that it can be applied in practice, and the relatively low computational cost also shows that the present invention consumes very little resources. Therefore, it demonstrates the efficiency and superiority of the design algorithm of the present invention for the shape control of continuum robots.

[0117] Table 1

[0118]

[0119] In some optional embodiments, for step B, the specific scheme is as follows:

[0120] First, at the nth moment, the shape characteristic parameter error of shape control is defined for the continuum robot system, that is, the error function between the expected shape and the characteristic parameters corresponding to the robot shape measured by the current sensor:

[0121] e(t)=x d (t)-x a (t) (10)

[0122] Among them, e(t) represents the shape feature parameter error at time t, x d (t) represents the expected shape characteristic parameters at time t, x a (t) represents the actual shape characteristic parameters fed back by the sensor at time t;

[0123] According to the design formula of the zeroing neural network:

[0124]

[0125] in, represents the derivative of the shape feature parameter error function at time t, γ1>0 is the convergence parameter of the shape feature parameter error function, and Φ(·) represents the activation function of the error. Here, the activation function is set to a linear activation function, that is, Φ(x) = x. For convenience, the variables (t) are omitted in subsequent formulas. Expanding formula (11) yields:

[0126]

[0127] Since the basic shape control problem is to control the arm shape to the desired shape, the characteristic parameter value of the desired control shape should be constant, so Substituting into formula (12) we get The expression:

[0128]

[0129] in, Indicates the change of the actuator, represents the estimate of the Jacobian matrix, express Moore-Penrose generalized inverse, x d represents the expected shape characteristic parameter, x a Represents the actual shape characteristic parameters of the robot. Since the dimensions of the actuator q and the characteristic parameters x may be inconsistent, the estimated Jacobian matrix It may not be a square, so here express The Moore-Penrose generalized inverse of . This gives Figure 4 Change in actuator The estimation formula of .

[0130] In some optional embodiments, for step C, the specific scheme is as follows:

[0131] After completing step B, define the velocity error of the robot's current shape feature parameters. The error function is the derivative value of the shape feature parameters fed back by the sensor. and the Jacobian matrix estimated at the previous moment Derivative value of the actuator The error between them is:

[0132]

[0133] Among them, ∈(t) represents the parameter speed error at time t, Represents the derivative value of the actual shape characteristic parameter fed back by the sensor at time t, represents the estimated value of the Jacobian matrix at time t, Indicates the change of the actuator at time t;

[0134] Similarly, according to the design formula of the zeroing neural network:

[0135]

[0136] in, represents the derivative value of the parameter velocity error function at time t, γ2>0 is the convergence parameter of the parameter velocity error function, Φ(·) represents the activation function of the error, and the activation function is set to a linear activation function as above, and (t) is omitted in the formula. Expanding formula (15) yields:

[0137]

[0138] Thus, the change in the estimated value of the robot Jacobian matrix can be obtained The expression:

[0139]

[0140] in, represents the estimated change in the Jacobian matrix, Represents the derivative value of the actual shape characteristic parameter fed back by the sensor, represents the estimate of the Jacobian matrix, Indicates the change of the actuator, The acceleration value representing the actual shape characteristic parameter fed back by the sensor, represents the estimated actuator acceleration, express The Moore-Penrose generalized inverse of Figure 4 Estimated change in the Jacobian matrix

[0141] In some optional embodiments, for step D, the specific scheme is as follows:

[0142] Observing the calculation formula (17), it can be found that the calculation of the estimator requires the derivative value of the shape characteristic parameter change and the acceleration of the actuator changes The derivative values ​​of each parameter can be obtained through sensor feedback, and the acceleration of the actuator changes It can be solved by the backward Euler method:

[0143]

[0144] Where Δt represents the time step of the calculation program execution, which is set to 0.01s in the simulation task and 0.1s in the experimental task. Finally, the change of the actuator is solved according to formula (13) and formula (17) respectively and the Jacobian matrix to estimate the variation The values ​​of the actuator and robot Jacobian matrices at the next moment can be calculated:

[0145]

[0146]

[0147] Among them, q(t n+1 ) represents t n+1 The actuator control input of the continuum robot at time q(t n ) represents t n The actuator control input of the moment continuum robot, Indicates t n The change of the actuator at a moment, Indicates t n+1 The estimated value of the Jacobian matrix at time t, Indicates t n The estimated value of the Jacobian matrix at time t, Indicates t n The estimated change in the Jacobian matrix at time t, Δt represents the preset time step, and the calculated actuator values ​​and the predicted Jacobian matrix will be used for the continuum robot shape control at the next moment.

[0148] In the physical experiment, a one-segment rope-driven robot based on the piecewise constant curvature hypothesis is used as the control object. The rope-driven robot is controlled by four motors, which are divided into two groups facing each other. The robot's actuator is the rotation angle of each group of driving motors, that is, First, initialize the actuator q(t0) of the continuum robot arm at t0=0 to [0,0] T rad, where the actuator represents the length of the rope that controls the corresponding segment. The convergence parameter of the zeroing neural network in the initial control system is γ1 = γ2 = 0.1. The initialization of the Jacobian matrix of the arm is shown in the same formula (7). Since the length of the rope-driven robot cannot be changed, the curvature and deflection angle of the above shape parameters can determine the shape of the arm. Initialize the characteristic parameters corresponding to the expected shape in Represent the curvature and deflection angle of the i-th arm, respectively, and their units are m -1 , rad. Define the total duration T of the control task d =10 seconds.

[0149] Based on the above technical solution, the rope-driven robot is controlled to complete the shape control task. The mathematical calculations in the above process are performed by MATLAB software on the host computer, and the resulting input control signal is then transmitted to the robot. Similar to the simulation, the mean square error (RMSE) of the shape characteristic parameters and the Cartesian coordinate error (Car_err) of the shape are used to evaluate the effectiveness of the continuum robot's shape control.

[0150] Figure 8 and Figure 9The error and evaluation index change diagrams of the shape feature parameters of the control task and the change diagram of the actuator during the task are respectively shown. φ Denotes the deflection angle error, e k represents the curvature error, q1 and q2 represent the actuator values ​​under different control tasks. d =10 seconds, the mean square error of the shape feature parameters is 8.74×10 -3 , the Cartesian coordinate error is 1.56×10 -4 m. It can be seen that at t = 6 seconds, the shape and posture have almost converged to the expected shape and posture. This demonstrates the effectiveness of the control scheme of the present invention for the shape control of physical robots.

[0151] The above describes the method steps and experimental results of the embodiment of the present invention. It can be recognized that the embodiment of the present invention can realize the control of the arm shape when the model of the continuum robot system is unknown, thereby solving the challenges brought by model uncertainty or unknown model, avoiding the complex process of modeling the robot arm, and the control scheme has good portability for continuum robots of different types and structures; the embodiment of the present invention only needs to use the parameters and derivative data of sensor feedback to complete the shape control of the continuum robot in real time, avoiding the large amount of pre-training process in other model-free methods, and greatly reducing the resources consumed to complete the task; the embodiment of the present invention can realize the precise shape control of the continuum robot, and the control effect is comparable to or even exceeds the model-based shape control method, thereby expanding the application scenarios of the continuum robot.

[0152] Compared with the prior art, the embodiments of the present invention also have the following advantages:

[0153] 1) The present invention designs a solution to make the shape control of continuum robots more universal. This solution is not restricted by the robot model, that is, a model-free continuum robot shape control method. This method can complete the control of the continuum robot without knowing the robot's mathematical model.

[0154] 2) This invention addresses the resource-intensive nature of existing model-free shape control methods, which require pre-training. To this end, the control method designed in this invention utilizes only sensor data transmitted back to the robot to achieve real-time shape control of the continuum robot, eliminating the need for pre-training and significantly reducing the resources required to complete the shape control task.

[0155] 3) This invention addresses the problem of suboptimal control performance in current shape control methods. To this end, the invention defines shape errors based on a zeroing neural network design formula. It estimates the Jacobian matrix of the continuum robot based on shape data transmitted by sensors, allowing the system to autonomously learn the robot's mathematical model. This results in a shape control method with improved control performance, surpassing model-based control methods.

[0156] Reference Figure 10 , an embodiment of the present invention provides a continuum robot model-free shape control system, comprising:

[0157] Parameter initialization module, used to initialize the actuators of the continuum robot arm, control system related parameters, the initial value of the Jacobian matrix of the robot system itself, and control task related parameters;

[0158] an actuator change calculation module, for defining a shape characteristic parameter error function for the continuum robot system, applying a zeroing neural network model to the shape characteristic parameter error function, deriving an actuator update formula based on the first design formula, and then calculating the actuator change based on an estimated value of the Jacobian matrix;

[0159] A Jacobian matrix change calculation module is used to define a parameter velocity error function for the continuum robot system, apply a zeroing neural network model to the parameter velocity error function, derive an update formula for the Jacobian matrix based on the second design formula, and then calculate an estimated change in the Jacobian matrix based on the acceleration values ​​of the actual shape feature parameters fed back by the sensor and the estimated actuator acceleration;

[0160] The shape control module is used to learn the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment based on the change of the actuator and the estimated change of the Jacobian matrix, and to perform shape control on the continuum robot at the next moment based on the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment.

[0161] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0162] Reference Figure 11 , an embodiment of the present invention provides a model-free shape control device for a continuum robot, comprising:

[0163] at least one processor;

[0164] at least one memory for storing at least one program;

[0165] When the at least one program is executed by the at least one processor, the at least one processor implements the above-mentioned model-free shape control method for a continuum robot.

[0166] The contents of the above method embodiments are all applicable to the present device embodiments. The functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0167] An embodiment of the present invention further provides a computer-readable storage medium storing a program executable by a processor. When the program is executed by the processor, it is used to execute the above-mentioned method for model-free shape control of a continuum robot.

[0168] A computer-readable storage medium according to an embodiment of the present invention can execute a model-free shape control method for a continuum robot provided by an embodiment of the method of the present invention, can execute any combination of implementation steps of the embodiment of the method, and has the corresponding functions and beneficial effects of the method.

[0169] The embodiment of the present invention also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device performs Figure 1 The method shown.

[0170] In some optional embodiments, the function / operation mentioned in the block diagram may not occur in the order mentioned in the operation diagram. For example, depending on the function / operation involved, the two boxes shown in succession can actually be executed substantially simultaneously or the above-mentioned boxes can sometimes be executed in reverse order. In addition, the embodiment presented and described in the flow chart of the present invention is provided in an exemplary manner for the purpose of providing a more comprehensive understanding of the technology. The disclosed method is not limited to the operation and logic flow presented herein. Optional embodiments are contemplated in which the order of the various operations is changed and the sub-operations described as a part of a larger operation are performed independently.

[0171] In addition, although the present invention is described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the above-mentioned functions and / or features can be integrated into a single physical device and / or software module, or one or more functions and / or features can be implemented in separate physical devices or software modules. It is also understood that a detailed discussion of the actual implementation of each module is not necessary for understanding the present invention. More specifically, given the properties, functions, and internal relationships of the various functional modules in the devices disclosed herein, the actual implementation of the module will be understood within the routine skills of an engineer. Therefore, a person skilled in the art can implement the present invention set forth in the claims using ordinary skills without undue experimentation. It is also understood that the specific concepts disclosed are merely illustrative and are not intended to limit the scope of the present invention, which is determined by the full scope of the appended claims and their equivalents.

[0172] If the above functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the above methods of each embodiment of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), disk or optical disk, and other media that can store program code.

[0173] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0174] More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic devices), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable media on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other media, followed by editing, deciphering, or processing in another suitable manner as necessary, and then stored in a computer memory.

[0175] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0176] In the above description of this specification, reference to the terms "one embodiment / example," "another embodiment / example," or "certain embodiments / examples" means that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

[0177] While embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions, and variations may be made to the embodiments without departing from the principles and spirit of the invention, and that the scope of the invention is defined by the claims and their equivalents.

[0178] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A model-free shape control method for a continuum robot, characterized in that: The following steps are involved: Initialize the actuators of the continuum robot arm, control system related parameters, the initial value of the Jacobian matrix of the robot system itself, and control task related parameters; defining a shape characteristic parameter error function for the continuum robot system, applying a zeroing neural network model to the shape characteristic parameter error function, deriving an actuator update formula based on the first design formula, and then calculating an actuator change based on an estimated value of the Jacobian matrix; defining a parametric velocity error function for the continuum robot system, applying a zeroing neural network model to the parametric velocity error function, deriving an update formula for the Jacobian matrix based on a second design formula, and calculating an estimated change in the Jacobian matrix based on actual acceleration values ​​of shape characteristic parameters fed back by sensors and estimated actuator accelerations; According to the variation of the actuator and the estimated variation of the Jacobian matrix, the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment are learned, and the shape of the continuum robot at the next moment is controlled according to the actuator control input and the estimated value of the Jacobian matrix of the continuum robot at the next moment; The shape feature parameter error function is: in, express The shape characteristic parameter error at the moment, express The shape characteristic parameters expected at each moment, express The actual shape characteristic parameters fed back by the sensor at every moment; The first design formula of the zeroing neural network model is: in, Represents the shape feature parameter error function in The derivative value at time, is the convergence parameter of the shape feature parameter error function, Activation function representing the error; The parameter velocity error function is: in, express The parameter speed error at the moment, The actual shape characteristic parameters of the sensor feedback are The derivative value at time, express The estimated value of the Jacobian matrix at time t, express The change of the actuator at the moment; The second design formula of the zeroing neural network model is: in, Indicates the parameter velocity error function in The derivative value at time, is the convergence parameter of the parametric velocity error function, Activation function representing the error.

2. A model-free shape control method for a continuum robot according to claim 1, characterized in that: The control system related parameters include the convergence parameters of the zeroing neural network model, the control task related parameters include the control task duration and the shape characteristic parameters corresponding to the expected shape, the shape characteristic parameter error function is a function of the error between the expected shape characteristic parameters and the actual shape characteristic parameters fed back by the sensor with respect to time, and the parameter speed error function is a function of the error between the derivative value of the actual shape characteristic parameter fed back by the sensor and the product of the estimated value of the Jacobian matrix at the previous moment and the change in the actuator with respect to time.

3. The model-free shape control method for a continuum robot according to claim 1, characterized in that: The update formula of the executor is: in, Indicates the change of the actuator, represents the estimate of the Jacobian matrix, express The Moore-Penrose generalized inverse, represents the expected shape characteristic parameters, Represents the actual shape characteristic parameters of the robot.

4. The model-free shape control method for a continuum robot according to claim 1, characterized in that: The update formula of the Jacobian matrix is: in, represents the estimated change in the Jacobian matrix, Represents the derivative value of the actual shape characteristic parameter fed back by the sensor, represents the estimate of the Jacobian matrix, Indicates the change of the actuator, The acceleration value representing the actual shape characteristic parameter fed back by the sensor, represents the estimated actuator acceleration, express Moore-Penrose generalized inverse.

5. A model-free shape control method for a continuum robot according to any one of claims 1 to 4, characterized in that: The estimated values ​​of the actuator control input and Jacobian matrix of the continuum robot at the next moment are calculated as follows: in, express The actuator control input of the moment continuum robot, express The actuator control input of the moment continuum robot, express The change of the actuator at a moment, express The estimated value of the Jacobian matrix at time t, express The estimated value of the Jacobian matrix at time t, express The estimated change in the Jacobian matrix at time t, Indicates the preset time step.

6. A model-free shape control system for a continuum robot, characterized in that: include: Parameter initialization module, used to initialize the actuators of the continuum robot arm, control system related parameters, the initial value of the Jacobian matrix of the robot system itself, and control task related parameters; an actuator change calculation module, configured to define a shape characteristic parameter error function for the continuum robot system, apply a zeroing neural network model to the shape characteristic parameter error function, derive an actuator update formula based on the first design formula, and then calculate an actuator change based on an estimated value of the Jacobian matrix; a Jacobian matrix change calculation module, configured to define a parameter velocity error function for the continuum robot system, apply a zeroing neural network model to the parameter velocity error function, derive an update formula for the Jacobian matrix based on a second design formula, and then calculate an estimated change in the Jacobian matrix based on the acceleration values ​​of the actual shape feature parameters fed back by the sensor and the estimated actuator acceleration; a shape control module, configured to learn the actuator control input and the estimated Jacobian matrix of the continuum robot at the next moment based on the actuator change and the estimated Jacobian matrix change, and perform shape control on the continuum robot at the next moment based on the actuator control input and the estimated Jacobian matrix of the continuum robot at the next moment; The shape feature parameter error function is: in, express The shape characteristic parameter error at the moment, express The shape characteristic parameters expected at each moment, express The actual shape characteristic parameters fed back by the sensor at every moment; The first design formula of the zeroing neural network model is: in, Represents the shape feature parameter error function in The derivative value at time, is the convergence parameter of the shape feature parameter error function, Activation function representing the error; The parameter velocity error function is: in, express The parameter speed error at the moment, The actual shape characteristic parameters of the sensor feedback are The derivative value at time, express The estimated value of the Jacobian matrix at time t, express The change of the actuator at the moment; The second design formula of the zeroing neural network model is: in, Indicates the parameter velocity error function in The derivative value at time, is the convergence parameter of the parametric velocity error function, Activation function representing the error.

7. A model-less shape control device for a continuum robot, characterized in that: include: at least one processor; at least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the model-free shape control method for a continuum robot according to any one of claims 1 to 5.

8. A computer-readable storage medium storing a program executable by a processor, characterized in that: The processor-executable program is used to perform a continuum robot model-free shape control method according to any one of claims 1 to 5 when executed by the processor.

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