Visual servo tracking control method for mobile robot based on adaptive dynamic programming

Abstract

The present invention discloses a mobile robot visual servo tracking control method based on adaptive dynamic programming. The method comprises the following steps: a current image, an expected image and a reference image of coplanar feature points are photographed by a camera on the mobile robot, and the current posture information and the expected posture information of the mobile robot are calculated by using the homography technology, and a tracking error model is obtained in combination with the robot kinematics; the optimal control problem of the tracking error model is converted into a method for solving the Hamilton-Jacobi-Bellman equation; the Hamilton-Jacobi-Bellman equation is solved by using an adaptive online learning algorithm using the actual state information of the mobile robot to obtain an optimal value function, and the mobile robot is controlled by using the optimal control input corresponding to the optimal value function. The present invention can realize that the mobile robot completes the trajectory tracking task and ensures the system stability by using visual information, can realize the expected optimal performance index, can reduce the control cost, can also improve the tracking effect of the mobile robot, and can improve the controller performance.

Description

Technical Field

[0001] The invention relates to the fields of intelligent control and mobile robot control, and in particular to a mobile robot visual servo tracking control method based on adaptive dynamic programming. Background Art

[0002] With the development of mobile robot control technology, mobile robots have now been widely used in many aspects such as industrial production, national defense and military, and life services. In recent years, visual sensors have gradually become economical and easy to obtain. In addition, they have the characteristics of rich environmental information, strong external perception ability and wide application range, so they are widely equipped with mobile robots and other intelligent systems. Due to the role of visual sensors, the flexibility and intelligence of mobile robots have been greatly improved, and they can adapt to more complex environments. The positioning, environmental perception and control technology of vision-based robots has also been greatly developed. Therefore, vision-based mobile robot trajectory tracking has attracted the attention and research of a large number of scholars.

[0003] Classical visual servo control is mainly divided into image-based, position-based, and hybrid visual servo control. Image-based visual servo control is controlled by defining the error signal in the two-dimensional image plane. It does not need to use the three-dimensional posture information of the mobile robot, and it is robust to system disturbances, but it is difficult to control the deflection posture of the mobile robot. Position-based visual servo control requires the definition of the error signal in the three-dimensional Euclidean space. Although three-dimensional reconstruction is required, direct control of the error in the three-dimensional space can ensure its convergence. Considering that the system model of the visual servo trajectory tracking control problem of the mobile robot is a time-varying affine nonlinear system. Adaptive dynamic programming is an effective method to solve the tracking control problem of affine nonlinear systems. It is not easy to solve the optimal control of the mobile robot visual servo trajectory tracking based on adaptive dynamic programming, because it requires the solution of the Milton-Jacobi-Bellman equation. For time-invariant nonlinear systems, the Milton-Jacobi-Bellman equation is a time-invariant partial differential equation and its analytical solution cannot be obtained. At present, most of the solution methods are to design a suitable neural network structure to approximate the unknown terms. Different from the above-mentioned general nonlinear systems, due to the inherent time-varying characteristics of the mobile robot system model, the HJB equation in the optimal control problem contains two partial differential terms and the valued function is a function of state and time, which makes the problem more complicated. The optimal control of time-varying nonlinear systems is still different from that of time-invariant systems, and brings many challenges. Summary of the invention

[0004] The invention provides a mobile robot visual servo tracking control method based on adaptive dynamic programming, which is used to solve the technical problems of poor control effect and high control cost of the existing mobile robot.

[0005] In order to solve the above technical problems, the technical solution proposed by the present invention is:

[0006] A mobile robot visual servo tracking control method based on adaptive dynamic programming includes the following steps:

[0007] The current image, expected image and reference image of coplanar feature points are captured by a camera on the mobile robot; based on the current image, expected image and reference image, the current posture information and expected posture information of the mobile robot are calculated by using homography technology; based on the calculated current posture information and expected posture information of the mobile robot, a tracking error model is obtained in combination with robot kinematics;

[0008] The optimal control problem of the tracking error model is transformed into solving the Hamilton-Jacobi-Bellman equation. The Hamilton-Jacobi-Bellman equation is solved by an adaptive online learning algorithm using the actual state information of the mobile robot to obtain the optimal value function, and the mobile robot is controlled by the optimal control input corresponding to the optimal value function.

[0009] Preferably, the current image, the expected image and the reference image of the coplanar feature points are photographed by a camera on the mobile robot; based on the current image, the expected image and the reference image, the current posture information and the expected posture information of the mobile robot are calculated by using homography technology; the following steps are included:

[0010] The coordinate system of the mobile robot and the camera mounted on the mobile robot are set to coincide, four coplanar feature points in the coordinate system space are selected as target points, and the pixel coordinates of the current image, the expected image and the reference image of the camera target point are reconstructed in the Euclidean manner based on the camera model, and the pixel coordinates of the current image, the expected image and the reference image after the Euclidean reconstruction are normalized;

[0011] The normalized pixel coordinates of the current image, expected image and reference image are used to calculate the homography matrices of the current position and expected position of the mobile robot relative to the reference position, and the current pose and expected pose of the mobile robot are obtained based on the homography technology.

[0012] Preferably, the normalization formula is as follows:

[0013] m i =K -1 p i

[0014] Among them, K is the camera calibration matrix, p i are homogeneous pixel coordinates.

[0015] Preferably, based on the calculated current posture information and the expected posture information of the mobile robot, and in combination with the robot kinematics, a tracking error model is obtained, which includes the following steps:

[0016] Calculate the position error e(t) of the mobile robot in the current camera coordinate system, and obtain the tracking error model based on the kinematic model of the mobile robot Among them, f(e(t),t) is the nonlinear part of the tracking error model with respect to the state e(t), g(e(t)) is the control matrix, and u(e(t),t) is the control input.

[0017] Preferably, the Hamilton-Jacobi-Bellman equation is:

[0018]

[0019] in, It means to find the partial derivative with respect to time t, V * (e, t) is the optimal value function to be obtained, f(e, t) is the nonlinear part of the tracking error model with respect to the state e(t); Q(e) is a positive definite function, and g(e) is the control matrix; It represents the partial derivative with respect to e(t), and R is a symmetric positive definite matrix.

[0020] Preferably, using an adaptive online learning algorithm to solve the Hamilton-Jacobi-Bellman equation to obtain the optimal value function comprises the following steps:

[0021] Based on the current actual system state information, solve the following equation to calculate V(e,t):

[0022]

[0023] Where Δt is the sampling time interval, L(e(τ),u(e(τ))) represents the utility function;

[0024] 2) Calculate the control input signal u(e,t) using the following method:

[0025]

[0026] 3) Continuously learn online and repeat the first two steps to make the adaptive online learning algorithm converge.

[0027] Preferably, the adaptive online learning algorithm is an adaptive neural network algorithm. In each iteration, the network parameters of the adaptive neural network algorithm are updated using the following formula:

[0028]

[0029] Where W(t) is the weight of the neural network, φ(e(t)) is the activation function of the neural network, L(e(t),u(e(t))) represents the utility function, and α>0 is the learning rate of the neural network weights;

[0030] The control input signal u(e(t),t) is calculated using the following formula:

[0031]

[0032] Among them, R is a symmetric positive definite matrix and g(e(t)) is the control matrix.

[0033] The present invention has the following beneficial effects:

[0034] 1. The mobile robot visual servo tracking control method based on adaptive dynamic programming in the present invention can not only enable the mobile robot to complete the trajectory tracking task and ensure the system stability by using visual information, but also achieve the expected optimal performance indicators, reduce the control cost, improve the tracking effect of the mobile robot, and improve the controller performance.

[0035] 2. Compared with the existing control methods, the mobile robot visual servo tracking control method based on adaptive dynamic programming in the present invention can adjust the speed of the mobile robot in real time to cope with environmental changes through adaptive online learning, and also has a good tracking effect for trajectories with constantly changing speeds.

[0036] In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail below with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0038] Figure 1 The figure is a flow chart of a mobile robot visual servo tracking control method based on adaptive dynamic programming in a preferred embodiment of the present invention.

[0039] Figure 2 It is a tracking error state trajectory diagram of the mobile robot visual servo tracking control method based on adaptive dynamic programming in the preferred embodiment of the present invention.

[0040] Figure 3 The curves are the expected trajectory and actual motion trajectory of the mobile robot in the mobile robot visual servo tracking control method based on adaptive dynamic programming in the preferred embodiment of the present invention. DETAILED DESCRIPTION

[0041] The embodiments of the present invention are described in detail below with reference to the accompanying drawings, but the present invention can be implemented in many different ways as defined and covered by the claims.

[0042] Embodiment 1:

[0043] like Figure 1 As shown, the present invention discloses a mobile robot visual servo tracking control method based on adaptive dynamic programming, comprising the following steps:

[0044] The current image, the expected image and the reference image of the coplanar feature points are captured by a camera on the mobile robot; based on the current image, the expected image and the reference image, the current position and posture information and the expected position and posture information of the mobile robot are calculated by using homography technology; based on the calculated current position and posture information and the expected position and posture information of the mobile robot, a tracking error model is obtained in combination with robot kinematics;

[0045] The optimal control problem of the tracking error model is transformed into solving the Hamilton-Jacobi-Bellman equation; the Hamilton-Jacobi-Bellman equation is solved using an adaptive online learning algorithm using the actual state information of the mobile robot to obtain an optimal value function, and the mobile robot is controlled with the optimal control input corresponding to the optimal value function.

[0046] The mobile robot visual servo tracking control method based on adaptive dynamic programming in the present invention can not only enable the mobile robot to complete the trajectory tracking task and ensure the system stability by using visual information, but also achieve the expected optimal performance indicators, reduce the control cost, improve the tracking effect of the mobile robot, and improve the controller performance.

[0047] Embodiment 2:

[0048] Embodiment 2 is an extended embodiment of the embodiment, which differs from Embodiment 1 in that the specific steps of the mobile robot visual servo tracking control method based on adaptive dynamic programming are refined:

[0049] In this embodiment, if Figure 1 As shown, a mobile robot visual servo tracking control method based on adaptive dynamic programming is disclosed; comprising:

[0050] Step S1: The current image, expected image and reference image of the coplanar feature points are captured by the camera on the mobile robot, and the current posture information and expected posture information (i.e., translation amount and rotation angle) of the mobile robot are obtained by using the homography technology, and the tracking error model is obtained by combining the robot kinematics:

[0051] Step S11: Set the coordinate system of the mobile robot to coincide with the coordinate system of the camera mounted on it, select four coplanar feature points in the space as target points, obtain the measurable pixel coordinates from the feature point image taken by the camera, and perform Euclidean reconstruction based on the pinhole camera model. The normalized three-dimensional coordinates are given by m i =K -1 p i Calculated, where K is the camera calibration matrix, p i is the homogeneous pixel coordinate;

[0052] Step S12: using the current, expected and reference normalized three-dimensional coordinates of the mobile robot, the homography matrices of the current position and expected position of the mobile robot relative to the reference position are calculated, and the current posture and expected posture of the mobile robot are obtained based on the homography technology;

[0053] Step S13: By transforming the coordinate system, the desired posture information is converted into the current camera coordinate system, and then the posture error e(t) of the mobile robot is calculated, and the tracking error model is obtained based on the kinematic model of the mobile robot.

[0054] Specifically, step S1 includes the following contents:

[0055] The current camera coordinate system is recorded as F c , F c The origin is the optical center of the camera, the x-axis is parallel to the wheel axis of the mobile robot, the z-axis is the optical axis of the camera, and the y-axis is perpendicular to the motion plane xz of the mobile robot. d and F * Represent the camera coordinate system and the fixed reference coordinate system of the desired trajectory respectively; select four feature points, which are located in the camera F c The homogeneous pixel coordinates that can be measured are The characteristic point in F can be calculated by the following formula c Normalized 3D coordinates in:

[0056] m i c =K -1 p i c

[0057] Among them, K is the camera calibration matrix, and the feature points are in F d and F * The normalized three-dimensional coordinates in are and By its homography relationship The homography matrix H can be calculated c ,H d , using the direct linear transformation algorithm to transform H cDecompose to get the corresponding translation and rotation [x,z,θ] T , H d Decompose to get [x d ,z d ,θ d ] T , the pose error is defined as:

[0058]

[0059] Where T is the coordinate system F c With F d The transformation matrix between them, the kinematic model of the mobile robot is expressed as:

[0060]

[0061] Where v and ω represent the linear velocity and angular velocity of the mobile robot respectively. Then, the time derivative of the error e(t) is calculated and combined with the kinematic model of the mobile robot to obtain the tracking error model:

[0062] Step S2: According to the obtained tracking error model, an adaptive evaluation structure based on a neural network is designed to achieve the optimal performance index and calculate the optimal control input through the evaluation network:

[0063] Step S21: converting the optimal control problem of the tracking error model into solving the Hamilton-Jacobi-Bellman equation;

[0064] Step S22: Use the evaluation neural network to approximate the value function and calculate the optimal control input, and design an adaptive evaluation structure based on the neural network.

[0065] Step S3: Implementation of the visual servo tracking controller based on adaptive dynamic programming, and realizing the online operation of the visual servo tracking controller through adaptive dynamic programming:

[0066] Step S31: Using the error model state e(t) and tracking error model state equation The weights of the neural network are updated through learning in the following way:

[0067]

[0068] Among them, W(t) is the weight of the neural network, φ(e(t)) is the activation function of the neural network, symbol represents the partial derivative with respect to e(t), L(e(t),u(e(t))) represents the utility function, and α>0 is the learning rate of the neural network weights;

[0069] Step S32: Calculate the control input signal in real time using the following method:

[0070]

[0071] Among them, R is a symmetric positive definite matrix and g(e(t)) is the control matrix.

[0072] Specifically, the optimal control problem of the tracking error model is transformed into solving the Hamilton-Jacobi-Bellman equation of the following form:

[0073]

[0074] in, It means to find the partial derivative with respect to time t, V * (e, t) is the optimal value function to be found, Q(e) is a positive definite function,

[0075] Using the state information of the actual system, an adaptive online learning algorithm is used to solve the Hamilton-Jacobi-Bellman equation to obtain the optimal value function V * (e,t).

[0076] Among them, the adaptive online learning algorithm includes:

[0077] 1) Solve the following equation based on the current actual system state information to calculate V(e,t):

[0078] Among them, τ is a replacement for the parameter t.

[0079] 2) Calculate the control input signal using the following method:

[0080]

[0081] 3) Continuously learn online and repeat the first two steps to make the adaptive online learning algorithm converge.

[0082] In order to realize the above-mentioned adaptive online learning algorithm, an adaptive evaluation structure based on a neural network is designed. The evaluation neural network is used to approximate the value function and calculate the optimal control input. The weight of the evaluation neural network is updated using formula (1), and the control input signal is calculated online in real time using formula (2), which acts on the mobile robot visual servo trajectory tracking process. Figure 2 The system state simulation diagram of the mobile robot visual servo trajectory tracking control of the present invention is shown. Figure 3 The expected trajectory of the visual servo trajectory tracking control of the mobile robot of the present invention and the actual motion trajectory of the mobile robot are displayed, from which it can be seen that the convergence speed of the tracking error is fast and the control effect is good.

[0083] In summary, the mobile robot visual servo tracking control method based on adaptive dynamic programming in the present invention can not only enable the mobile robot to complete trajectory tracking tasks and ensure system stability by using visual information, but also achieve the expected optimal performance indicators, reduce control costs, improve mobile robot tracking effects, and improve controller performance.

[0084] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A mobile robot visual servo tracking control method based on adaptive dynamic programming, characterized in that: The following steps are involved: The current image, the expected image and the reference image of the coplanar feature points are captured by a camera on the mobile robot; based on the current image, the expected image and the reference image, the current position and posture information and the expected position and posture information of the mobile robot are calculated by using homography technology; based on the calculated current position and posture information and the expected position and posture information of the mobile robot, a tracking error model is obtained in combination with robot kinematics; The optimal control problem of the tracking error model is transformed into solving the Hamilton-Jacobi-Bellman equation; Using actual state information of the mobile robot, an adaptive online learning algorithm is used to solve the Hamilton-Jacobi-Bellman equation to obtain an optimal value function, and the mobile robot is controlled with an optimal control input corresponding to the optimal value function; Based on the calculated current posture information and expected posture information of the mobile robot, and combined with the robot kinematics, a tracking error model is obtained, including the following steps: Calculate the position error e(t) of the mobile robot in the current camera coordinate system, and obtain the tracking error model based on the kinematic model of the mobile robot Among them, f(e(t),t) is the nonlinear part of the tracking error model with respect to the state e(t), g(e(t)) is the control matrix, and u(e(t),t) is the control input.

2. The mobile robot visual servo tracking control method based on adaptive dynamic programming according to claim 1 is characterized in that: The method comprises the following steps: capturing a current image, an expected image and a reference image of coplanar feature points by a camera on a mobile robot; calculating the current posture information and the expected posture information of the mobile robot based on the current image, the expected image and the reference image and using homography technology; and comprising the following steps: The coordinate system of the mobile robot and the camera mounted on the mobile robot are set to coincide, four coplanar feature points in the coordinate system space are selected as target points, and the pixel coordinates of the current image, the expected image and the reference image of the camera target point are reconstructed in the Euclidean manner based on the camera model, and the pixel coordinates of the current image, the expected image and the reference image after the Euclidean reconstruction are normalized; The normalized pixel coordinates of the current image, expected image and reference image are used to calculate the homography matrices of the current position and expected position of the mobile robot relative to the reference position, and the current pose and expected pose of the mobile robot are obtained based on the homography technology.

3. The mobile robot visual servo tracking control method based on adaptive dynamic programming according to claim 2 is characterized in that: The normalization formula is as follows: m i =K -1 p i Among them, K is the camera calibration matrix, p i are homogeneous pixel coordinates.

4. The mobile robot visual servo tracking control method based on adaptive dynamic programming according to claim 3 is characterized in that: The Hamilton-Jacobi-Bellman equation is: in, It means to find the partial derivative with respect to time t, V * (e, t) is the optimal value function to be obtained, f(e, t) is the nonlinear part of the tracking error model with respect to the state e(t); Q(e) is a positive definite function, and g(e) is the control matrix; It represents the partial derivative with respect to e(t), and R is a symmetric positive definite matrix.

5. The mobile robot visual servo tracking control method based on adaptive dynamic programming according to claim 4 is characterized in that: The adaptive online learning algorithm is used to solve the Hamilton-Jacobi-Bellman equation to obtain the optimal value function, including the following steps: Based on the current actual system state information, solve the following equation to calculate V(e,t): Where Δt is the sampling time interval, L(e(τ),u(e(τ))) represents the utility function; 2) Calculate the control input signal u(e,t) using the following method: 3) Continuously learn online and repeat the first two steps to make the adaptive online learning algorithm converge.

6. The mobile robot visual servo tracking control method based on adaptive dynamic programming according to claim 5 is characterized in that: The adaptive online learning algorithm is an adaptive neural network algorithm. In each iteration, the following formula is used to update the network parameters of the adaptive neural network algorithm: Where W(t) is the weight of the neural network, φ(e(t)) is the activation function of the neural network, L(e(t),u(e(t))) represents the utility function, and α>0 is the learning rate of the neural network weights; The control input signal u(e(t),t) is calculated using the following formula: Among them, R is a symmetric positive definite matrix and g(e(t)) is the control matrix.

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