A Sliding Reverse Constraint Control Method for a Flying Away Type Line Inspection Robot in a Flexible Cable Environment

Abstract

The present invention proposes a reverse constraint control method for sliding of a flying type line inspection robot in a flexible cable environment. The method includes: establishing a state variable equation model for multivariable model predictive control of the flying type line inspection robot, and performing model predictive control on the state equation model; within each control cycle, comparing the output signal value of the controller to obtain a slip rate, using the slip rate as one of the constraints of the objective function to form a reverse constraint of the slip rate on the control system, solving the optimal solution of the objective function through a genetic algorithm planner to obtain the reference input of the multivariable model predictive control; and using the reference input to perform control allocation on the actual input of the multivariable model predictive control. The method proposed by the present invention can be used for input control of a model predictive control system, effectively solves the problem of reverse constraints existing in a multivariable model predictive control system, and improves the applicable range of the model predictive controller.

Description

Technical Field

[0001] The present invention relates to the technical field of control of flying line inspection robots, and particularly to a reverse constraint control method for sliding in a flexible cable environment. Background Art

[0002] The flying line inspection robot for power inspection is hung on the power line by flying and slides along the elastic cable in a catenary shape for a long distance. Affected by environmental factors such as the deformation of the flexible cable caused by the self-weight of the robot and the wind swing at high altitude, the robot will slip when walking on the line, seriously affecting the walking performance and inspection quality of the robot. At this time, it is necessary to automatically and finely adjust the pressure generated by the pressing mechanism to suppress the walking slip. Otherwise, too much pressure will reduce the walking speed and affect the working efficiency of the robot; too little pressure will not be able to effectively suppress the slip. Moreover, when going uphill, as the walking process progresses, the inclination angle of the robot along the power line will increase, increasing the demand for the pressing force.

[0003] Multivariable model predictive control is a local optimal algorithm, commonly used in robot control. This algorithm determines the control action for the future by optimizing a certain performance index at each moment through a prediction model, feedback correction, and rolling optimization. It uses a non-parametric model based on impulse response as the internal model, predicts the future output state of the system based on the input-output states in the past and future, performs feedback correction on the output error of the internal model, compares it with the preset trajectory, applies a quadratic performance index for rolling optimization, and then calculates the control applied to the system at the current moment, thus completing the entire action cycle.

[0004] For a multivariable model predictive control system, although the control quantity at each moment of the system is optimal for the current moment, this algorithm cannot effectively handle the problem of reverse constraints. For a flying line inspection robot in a flexible cable environment, it is necessary to quickly and accurately control the pressing force within a suitable range, that is, dynamically adjust the actual input according to the value of the slip rate η. The slip rate is affected by the numerical relationship between multiple outputs at the current moment, constituting the output reverse constraint of this control system. Therefore, the usual multivariable model predictive control is difficult to directly use or achieve good control effects. Based on this, the present invention proposes a hierarchical control method of multivariable model predictive control based on reverse constraint genetic algorithm to solve the problem of reverse constraint hierarchical control in a multi-input multi-output system. Summary of the Invention

[0005] Aiming at the problem of reverse constraints existing in the multi-input multi-output control system of a flying line inspection robot, the present invention proposes a reverse constraint control implementation method applicable to multivariable model predictive control.

[0006] The present invention adopts the following technical solutions.

[0007] A method for controlling the direction constraint of the flexible guiding and space sliding of a flying-away type line inspection robot, including:

[0008] Define the state variables of the multivariable model predictive control system of the flying-away type line inspection robot, and establish a state variable equation model for multivariable model prediction;

[0009] Perform model predictive control on the state variable equation model.

[0010] Establish an objective function for model predictive control, solve the optimal solution of the objective function through a genetic algorithm, and obtain the reference input for multivariable model predictive control;

[0011] Use the reference input to perform control allocation on the actual input quantity of the multivariable model predictive control.

[0012] Further, the defining of the state variables of the multivariable model predictive control system and the establishing of the state variable equation model of the multivariable model predictive control system include:

[0013] Define the state variable x of the multivariable model predictive control system based on the flying-away type line inspection robot as follows:

[0014] x = [x1, x2] T = [x, v] T , (1)

[0015] wherein, x1 represents the displacement x of walking on the line, and x2 represents the speed v of walking on the line;

[0016] For the entire multivariable model predictive control system, its control input quantities are the driving motor output torque T and the pressing motor pressing force P. Establish the state variable equation model of the multivariable model predictive control as follows:

[0017]

[0018] In the formula, m is the mass of the unmanned aerial vehicle, ε is the friction coefficient, g is the acceleration due to gravity, θ is the inclination angle of the unmanned aerial vehicle, R is the radius of the driving wheel. Among them, the inclination angle of the unmanned aerial vehicle is used as an interference quantity in the form of a sine function, that is

[0019] Further, the performing of model predictive control on the state variable equation model, the establishing of the objective function of model predictive control, and the solving of the optimal solution of the objective function through a genetic algorithm to obtain the reference input of the model predictive control system include:

[0020] Discretize the control system to obtain a discretized model, and derive the predicted output quantity derived from the discretized model prediction.

[0021] Compare the predicted output with the target output, establish the objective function of model predictive control, and solve the optimal solution of the objective function through the genetic algorithm to obtain the reference input of the control input, including:

[0022] Define the output variables of the multivariable model input, including:

[0023] y = [y1 y2 y3 y4] T = [x, v, ω1, ω2] T , (3)

[0024] Among them, y1 represents the displacement x of walking on the line, y2 represents the speed v of walking on the line, y3 represents the angular velocity ω1 of the driving wheel, and y4 represents the angular velocity ω2 of the driven wheel;

[0025] In each control period, by comparing the output signal values of the controller, the actual slip ratio η = y3 / y4 is obtained;

[0026] In each control period, taking the slip ratio as one of the constraints, establish the objective function of model predictive control, and solve the optimal solution of the objective function through the genetic algorithm to obtain the reference input of the multivariable model predictive control system, including:

[0027] The state space equation of the model predictive control system is:

[0028]

[0029] Among them, x1 represents the displacement x of walking on the line, x2 represents the speed v of walking on the line, u1 represents the driving motor torque T, u1 represents the pressing force P of the pressing motor, and ω i represents the disturbance quantity; in addition, the coefficient matrices A and B are respectively:

[0030]

[0031] Discretize the state space equation, compare the predicted output obtained from the discretized model prediction with the target output, establish the objective function of model predictive control, and solve the optimal solution of the objective function through the genetic algorithm to obtain the control law of the control input, thereby obtaining the reference input of the multivariable model predictive algorithm. Include:

[0032] The pressing force requirement for the robot not to slip is:

[0033]

[0034] For the objective function set of model predictive control:

[0035]

[0036] Solving the optimal control law through a genetic algorithm, including:

[0037] Establish a constraint domain for solving based on the genetic algorithm:

[0038]

[0039] Obtain the optimal solution through the genetic algorithm.

[0040] Furthermore, the optimal control law obtained by using the genetic algorithm is used to perform control allocation on the true input quantity of the model predictive control system, including:

[0041] Establish the objective function for performing control allocation on the true input quantity of the multivariable model predictive control system as:

[0042]

[0043]

[0044] wherein, [T - , T + , [P - , P + are respectively the output torque constraint condition of the driving motor and the output pressure constraint condition of the pressing motor, and λ T , λ p are respectively the weight coefficient matrices of the two variables;

[0045] Solve the optimal solution of the objective function through the sequential quadratic programming method to obtain the optimal matching control quantities of the driving motor torque and the pressing motor output pressure of the multivariable model predictive control system, and perform control allocation through the optimal matching control quantities of the driving motor torque and the pressing motor output pressure and the true input quantity of the multivariable model predictive control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, examples of the embodiments are shown in the drawings. The embodiments described below with reference to the drawings are exemplary and are only used to explain the present invention and should not be construed as limiting the present invention.

[0047] Figure 1 Schematic diagram of a flying-type line inspection robot provided by an embodiment of the present invention; including a main driving wheel 1, auxiliary wheels 2, 4, and a pressing wheel 3.

[0048] Figure 2 Schematic diagram of the implementation principle of a multivariable model predictive control method based on a genetic algorithm provided by an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0049] The embodiments of the present invention will be described in detail below, and examples of the embodiments are given in the accompanying drawings.

[0050] Those skilled in the art of the present technology can understand that: Unless otherwise defined, all terms (including technical terms and scientific terms) used herein have the same meaning as the general understanding of those of ordinary skill in the field to which the present invention belongs.

[0051] For the convenience of understanding the embodiments of the present invention, the following will further explain and illustrate with several specific embodiments in conjunction with the accompanying drawings, and each embodiment does not constitute a limitation on the embodiments of the present invention.

[0052] Aiming at the problem of reverse constraint of the output quantity in the multi-input multi-output control system of the flying-away type line inspection robot, the present invention proposes a control method combining a genetic algorithm based on reverse constraint programming and multi-variable model predictive control, which can effectively achieve the closed-loop control of the system and is used to achieve the high-precision control of the flying-away type line inspection robot.

[0053] Figure 1 FIG. is a schematic structural diagram of the flying-away type line inspection robot according to an embodiment of the present invention, where 1 is a driving wheel, 2 and 4 are guiding wheels, and 3 is a main pressing wheel.

[0054] The following conducts modeling and analysis on the on-line inspection control system of the flying-away type line inspection robot:

[0055] Step 1: Model Predictive Control (MPC);

[0056] First, define the state variable x of the on-line inspection system of the flying-away type line inspection robot as follows:

[0057] x = [x1, x2] T = [x, v] T

[0058] Among them, x1 represents the displacement x of walking on the line, and x2 represents the speed v of walking on the line.

[0059] For the entire multi-variable model predictive control system, its control input quantities are the output torque T of the driving motor and the pressing force P of the pressing motor. The state variable equation model of the multi-variable model predictive control is established as follows:

[0060]

[0061] In the formula, m is the mass of the unmanned aerial vehicle, ε is the friction coefficient, g is the acceleration due to gravity, θ is the inclination angle of the unmanned aerial vehicle, R is the radius of the driving wheel. Among them, the inclination angle of the unmanned aerial vehicle is used as an interference quantity in the form of a sine function, that is

[0062] Define the output variables of the multi-variable model input as follows:

[0063] y = [y1 y2 y3 y4] T = [x, v, ω1, ω2] T

[0064] Among them, y1 represents the displacement x of the on-line inspection, y2 represents the speed v of the on-line inspection, y3 represents the angular velocity ω1 of the driving wheel, and y4 represents the angular velocity ω2 of the driven wheel;

[0065] The on-line inspection mechanism has 2 actuators, and the upper and lower limits of the execution range are set for each actuator. Each actuator corresponds to 1 input control variable, and the on-line walking mechanism has 2 input control variables.

[0066] The on-line walking system has 2 control input variables: the driving motor output torque T and the pressing force P of the pressing mechanism, expressed as the 2D column vector u = [u1 u2] T ; among them, u1 represents the driving torque T, and u2 represents the pressing force P.

[0067] There are upper and lower limits for each control input, expressed as

[0068] The state equation of the on-line walking system of the flying type line inspection robot:

[0069]

[0070] Establish a prediction model with model length N and prediction step K; the specific process of establishing the model predictive control model is:

[0071]

[0072] Define:

[0073]

[0074] Then the prediction error value of the process quantity for each step is:

[0075] Δx m (k + 1) = A m Δx m (k) + B m Δu(k)

[0076] Correspondingly, the prediction error of the output variable for each step is:

[0077] Δy(k + 1) = C m Δx m (k + 1) = C m A m Δx m (k) + C m Bm Δu(k)

[0078] where Δy(k + 1) = y(k + 1) - y(k);

[0079] Here, a new state variable vector is selected: x(k) = [Δx m (k) T , y(k) T T ; and we can get:

[0080]

[0081]

[0082] where: I q×q represents the identity matrix, is the zero matrix.

[0083] Simplify the above equation to:

[0084]

[0085] where A, B, C correspond to the above equation.

[0086] Define vectors Y and ΔU:

[0087]

[0088] Based on the above, obtain the process prediction result within the step size:

[0089]

[0090] Substitute into the system model:

[0091]

[0092] where:

[0093]

[0094] Step 2: Inverse constraint programming based on genetic algorithm;

[0095] The pressing force requirement for the robot not to slip is:

[0096] Establish a set of model predictive control objective functions with the slip rate as one of the constraints:

[0097]

[0098] Establish the constraint domain as:

[0099] ​

[0100] The optimal solution is obtained through a genetic algorithm. The reference input is obtained.

[0101] Step 3: Control allocation;

[0102] Using the reference input obtained in Step 2, the actual input of the control system is controlled and allocated to obtain the true input quantity of the system.

[0103] It is proposed to adopt an optimization-based control allocation method to allocate the actual input control quantity of the model predictive control system to obtain the optimal control input.

[0104] The reference input quantity u(k i )* is reflected in the optimization objective function in the form of constraints. In the process of model predictive control, the energy consumption of each driving component is represented by the function W i (u i ). Considering the optimal energy consumption without slipping, the objective function for controlling and allocating the true input quantity of the multivariable model predictive control system is:

[0105]

[0106]

[0107] Among them, [T - , T + , [P - , P + are the output torque constraint condition of the driving motor and the output pressure constraint condition of the pressing motor respectively, and λ T , λ p are the weight coefficients of the two variables respectively.

[0108] The optimal solution of

[0103] is solved by the sequential quadratic programming method to obtain the optimal matching control quantities of the driving motor torque and the pressing motor output pressure of the multivariable model predictive control system, and the true input quantity of the multivariable model predictive control system is controlled and allocated through the optimal matching control quantities of the driving motor torque and the pressing motor output pressure.

[0109] In summary, the method proposed in the embodiment of the present invention can be used for the input control of a multivariable model predictive control system, effectively solving the output reverse constraint control problem in the multivariable model predictive control system. The output following control of the multivariable model predictive control system is realized, and the output response and energy consumption efficiency of the multivariable model predictive control are improved.

Claims

1. A method for controlling the reverse restraint of a flying-type line inspection robot during sliding in a flexible cable environment, characterized in that, Including: Step 1: Define the state variables of the flying wire - following robot for multivariable model predictive control, and establish the state - variable equation model of multivariable model prediction; within each control period, by comparing the output signal values of the controller, obtain the actual slip ratio. Step 2: Within each control period, compare the relationship between the actual slip ratio and the target slip ratio, establish an objective function with the slip ratio as one of the constraints, and solve the optimal solution of the objective function through the genetic algorithm to obtain the reference input quantity of multivariable model control. Step 3: Use the reference input quantity to perform control allocation on the actual input quantity of multivariable model predictive control. Establish the state - variable equation model of multivariable model predictive control, including: Step 1: Define the state variable \(x\) of the flying wire - following robot as follows: x = [x1, x2] T = [x, v] T (1) Among them, \(x_1\) represents the displacement \(x\) of walking on the wire, and \(x_2\) represents the speed \(v\) of walking on the wire. Step 2: For the entire multivariable model predictive control, its control input quantities are the driving - motor output torque \(T\) and the pressing - motor pressing force \(P\). Establish the state - variable equation model of multivariable model predictive control as follows: In the formula, \(m\) is the mass of the unmanned aerial vehicle, \(\varepsilon\) is the friction coefficient, \(g\) is the acceleration due to gravity, \(\theta\) is the inclination angle of the unmanned aerial vehicle, \(R\) is the radius of the driving wheel. Among them, the inclination angle of the unmanned aerial vehicle is used as a disturbance quantity in the form of a sine function, that is, \(\omega=\sin\theta\). Step 3: Define the output variables of the multivariable model input, including: y = [y1 y2 y3 y4] T = [x, v, ω1, ω2] T (4) Among them, \(y_1\) represents the displacement \(x\) of walking on the wire, \(y_2\) represents the speed \(v\) of walking on the wire, \(y_3\) represents the angular velocity \(\omega_1\) of the driving wheel, and \(y_4\) represents the angular velocity \(\omega_2\) of the driven wheel. Perform model predictive control on the state - variable equation. Within each control period, when the robot moves a long distance along a catenary - shaped elastic cable, it is disturbed by environmental factors such as the deformation of the flexible cable caused by the robot's own weight and the wind swing at high altitude, resulting in a slipping phenomenon when the robot walks on the wire; by comparing the output signal values of the control system, the actual slip ratio can be obtained; within each control period, compare the actual slip ratio with the target slip ratio, establish an objective function with the slip ratio as one of the constraints, and solve the optimal solution of the objective function through the genetic algorithm to obtain the reference input of the multivariable model predictive control system, including: Step 1: Define the control variables of the control system \(u = [u_1\ u_2]\) T ; where \(u_1\) represents the driving torque \(T\), and \(u_2\) represents the pressing force \(P\). Step 2: Establish a control model for the multivariable model predictive control. Step 3: Discretize the control model to obtain a discretized model. Establish an objective function of model predictive control for the predicted output and the target output derived from the discretized model. By using the slip ratio as one of the constraint conditions and using the genetic algorithm to solve the optimal solution of the objective function of the model predictive control, obtain the reference input of the control input. Establish an objective function of predictive - model control for the predicted output and the target output derived from the discretized model. Through multi - objective programming with the slip ratio as one of the constraint conditions and solve the optimal solution of the objective function through the genetic algorithm, thereby obtaining the reference input of the multivariable control system, including: Step 1: The pressing - force requirement for the robot not to slip is: Step 2: Define the slip ratio \(\eta = y_3 / y_4\). Step 3: Establish an objective function: Establish a constraint domain with the slip ratio as one of the constraints: Step 4: Solve the optimal solution of the objective function by means of a genetic algorithm to obtain the reference input of the multivariable model predictive control.

2. The method according to claim 1, wherein The control allocation of the true input quantity of the multivariable model predictive control system by using the reference input of the multivariable model predictive control includes: Step 1: Among them, [T - , T + , [P - , P + are the output torque constraint condition of the drive motor and the output pressure constraint condition of the pressing motor respectively, λ T , λ p are the weight coefficients of the two variables respectively; Step 2: Solve the optimal solution of the objective function by means of sequential quadratic programming to obtain the optimal matching control quantities of the driving motor torque and the pressing motor output pressure of the multivariable model predictive control system, and perform control allocation on the true input quantity of the model predictive control system by using the optimal matching control quantities of the driving motor torque and the pressing motor output pressure.

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