Gait control method for photovoltaic array cleaning robot

Abstract

The invention relates to a gait control method for a photovoltaic array cleaning robot, and the method comprises the steps: building a kinematic model of the photovoltaic array cleaning robot based on the mass center of the robot, introducing a gray Markov model, carrying out the improvement through employing a metabolism method, and predicting a corresponding optimal gait track in combination with the motion characteristics of the robot. And calculating two parameters of the tail end spring displacement and the attitude angle to realize the design of a gait control algorithm. According to the photovoltaic array cleaning device, the photovoltaic array can be comprehensively cleaned, the cleaning coverage rate is high, and the actual requirements of photovoltaic array cleaning work are met. By means of the method, the gait control problem of the photovoltaic array cleaning robot in the complex environment can be effectively solved, and therefore higher-degree automation and intelligence are achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of automatic control, in particular to a gait control method of a photovoltaic array cleaning robot. Background Art

[0002] As the global energy crisis intensifies and environmental pollution becomes increasingly serious, solar energy as a clean, renewable energy source has attracted more and more attention. As the main way to utilize solar energy, the operating efficiency and power generation of photovoltaic power generation systems are directly related to the utilization rate of solar energy. However, during the operation of photovoltaic power generation systems, the accumulation of pollutants such as dust and dirt will reduce the light transmittance of the photovoltaic module surface, thereby affecting the power generation efficiency. In order to solve this problem, photovoltaic cleaning robots came into being.

[0003] The photovoltaic cleaning robot is an automated device specially used for cleaning photovoltaic power generation systems. Its main function is to remove dust, dirt and other pollutants on the surface of photovoltaic modules to ensure the normal operation and power generation efficiency of photovoltaic power generation systems. The working principle of the photovoltaic cleaning robot mainly includes the following aspects:

[0004] 1. Automatic navigation: The photovoltaic cleaning robot is equipped with a high-precision GPS positioning system and an inertial navigation system to realize automatic identification and positioning of the photovoltaic power generation system. During the cleaning process, the robot can automatically walk according to the preset cleaning route to avoid repeated cleaning and missed cleaning, thereby improving cleaning efficiency.

[0005] 2. Intelligent detection: The photovoltaic cleaning robot is equipped with advanced photoelectric sensors and ultrasonic sensors, which can detect the degree of contamination and type of dirt on the surface of photovoltaic modules in real time. By detecting the degree of contamination, the robot can automatically adjust the cleaning strategy to ensure the best cleaning effect.

[0006] 3. Efficient cleaning: The photovoltaic cleaning robot uses a high-pressure water jet system to flush the surface of the photovoltaic module through high-pressure water flow to wash away the dirt. At the same time, the robot is also equipped with a soft brush and a water absorber to scrub and absorb stubborn dirt to ensure the cleanliness of the photovoltaic module surface.

[0007] 4. Safety protection: During operation, the photovoltaic cleaning robot can monitor the surrounding environment in real time through laser radar and camera to avoid collision with photovoltaic components, brackets and other equipment. In addition, the robot is also waterproof, dustproof, and antifreeze, and can work normally in harsh environments.

[0008] 5. Remote monitoring: The photovoltaic cleaning robot is equipped with a wireless communication module, which can realize remote communication with the host computer. Through the host computer, the operator can monitor the robot's working status, cleaning progress and fault information in real time, which is convenient for timely scheduling and maintenance.

[0009] The structural feature of the photovoltaic array cleaning robot is a crawler-type walking design. Through the raised adhesive and groove design of the rubber crawler, it can easily achieve forward, backward, left and right turns and other movements. However, there are usually large height differences and unevenness between photovoltaic module arrays. The robot needs to be able to adaptively adjust its walking posture and speed to ensure stable walking and avoid collisions with photovoltaic panels.

[0010] At the same time, the photovoltaic array cleaning robot is affected by the terrain distribution of the photovoltaic array in actual application, resulting in poor cleaning effect under control. Summary of the invention

[0011] The purpose of the present invention is to overcome the shortcomings of the prior art, propose a gait control method for a photovoltaic array cleaning robot, establish a kinematic model of the photovoltaic array cleaning robot based on the robot's center of mass, introduce a grey Markov model, adopt the metabolic method for improvement, combine the robot's motion characteristics, predict the corresponding optimal gait trajectory, calculate the two parameters of the end spring displacement and the posture angle, and realize the design of a gait control algorithm.

[0012] The present invention solves the technical problem by adopting the following technical solutions:

[0013] The gait control method of a photovoltaic array cleaning robot comprises the following steps:

[0014] Step 1: According to the position information of the robot, obtain the generalized coordinates of the robot in the coordinate system;

[0015] Step 2: construct a kinematic model of the robot according to the generalized coordinates of the robot in the coordinate system obtained in step 1;

[0016] Step 3: Predict the optimal gait trajectory of the robot based on the constructed kinematic model, grey Markov model and metabolic mechanism.

[0017] Moreover, the specific implementation method of step 1 is: set the center of mass of the robot and its geometric center at the same point, establish a rectangular coordinate system with the center of mass of the robot as the origin, and define the components of the center of mass motion speed on the two coordinate axes during the robot motion:

[0018]

[0019] Among them, x and y represent the components of the robot's center of mass velocity on the x and y coordinate axes respectively, and v t represents the instantaneous motion speed of the robot's center of mass, and θ represents the motion posture angle; further sorting yields:

[0020] xsinθ-ycosθ=0

[0021] Analyze the geometric relationship between the robot's center of mass and the front wheel's geometric center:

[0022]

[0023] Where c represents the geometric center of the robot's front wheel, x c ,y c represents the coordinate value of the point, and d represents the vertical distance between the geometric center of the front wheel and the center of mass of the robot;

[0024] The geometric relationship between the robot's center of mass and the front wheel's geometric center is derived to obtain the robot's generalized coordinates in the coordinate system:

[0025] q=[x c ,y c ,θ]

[0026] Where q represents the generalized coordinates of the robot.

[0027] Moreover, the specific implementation method of step 2 is: introduce the Pfaffian constraint equation to establish the constraint matrix of the robot's generalized coordinates:

[0028] A(q)=[cosθ-sinθ-d][S(q)]

[0029] Among them, A(q) represents the generalized coordinate constraint matrix, S(q) represents the full rank matrix; considering the rotation characteristics of the robot during the movement, the translational velocity and angular velocity of the robot are input into the matrix to obtain the robot's motion velocity constraint matrix:

[0030]

[0031] Among them, V represents the robot motion velocity constraint matrix, v represents the translation velocity of the robot's generalized coordinates, and ω represents the angular velocity. The kinematic model of the robot is established. Through the mapping relationship between the generalized coordinates and the local coordinates of the center of mass, the differential expression of the kinematic model is obtained:

[0032]

[0033] Among them, Q represents the robot kinematic model expression, V x and V y Respectively represent the components of the matrix on the two coordinate axes, and ρ represents the mapping matrix.

[0034] Moreover, the specific implementation method of step 3 is: construct a function that efficiently generates random real numbers in the interval [0,1], directly apply these random real numbers to the kinematic model equations, and directly solve the spatial position of the robot's end effector under different conditions:

[0035]

[0036] Where D represents the robot motion boundary, α max , α min They represent the maximum and minimum rotation angles of the robot wheel hub, R represents a random function, and j represents a random real number generated by the function;

[0037] The grey Markov model is introduced to predict the optimal trajectory of photovoltaic array cleaning. The gait trajectory of the robot when performing photovoltaic array cleaning is assumed to be a random process, so as to establish a random sequence of the robot's gait trajectory state:

[0038] {X n ,n=1,2,…}

[0039] Among them, X n represents a discrete point in the motion trajectory space, and n represents the number of possible values ​​of the discrete point;

[0040] Considering this random sequence as a Markov chain, combined with the solved robot motion boundary, a basic grey Markov model is established:

[0041]

[0042] Among them, P represents the probability of one-step state transition, B(X n ) represents the state vector of the corresponding discrete point, ε represents the gray coefficient; the metabolic mechanism is integrated into the traditional gray Markov model, and the model prediction sequence under the improved metabolic method is:

[0043]

[0044] in, represents the improved prediction sequence, β represents the parameter vector to be estimated of the model, e represents the natural constant, and k represents the unbiased gray coefficient;

[0045] Through the improvement of the metabolic method, the one-step state transition probability in the basic model is improved into the form of a two-step transition probability matrix:

[0046]

[0047] Among them, P (k) represents the two-step transition probability matrix of the improved grey Markov model, P 11 (k) etc. are all matrix vectors;

[0048] The optimal gait trajectory of the photovoltaic array cleaning robot is predicted using the improved grey Markov model:

[0049]

[0050] Among them, F(n) represents the optimal gait, t represents the movement time of the robot, and s represents the model row vector;

[0051] According to the predicted optimal gait trajectory, the terminal spring displacement and attitude angle parameters of the robot gait control are calculated to generate the gait control algorithm of the photovoltaic array cleaning robot;

[0052] Calculate the end spring displacement control parameters of the robot's gait:

[0053]

[0054] Among them, u represents the end spring displacement control parameter, m represents the overall mass of the robot, K represents the stiffness coefficient of the end spring, g represents the acceleration of gravity, G represents the degree of freedom of gait control, and L represents the length of the robot walking unit.

[0055] Calculate the attitude angle control parameters of the robot's gait:

[0056]

[0057] in, represents the attitude angle control parameter, α represents the tilt angle of the photovoltaic array, and v0 represents the yaw speed of the robot. By calculating the two parameters, the results are used as the optimal control parameters output by the algorithm to realize the gait control of the photovoltaic array cleaning robot.

[0058] The advantages and positive effects of the present invention are:

[0059] The present invention establishes a kinematic model of a photovoltaic array cleaning robot based on the robot's center of mass, introduces a gray Markov model, uses the metabolic method for improvement, combines the robot's motion characteristics, predicts the corresponding optimal gait trajectory, calculates the two parameters of the terminal spring displacement and the attitude angle, and implements the design of a gait control algorithm. The present invention can comprehensively clean the photovoltaic array with a high cleaning coverage rate, meeting the actual needs of photovoltaic array cleaning work. The method of the present invention can effectively handle the gait control problem of the photovoltaic array cleaning robot in a complex environment, thereby achieving a higher degree of automation and intelligence. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 A schematic diagram of a photovoltaic array cleaning robot used in an embodiment of the present invention;

[0061] Figure 2 The displacement curve of the spring at the end of the robot according to the embodiment of the present invention;

[0062] Figure 3The gait posture angle change curve of the robot in the embodiment of the present invention;

[0063] Figure 4 It is a schematic diagram comparing the embodiment of the present invention with other control algorithms. DETAILED DESCRIPTION

[0064] The present invention is further described in detail below with reference to the accompanying drawings.

[0065] The gait control method of a photovoltaic array cleaning robot comprises the following steps:

[0066] Step 1: According to the position information of the robot, obtain the generalized coordinates of the robot in the coordinate system.

[0067] Set the robot's center of mass and its geometric center to be at the same point, establish a rectangular coordinate system with the robot's center of mass as the origin, and define the components of the center of mass motion velocity on the two coordinate axes during the robot's motion:

[0068]

[0069] Among them, x and y represent the components of the robot's center of mass velocity on the x and y coordinate axes respectively, and v t represents the instantaneous motion speed of the robot's center of mass, and θ represents the motion posture angle; further sorting yields:

[0070] xsinθ-ycosθ=0

[0071] Analyze the geometric relationship between the robot's center of mass and the front wheel's geometric center:

[0072]

[0073] Where c represents the geometric center of the robot's front wheel, x c ,y c represents the coordinate value of the point, and d represents the vertical distance between the geometric center of the front wheel and the center of mass of the robot;

[0074] The geometric relationship between the robot's center of mass and the front wheel's geometric center is derived to obtain the robot's generalized coordinates in the coordinate system:

[0075] q=[x c ,y c ,θ]

[0076] Where q represents the generalized coordinates of the robot.

[0077] Step 2: Based on the generalized coordinates of the robot in the coordinate system obtained in step 1, construct a kinematic model of the robot.

[0078] The Pfaffian constraint equation is introduced to establish the constraint matrix of the robot's generalized coordinates:

[0079] A(q)=[cosθ-sinθ-d][S(q)]

[0080] Among them, A(q) represents the generalized coordinate constraint matrix, S(q) represents the full rank matrix; considering the rotation characteristics of the robot during the movement, the translational velocity and angular velocity of the robot are input into the matrix to obtain the robot's motion velocity constraint matrix:

[0081]

[0082] Among them, V represents the robot motion velocity constraint matrix, v represents the translation velocity of the robot's generalized coordinates, and ω represents the angular velocity. The kinematic model of the robot is established. Through the mapping relationship between the generalized coordinates and the local coordinates of the center of mass, the differential expression of the kinematic model is obtained:

[0083]

[0084] Among them, Q represents the robot kinematic model expression, V x and V y Respectively represent the components of the matrix on the two coordinate axes, and ρ represents the mapping matrix.

[0085] Step 3: Predict the optimal gait trajectory of the robot based on the constructed kinematic model, grey Markov model and metabolic mechanism.

[0086] In view of the operational challenges of photovoltaic array cleaning robots in photovoltaic power stations with complex terrain, changing environment and limited space, the robot has high path planning complexity, insufficient real-time gait adjustment ability and limited walking speed. The kinematic model of the photovoltaic array cleaning robot was constructed to deeply analyze its motion characteristics.

[0087] Based on the actual needs of cleaning work, the grey Markov model is introduced and improved, aiming to accurately predict and optimize the optimal gait trajectory parameters of the robot, thereby improving work efficiency and adaptability.

[0088] Specifically, a pseudo-random number generation mechanism is directly embedded in the robot's kinematic equations to dynamically simulate the robot's motion behavior under different working conditions.

[0089] By constructing a function that efficiently generates random real numbers in the interval [0,1], these random real numbers are directly applied to the kinematic model equations, and the spatial position of the robot's end effector under different conditions is directly solved. This not only simplifies the process of solving the spatial range of the robot's motion boundary, but also enhances the randomness and authenticity of the simulation results, which helps to more comprehensively evaluate the robot's ability to operate in complex environments. The solution expression is:

[0090]

[0091] Where D represents the robot motion boundary, α max , α min They represent the maximum and minimum rotation angles of the robot wheel hub, R represents a random function, and j represents a random real number generated by the function;

[0092] The grey Markov model is introduced to predict the optimal trajectory of photovoltaic array cleaning. The gait trajectory of the robot when performing photovoltaic array cleaning is assumed to be a random process, so as to establish a random sequence of the robot's gait trajectory state:

[0093] {X n ,n=1,2,…}

[0094] Among them, X n represents a discrete point in the motion trajectory space, and n represents the number of possible values ​​of the discrete point;

[0095] Considering this random sequence as a Markov chain, combined with the solved robot motion boundary, a basic grey Markov model is established:

[0096]

[0097] Among them, P represents the probability of one-step state transition, B(X n ) represents the state vector of the corresponding discrete point, ε represents the gray coefficient;

[0098] In view of the limitations of the traditional grey Markov model, its basic framework has been innovatively improved, with the core being the incorporation of a metabolic mechanism. This mechanism can dynamically remove the oldest data points to continuously update the data sequence, ensuring more accurate capture of the latest system dynamics, thereby significantly improving prediction accuracy: positioning accuracy is precisely controlled within the range of 5 to 10 cm, path tracking accuracy is improved to between 20 and 50 cm, and the average error of trajectory tracking is successfully reduced to less than 20 mm. The model prediction sequence improved by the metabolic method is:

[0099]

[0100] in, represents the improved prediction sequence, β represents the parameter vector to be estimated of the model, e represents the natural constant, and k represents the unbiased gray coefficient;

[0101] Through the improvement of the metabolic method, the one-step state transition probability in the basic model is improved into the form of a two-step transition probability matrix:

[0102]

[0103] Among them, P (k) represents the two-step transition probability matrix of the improved grey Markov model, P 11 (k) etc. are all matrix vectors;

[0104] The optimal gait trajectory of the photovoltaic array cleaning robot is predicted using the improved grey Markov model:

[0105]

[0106] Among them, F(n) represents the optimal gait, t represents the movement time of the robot, and s represents the model row vector;

[0107] According to the predicted optimal gait trajectory, the terminal spring displacement and attitude angle parameters of the robot gait control are calculated to generate the gait control algorithm of the photovoltaic array cleaning robot;

[0108] Calculate the end spring displacement control parameters of the robot's gait:

[0109]

[0110] Among them, u represents the end spring displacement control parameter, m represents the overall mass of the robot, K represents the stiffness coefficient of the end spring, g represents the acceleration of gravity, G represents the degree of freedom of gait control, and L represents the length of the robot walking unit.

[0111] Calculate the attitude angle control parameters of the robot's gait:

[0112]

[0113] in, represents the attitude angle control parameter, α represents the tilt angle of the photovoltaic array, and v0 represents the yaw speed of the robot. By calculating the two parameters, the results are used as the optimal control parameters output by the algorithm to realize the gait control of the photovoltaic array cleaning robot.

[0114] According to the above photovoltaic array cleaning robot gait control method, a photovoltaic array cleaning robot is controlled using different algorithms to verify the effect of the present invention.

[0115] Figure 1The photovoltaic array cleaning robot used in the embodiment of the present invention is shown in the figure. A 0-100V adjustable power supply is selected as the experimental power supply, and a 12V PWM voltage and speed regulation motion control method is adopted to ensure the stable execution of the experimental control parameters.

[0116] The specific operating parameters are shown in Table 1.

[0117] Table 1. Operation parameters of photovoltaic array cleaning robot

[0118] Parameters Parameter Value Motor power 130W Roller brush length 1100mm Walking speed 25~40m / min Roller brush speed 400~550rpm Roller brush diameter 130mm Work efficiency 0.8~1.2MWP Operating voltage 24V

[0119] The devices connected to the photovoltaic array cleaning robot are shown in Table 2.

[0120] Table 2 Overview of robot connection devices

[0121] Device Name quantity Robot Motion Chassis 1 DC Motor Speed ​​Controller 1 Adjustable power supply 1 Microcontroller 1 multimeter 2 Oscilloscope 1

[0122] Photovoltaic panels are used to build a real photovoltaic array cleaning robot walking environment. The photovoltaic panels used are of the monocrystalline silicon type, and the technical parameters are shown in Table 3.

[0123] Table 3 Photovoltaic panel parameters

[0124] Parameters Parameter Value Voltage 18V Adjustable angle 90° power 300W Number of batteries 48 pieces thickness 25mm Number of cores 108 pieces

[0125] 36, 60 and 72 photovoltaic array environments were constructed respectively. Taking the photovoltaic array environment of 36 photovoltaic panels as an example, the method of the present invention was used to control the gait of the cleaning robot. The surface of the photovoltaic array was set to be shallow dirt without long-term accumulated stubborn dirt. Based on this, the control result of the algorithm of the present invention was obtained. Under the analysis of the improved grey Markov model, the control parameters of the terminal spring of the photovoltaic array cleaning robot were obtained, and the final spring displacement result was as follows Figure 2 shown.

[0126] like Figure 2 As shown in the figure, under the control of the algorithm of the present invention, the end spring in the robot motion chassis shows a relatively regular displacement characteristic. This displacement curve result shows that the robot motion gait under the current control parameters is relatively stable.

[0127] The robot motion posture angle is analyzed, and the results are as follows Figure 3 shown.

[0128] like Figure 3 As shown in the figure, the robot's attitude angle changes slightly within a certain range during the movement, indicating that the robot continuously adjusts its attitude angle under the control of the algorithm of the present invention to adapt to the tilted environment of the photovoltaic array and complete the climbing process. The robot's gait is effectively controlled and can complete the cleaning of the photovoltaic array, which has a certain feasibility.

[0129] To ensure the validity of the experimental results, this comparative test conducted a total of 6 experimental groups, of which Group A and Group B were 36 panels, Group C and Group D were 60 panels, and Group E and Group F were 72 panels. The robot's walking cleaning area coverage rate under each method's gait control was counted to evaluate the control performance of each method. After testing, the robot gait control experimental results of each method were obtained as follows Figure 4 shown.

[0130] like Figure 4 As shown, the system cleans the photovoltaic array surface more comprehensively and can cover a larger area. However, other methods are somewhat different from the method of the present invention.

[0131] This system is aimed at the needs of panel array cleaning in the field of photovoltaic power generation. It proposes a gait control algorithm for a photovoltaic array cleaning robot based on an improved grey Markov model. Through gait control, the robot moves to various areas on the surface of the photovoltaic array, making the cleaning more comprehensive, covering more area, and achieving better cleaning effects, providing a more powerful guarantee for the stable operation and efficient power generation of the photovoltaic power generation system.

[0132] It should be emphasized that the embodiments described in the present invention are illustrative rather than restrictive. Therefore, the present invention includes but is not limited to the embodiments described in the specific implementation manner. Any other implementation manners derived by those skilled in the art based on the technical solution of the present invention also fall within the scope of protection of the present invention.

Claims

1. A gait control method for a photovoltaic array cleaning robot, characterized in that: The following steps are involved: Step 1: According to the position information of the robot, obtain the generalized coordinates of the robot in the coordinate system; Step 2: construct a kinematic model of the robot according to the generalized coordinates of the robot in the coordinate system obtained in step 1; Step 3: Predict the optimal gait trajectory of the robot based on the constructed kinematic model, grey Markov model and metabolic mechanism.

2. The photovoltaic array cleaning robot gait control method according to claim 1, characterized in that: The specific implementation method of step 1 is: set the center of mass of the robot and its geometric center to be at the same point, establish a rectangular coordinate system with the center of mass of the robot as the origin, and define the components of the center of mass motion speed on the two coordinate axes during the robot motion: Among them, x and y represent the components of the robot's center of mass velocity on the x and y coordinate axes respectively, and v t represents the instantaneous motion speed of the robot's center of mass, and θ represents the motion posture angle; further sorting yields: xsinθ-ycosθ=0 Analyze the geometric relationship between the robot's center of mass and the front wheel's geometric center: Where c represents the geometric center of the robot's front wheel, x c ,y c represents the coordinate value of the point, and d represents the vertical distance between the geometric center of the front wheel and the center of mass of the robot; The geometric relationship between the robot's center of mass and the front wheel's geometric center is derived to obtain the robot's generalized coordinates in the coordinate system: q=[x c ,y c ,θ] Where q represents the generalized coordinates of the robot.

3. The photovoltaic array cleaning robot gait control method according to claim 1, characterized in that: The specific implementation method of step 2 is: introduce the Pfaffian constraint equation to establish the constraint matrix of the robot's generalized coordinates: A(q)=[cosθ-sinθ-d][S(q)] Among them, A(q) represents the generalized coordinate constraint matrix, S(q) represents the full rank matrix; considering the rotation characteristics of the robot during the movement, the translational velocity and angular velocity of the robot are input into the matrix to obtain the robot's motion velocity constraint matrix: Among them, V represents the robot motion velocity constraint matrix, v represents the translation velocity of the robot's generalized coordinates, and ω represents the angular velocity. The kinematic model of the robot is established. Through the mapping relationship between the generalized coordinates and the local coordinates of the center of mass, the differential expression of the kinematic model is obtained: Among them, Q represents the robot kinematic model expression, V x and V y Respectively represent the components of the matrix on the two coordinate axes, and ρ represents the mapping matrix.

4. The photovoltaic array cleaning robot gait control method according to claim 1, characterized in that: The specific implementation method of step 3 is: construct a function that efficiently generates random real numbers in the interval [0,1], directly apply these random real numbers to the kinematic model equations, and directly solve the spatial position of the robot's end effector under different conditions: Where D represents the robot motion boundary, α max , α min They represent the maximum and minimum rotation angles of the robot wheel hub, R represents a random function, and j represents a random real number generated by the function; The grey Markov model is introduced to predict the optimal trajectory of photovoltaic array cleaning. The gait trajectory of the robot when performing photovoltaic array cleaning is assumed to be a random process, so as to establish a random sequence of the robot's gait trajectory state: {X n ,n=1,2,…} Among them, X n represents a discrete point in the motion trajectory space, and n represents the number of possible values ​​of the discrete point; Considering this random sequence as a Markov chain, combined with the solved robot motion boundary, a basic grey Markov model is established: Among them, P represents the probability of one-step state transition, B(X n ) represents the state vector of the corresponding discrete point, ε represents the gray coefficient; Integrating the metabolic mechanism into the traditional grey Markov model, the model prediction sequence under the improved metabolic method is: in, represents the improved prediction sequence, β represents the parameter vector to be estimated of the model, e represents the natural constant, and k represents the unbiased gray coefficient; Through the improvement of the metabolic method, the one-step state transition probability in the basic model is improved into the form of a two-step transition probability matrix: Among them, P (k) represents the two-step transition probability matrix of the improved grey Markov model, P 11 (k) etc. are all matrix vectors; The improved grey Markov model is used to predict the optimal gait trajectory of the photovoltaic array cleaning robot: Among them, F(n) represents the optimal gait, t represents the movement time of the robot, and s represents the model row vector; According to the predicted optimal gait trajectory, the terminal spring displacement and attitude angle parameters of the robot gait control are calculated to generate the gait control algorithm of the photovoltaic array cleaning robot; Calculate the end spring displacement control parameters of the robot's gait: Among them, u represents the end spring displacement control parameter, m represents the overall mass of the robot, K represents the stiffness coefficient of the end spring, g represents the acceleration of gravity, G represents the degree of freedom of gait control, and L represents the length of the robot walking unit. Calculate the attitude angle control parameters of the robot's gait: in, represents the attitude angle control parameter, α represents the tilt angle of the photovoltaic array, and v0 represents the yaw speed of the robot. By calculating the two parameters, the results are used as the optimal control parameters output by the algorithm to realize the gait control of the photovoltaic array cleaning robot.

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