A model predictive control method for parafoil system based on Gaussian process

Abstract

The present invention discloses a model predictive control method for a parafoil system based on a Gaussian process, comprising the following steps: establishing a simplified four-degree-of-freedom dynamic model of the parafoil; establishing an unmodeled dynamic part of the parafoil system based on a Gaussian regression process, and building a parafoil system prediction model in combination with the four-degree-of-freedom dynamic model of the parafoil; building a nonlinear model predictive controller based on a Gaussian process based on the parafoil system prediction model to achieve track tracking control of the parafoil system. The present invention is applied to the field of accurate parafoil airdrops, and by combining the Gaussian process to learn the unmodeled dynamics, the prediction results represent the real dynamics of the system as much as possible, thereby enabling the parafoil system to accurately track the reference trajectory, thereby improving the prediction ability of the model predictive control.

Description

Technical Field

[0001] The invention relates to the technical field of wing parachute precision airdropping, and in particular to a wing parachute system model predictive control method based on Gaussian process. Background Art

[0002] As one of the most effective airdrop methods in the world today, the Precision Aerial Delivery Systems (PADS) are being increasingly studied and applied in the fields of spacecraft recovery, material airdrop and airborne parachuting.

[0003] The research on the parafoil precision airdrop system has entered a period of initial maturity and continued exploration. This maturity and exploration is mainly reflected in the development of heavier loads and more reliable and robust tracking control algorithms. In addition to traditional tracking control algorithms such as proportional-integral-derivative control (PID), linear quadratic regulator (LQR), and sliding film control, the model predictive control (MPC) method widely used in the field of unmanned vehicles is a new idea. However, when the nominal model ignores the dynamic characteristics of the system that are not clearly described by the mathematical model (control response delay, material deformation, vertical wind and other factors), the performance of MPC may be impaired because the actual state of the system may not be predicted, resulting in inaccurate tracking.

[0004] In order to enable the parafoil system to accurately track the reference trajectory, thereby improving the prediction ability of model predictive control, the present invention combines Gaussian process to learn the unmodeled dynamics, so that the prediction results represent the real dynamics of the system as much as possible, thereby improving the performance of MPC, and proposes a parafoil system model predictive control method based on Gaussian process. Summary of the invention

[0005] In view of the above-mentioned deficiencies in the prior art, the present invention provides a model predictive control method for a parafoil system based on Gaussian process, which can effectively achieve precise tracking control of the parafoil system on a reference trajectory.

[0006] To achieve the above object, the present invention provides a model predictive control method for a parafoil system based on a Gaussian process, comprising the following steps:

[0007] Step 1, establishing a simplified four-degree-of-freedom dynamic model of the parafoil;

[0008] Step 2, establishing the unmodeled dynamic part of the parafoil system based on the Gaussian regression process, and building a parafoil system prediction model in combination with the parafoil four-degree-of-freedom dynamic model;

[0009] Step 3: Building a Gaussian process-based nonlinear model predictive controller based on the parafoil system prediction model to achieve track tracking control of the parafoil system.

[0010] In one embodiment, step 1 specifically includes:

[0011] The dynamic equation of the parafoil system is established as:

[0012] ;

[0013] in, , , are the positions of the parafoil system in the inertial coordinate system, is the relative air speed, is the relative heading angle, is the flight path angle, , is the wind speed component, is the weight coefficient, For asymmetric control deflection, , are the left and right trailing edge deflections, is the brake parameter;

[0014] set up is the parafoil state variable, For control input, the dynamic equation of the parafoil system is expressed as a nonlinear state space system:

[0015] ;

[0016] in, represents a function of state variables and control inputs;

[0017] use Y It represents the system output, that is, the four-degree-of-freedom dynamic model of the parafoil is:

[0018] ;

[0019] in, is the initial time, is the initial state.

[0020] In one embodiment, in step 2, the main goal of establishing the unmodeled dynamic part of the parafoil system based on the Gaussian regression process is to identify the unknown function of the nonlinear parafoil system model. , specifically:

[0021] ;

[0022] in, is the system observation value, w For process noise that conforms to Gaussian distribution, are the characteristic parameters of the parafoil system involved in Gaussian regression;

[0023] Unknown function is a Gaussian process with unknown parameters, which conforms to the Gaussian distribution, that is:

[0024] ;

[0025] in, , Evaluate the unknown function Function of mean and covariance, For unknown functions At the point The mean value of For unknown functions At the point , the relationship between

[0026] Assume the training data set is:

[0027] ;

[0028] in, is the input data set, is the dimension of the input data, is the number of observation pairs, Each column of Corresponds to an input data point; For the output dataset, is the dimension of the output data, Each line of Corresponds to an output data point;

[0029] According to the properties of Gaussian distribution, the distribution of prediction points is still Gaussian distribution, that is:

[0030] ;

[0031] in, represents the function related to Gaussian Process (GP), Refers to the state variable, is the mean of the distribution of prediction points, is the covariance of the distribution of prediction points;

[0032] Combined with training data set , and the predicted distribution, i.e. the unmodeled dynamics of the parafoil system.

[0033] In one embodiment, Gaussian regression involves characteristic parameters of the parafoil system Specifically:

[0034] ;

[0035] in, , is the introduced matrix, , For the k The state variables and control variables at each moment, T is the transpose of the matrix.

[0036] In one embodiment, the mean and covariance of the distribution of the prediction points are specifically:

[0037] ;

[0038] in, for m×n , representing the kernel function involved in the Gaussian distribution (for example: express The kernel function value between the two satisfies ), is the process noise w The variance of is the identity matrix, for The mean of .

[0039] In one embodiment, in step 2, the parafoil system prediction model is specifically:

[0040] ;

[0041] in, For the parafoil prediction output taking into account the unmodeled dynamics, The matrix selects the states affected by the model error according to the actual situation.

[0042] In one embodiment, step 3 specifically includes:

[0043] The control objective of the parafoil system model predictive control is to make the parafoil system trajectory as close to the reference trajectory as possible in the prediction time domain while reducing energy consumption;

[0044] The energy consumption value is the square integral of the control input in the time domain ,for:

[0045] ;

[0046] in, For the prediction time domain, For the The control input of the prediction step length is is the weight of the control input;

[0047] The objectives of the parafoil system tracking control problem are: to guide the parafoil from the initial position to the target position;

[0048] Therefore, the nonlinear model predictive controller of the parafoil system is:

[0049] ;

[0050] in, J is the objective function, is the input reference value of the controller, Is The predicted value calculated is is a custom weight constant, It is the maximum permissible value that the heading angle can reach under specific conditions;

[0051] Based on the nonlinear model predictive controller, an optimal control sequence for the parafoil system is obtained.

[0052] Compared with the prior art, the present invention has the following beneficial technical effects:

[0053] 1. The present invention combines Gaussian process to learn the unmodeled dynamics, so that the prediction results represent the real dynamics of the system as much as possible, so as to achieve accurate tracking of the reference trajectory by the parafoil system, thereby improving the prediction ability of model predictive control;

[0054] 2. The present invention can realize model predictive control without modeling and deriving a complex and accurate system dynamics model, thereby effectively reducing the complexity of tracking control calculations. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.

[0056] Figure 1 Flow chart of a model predictive control method for a parafoil system based on Gaussian process in an embodiment of the present invention;

[0057] Figure 2 It is an overall framework diagram of the parafoil model predictive control based on Gaussian process in an embodiment of the present invention;

[0058] Figure 3 Schematic diagram of the coordinate system involved in the four-degree-of-freedom dynamic nominal model in an embodiment of the present invention.

[0059] The realization of the purpose, functional features and advantages of the present invention will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0060] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] In addition, the technical solutions between the various embodiments of the present invention can be combined with each other, but it must be based on the fact that ordinary technicians in the field can implement it. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such combination of technical solutions does not exist and is not within the scope of protection required by the present invention.

[0062] This embodiment discloses a model predictive control method for a parafoil system based on a Gaussian process. On the basis of establishing a simplified four-degree-of-freedom dynamic model of the parafoil system, the Gaussian process is combined to learn the dynamics of the unmodeled part, so that the prediction results of the parafoil system prediction model represent the real dynamics of the parafoil system as much as possible, thereby enabling the parafoil system to accurately track the reference trajectory, thereby improving the prediction ability of the model predictive control.

[0063] refer to Figure 1 , Figure 2 In this embodiment, the model predictive control method of the parafoil system based on Gaussian process specifically includes the following steps:

[0064] Step 1, establish a simplified four-degree-of-freedom dynamic model of the parafoil, namely, the nominal model;

[0065] Step 2, establishing the unmodeled dynamic part of the parafoil system based on the Gaussian regression process, and building a parafoil system prediction model in combination with the parafoil four-degree-of-freedom dynamic model;

[0066] Step 3: Build a Gaussian process-based nonlinear model predictive controller based on the parafoil system prediction model to realize the track tracking control of the parafoil system.

[0067] In the process of establishing the four-degree-of-freedom dynamic model of the parafoil in step 1, the following basic assumptions are made:

[0068] 1. The changes in horizontal and vertical speeds of the parafoil during stable flight are negligible, and the speed during turning is approximately the speed during stable flight;

[0069] 2. Ignore the sideslip angle of the parafoil, and the heading angle of the parafoil is approximately equal to the yaw angle;

[0070] 3. Only horizontal wind exists, ignoring the torque caused by the vertical wind field and wind gradient;

[0071] 4. The same horizontal wind is at the same height within the parafoil flying field.

[0072] In addition, in the parafoil system, the inflatable canopy is essentially a wing with a low aspect ratio, so the combined parafoil system of the inflatable canopy and the load can be represented as a rigid body. In addition, the following coordinate system is defined:

[0073] 1. Earth Coordinate System :origin is an arbitrary point fixed relative to the Earth's surface, The axis points due north. The axis points due east. The axis is toward the center of the earth, and the earth coordinate system is the North-East-Down (NED) coordinate system, which is an inertial system.

[0074] 2. Body coordinate system :origin At the center of mass of the parafoil system, The axis is along the positive direction of the longitudinal axis in the symmetry plane of the parafoil. Perpendicular to Axis, positive downward in the symmetry plane, axis It complies with the right-hand rule;

[0075] 3. Airflow coordinate system :origin At the center of mass of the parafoil system, the axis The direction of the velocity vector relative to the air is positive, and the axis In the plane of symmetry of the system, perpendicular to the axis Pointing directly downward, axis Conforms to the right-hand rule.

[0076] In the specific implementation process, it is assumed that the parafoil system is always in a balanced flight state, and the forward rate is a function of the altitude and the yaw rate. For the purpose of path planning, refer to Figure 3 , the dynamic equation of the parafoil system can be established as:

[0077] (1)

[0078] in, , , are the positions of the parafoil system in the inertial coordinate system, is the relative air speed, is the relative heading angle, is the flight path angle, , is the wind speed component, is the weight coefficient, For asymmetric control deflection, , are the left and right trailing edge deflections, is the brake parameter;

[0079] In the dynamic equations of the parafoil system, the relative air velocity , flight path angle can be regarded as a constant, can be considered as a known function of heading rate, for Function of

[0080] set up is the parafoil state variable, For control input, the dynamic equation of the parafoil system is expressed as a nonlinear state space system:

[0081] (2)

[0082] in represents a function of state variables and control inputs;

[0083] use Y It represents the system output, that is, the four-degree-of-freedom dynamic model of the parafoil is:

[0084] (3)

[0085] in, is the initial time, is the initial state.

[0086] The nominal model of the parafoil system in formula (3) cannot describe the disturbance of dynamic characteristics such as control response delay and material deformation of the real parafoil system during the actual movement process. On this basis, in the specific implementation process of step 2, this embodiment estimates and learns the unmodeled dynamic part of the parafoil system, and predicts the model construction through the Gaussian regression process. Specifically, the main goal of establishing the unmodeled dynamic part of the parafoil system based on the Gaussian regression process is to identify the unknown function of the nonlinear parafoil system model. ,in, , specifically:

[0087] (4)

[0088] in, is the system observation value, w is the process noise that conforms to the Gaussian distribution, that is ;

[0089] is the characteristic parameter of the parafoil system involved in Gaussian regression, expressed as:

[0090] (5)

[0091] in, , is the introduced matrix, and , As a constant, by introducing the matrix , , thereby reducing the dimensionality of the learning problem, , For the k The state variables and control variables at each moment, T is the transpose of the matrix

[0092] Unknown function is a Gaussian process with unknown parameters, which conforms to the Gaussian distribution, that is:

[0093] (6)

[0094] in, , Evaluate the unknown function Function of mean and covariance, For unknown functions At the point The mean value of For unknown functions At the point , the relationship between

[0095] Assume the training data set is:

[0096] (7)

[0097] in, is the input data set, is the dimension of the input data, is the number of observation pairs, Each column of Corresponds to an input data point; For the output dataset, is the dimension of the output data, Each line of Corresponds to an output data point;

[0098] According to the properties of Gaussian distribution, the distribution of prediction points is still Gaussian distribution, that is:

[0099] (8)

[0100] in, represents the function related to Gaussian Process (GP), Refers to the state variable, is the mean of the distribution of prediction points, is the covariance of the predicted point distribution, specifically:

[0101] (9)

[0102] in, for m×n , representing the kernel function involved in the Gaussian distribution (for example: express The kernel function value between the two satisfies ), is the process noise w The variance of is the identity matrix, for The mean of

[0103] The resulting prediction distribution not only has the predicted value, but also gives the uncertainty of the prediction (measured by variance). , and the predicted distributions of equations (4) to (9), that is, the unmodeled dynamic part of the parafoil system.

[0104] Based on the nominal model of the parafoil system in formula (3), combined with the unmodeled dynamic part, the prediction model of the parafoil system can be obtained:

[0105] (10)

[0106] in, For the parafoil prediction output taking into account the unmodeled dynamics, The matrix is ​​to select the state affected by the model error according to the actual situation, for example This means that the interference between the nominal model and the true model only affects the first state quantity.

[0107] In the specific implementation process of step 3, the model predictive control of the parafoil is actually dealing with the optimal control problem. The control goal of the model predictive control of the parafoil system in this embodiment is to make the trajectory of the parafoil system as close to the reference trajectory as possible in the prediction time domain while reducing energy consumption. Among them, the energy consumption value in this embodiment is the square integral of the control input in the time domain ,Right now:

[0108] ;

[0109] in, For the prediction time domain, For the The control input of the prediction step length is is the weight of the control input;

[0110] In addition, the goal of the parafoil system tracking control problem is to guide the parafoil from the initial position to the target position, so the nonlinear model predictive controller of the parafoil system is:

[0111] ;

[0112] in, J is the objective function, is the input reference value of the controller, Is The predicted value calculated is is a custom weight constant, It is the maximum allowable value that the heading angle can reach under specific conditions.

[0113] Taking the observed value of the current state quantity of the real parafoil system as the initial value of the state quantity and inputting it into the nonlinear model predictive controller of the parafoil system, the optimal control sequence of the parafoil system can be obtained.

[0114] The above description is only a preferred embodiment of the present invention, and does not limit the protection scope of the present invention. All equivalent structural changes made by using the contents of the present invention specification and drawings under the inventive concept of the present invention, or directly / indirectly applied in other related technical fields are included in the protection scope of the present invention.

Claims

1. A model predictive control method for a parafoil system based on Gaussian process, characterized in that: The steps include: Step 1, establishing a simplified four-degree-of-freedom dynamic model of the parafoil; Step 2, establishing the unmodeled dynamic part of the parafoil system based on the Gaussian regression process, and building a parafoil system prediction model in combination with the parafoil four-degree-of-freedom dynamic model; Step 3: Building a Gaussian process-based nonlinear model predictive controller based on the parafoil system prediction model to achieve track tracking control of the parafoil system.

2. The Gaussian process-based model predictive control method for parafoil systems according to claim 1, characterized in that: Step 1 specifically includes: The dynamic equation of the parafoil system is established as: in, , , are the positions of the parafoil system in the inertial coordinate system, is the relative air speed, is the relative heading angle, is the flight path angle, , is the wind speed component, is the weight coefficient, For asymmetric control deflection, , are the left and right trailing edge deflections, is the brake parameter; set up is the parafoil state variable, For control input, the dynamic equation of the parafoil system is expressed as a nonlinear state space system: in, represents a function of state variables and control inputs; use Y It represents the system output, that is, the four-degree-of-freedom dynamic model of the parafoil is: in, is the initial time, is the initial state.

3. The Gaussian process-based model predictive control method for parafoil systems according to claim 2, characterized in that: In step 2, the main goal of establishing the unmodeled dynamic part of the parafoil system based on the Gaussian regression process is to identify the unknown function of the nonlinear parafoil system model. , specifically: in, is the system observation value, w For process noise that conforms to Gaussian distribution, are the characteristic parameters of the parafoil system involved in Gaussian regression; Unknown function is a Gaussian process with unknown parameters, which conforms to the Gaussian distribution, that is: in, , Evaluate the unknown function Function of mean and covariance, For unknown functions At the point The mean value of For unknown functions At the point , the relationship between Assume the training data set is: in, For the input data set, is the dimension of the input data, is the number of observation pairs, Each column of Corresponds to an input data point; For the output dataset, is the dimension of the output data, Each line of Corresponds to an output data point; According to the properties of Gaussian distribution, the distribution of prediction points is still Gaussian distribution, that is: in, represents the function associated with the Gaussian process, Refers to the state variable, is the mean of the distribution of prediction points, is the covariance of the distribution of the prediction points; Combined with training dataset , and the predicted distribution, i.e. the unmodeled dynamics of the parafoil system.

4. The Gaussian process-based model predictive control method for parafoil systems according to claim 3, characterized in that: Gaussian regression related parafoil system characteristic parameters Specifically: in, , is the introduced matrix, , For the k The state variables and control variables at each moment, T is the transpose of the matrix.

5. The Gaussian process-based model predictive control method for parafoil systems according to claim 3, characterized in that: The mean and covariance of the distribution of prediction points are specifically: in, for m×n The matrix represents the kernel function involved in the Gaussian distribution. is the process noise w The variance of is the identity matrix, for The mean of .

6. The model predictive control method for a parafoil system based on Gaussian process according to claim 3, 4 or 5, characterized in that: In step 2, the parafoil system prediction model is specifically: in, For the parafoil prediction output taking into account the unmodeled dynamics, The matrix selects the states affected by the model error according to the actual situation.

7. The Gaussian process-based model predictive control method for parafoil systems according to claim 6, characterized in that: Step 3 specifically includes: The control objective of the parafoil system model predictive control is to make the parafoil system trajectory as close to the reference trajectory as possible in the prediction time domain while reducing energy consumption; The energy consumption value is the square integral of the control input in the time domain ,for: in, For the prediction time domain, For the The control input of the prediction step length is is the weight of the control input; The objectives of the parafoil system tracking control problem are: to guide the parafoil from the initial position to the target position; Therefore, the nonlinear model predictive controller of the parafoil system is: in, J is the objective function, is the input reference value of the controller, Is The predicted value calculated is is a custom weight constant, It is the maximum permissible value that the heading angle can reach under specific conditions; Based on the nonlinear model predictive controller, an optimal control sequence for the parafoil system is obtained.

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