A robust constraint predictive control method and system for a quadrotor unmanned aerial vehicle

Abstract

The present invention discloses a robust constraint predictive control method for a quad-rotor unmanned aerial vehicle, constructs a dynamic model of a quad-rotor unmanned aerial vehicle, constructs a constraint predictive control model of the quad-rotor unmanned aerial vehicle based on the dynamic model, sets constraint conditions, and finally solves the constraint predictive control model of the quad-rotor unmanned aerial vehicle to complete the predictive control of the quad-rotor unmanned aerial vehicle. The scheme of the present invention can realize robust flight control and trajectory tracking of the quad-rotor unmanned aerial vehicle in an uncertain, interference and constrained environment, improve the robustness and stability of the uncertainty system of the quad-rotor unmanned aerial vehicle, and improve the real-time prediction of the system.

Description

Technical Field

[0001] The present invention belongs to the field of flight control and trajectory tracking of a quad-rotor unmanned aerial vehicle system, and in particular relates to a robust constraint predictive control method and system for a quad-rotor unmanned aerial vehicle. Background Art

[0002] At present, the research on the flight control methods of quadrotor drones is constantly deepening at home and abroad, among which robust control in complex environments has become the focus. Quadrotor drones often face various uncertain factors, interference and system constraints during flight, such as wind speed changes, airflow disturbances, system constraints and obstacles. These factors will cause drastic fluctuations and physical limitations in the flight state, thus affecting flight safety and stability. Existing control methods include traditional PID control, nonlinear control, adaptive control and modern control. Although they can cope with interference to a certain extent, in extreme cases, the robustness is still insufficient and most of them do not consider system constraints. In particular, many control strategies do not fully consider environmental uncertainty, nonlinear characteristics of the model and system constraints when designing, resulting in a significant reduction in control effect under uncertain and strong interference constraints. In terms of robustness analysis, existing technologies mostly rely on historical data, respond poorly to dynamic changes in the actual flight environment, and do not consider the constraints to ensure system safety. For example, although sliding mode control and fuzzy control perform well in dealing with disturbances, they rarely consider system input and output constraints. Under high-frequency and high-amplitude interference, the control accuracy may still decrease. In addition, although the use of learning methods such as neural networks can help improve adaptability, the training and optimization process of the model requires a large amount of data and time, which may be difficult to achieve in dynamic flight scenarios.

[0003] In general, the current control methods for quadrotor UAVs to maintain robustness under uncertainty, interference and constraints still have shortcomings, especially when dealing with rapidly changing, nonlinear strong interference and constrained environments. Further research on effective control algorithms and technologies is needed to improve the robustness and stability of UAVs in complex environments, thereby ensuring their safety and reliability in practical applications. Summary of the invention

[0004] In view of the above problems, the object of the present invention is to provide a robust constraint predictive control method and system for a quadrotor unmanned aerial vehicle.

[0005] The specific technical solution for achieving the purpose of the present invention is:

[0006] A robust constraint predictive control method for a quadrotor unmanned aerial vehicle comprises the following steps:

[0007] Step 1: Construct a dynamic model of the quadrotor drone;

[0008] Step 2: Build a constraint predictive control model for the quadrotor drone and set constraint conditions;

[0009] Step 3: Solve the constraint predictive control model of the quadrotor UAV and complete the predictive control of the quadrotor UAV.

[0010] Compared with the prior art, the present invention has the following beneficial effects:

[0011] This scheme proposes a robust constrained predictive control method for quadrotor UAVs, which realizes robust flight control and trajectory tracking of quadrotor UAVs in uncertain, disturbed and constrained environments; this scheme uses polytopes to describe the uncertainty system of the quadrotor UAV to describe the uncertainty and bounded range of the system, converts the cost function of the robust constrained predictive control model of the quadrotor UAV into a "minimum-maximum" optimization problem, establishes system control input constraints and output constraints represented by LMI linear matrix inequalities, obtains the optimal performance of the quadrotor UAV under the "worst" case of system parameter changes, and combines PID control to process the lifting and lowering state of the UAV, realizes robust flight constraint control of the quadrotor UAV, improves the robustness and stability of the uncertainty system of the quadrotor UAV, and improves the real-time performance of the system prediction.

[0012] The present invention is further described below in conjunction with specific implementation modes. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 It is a schematic flow chart of the robust constraint predictive control method for a quadrotor unmanned aerial vehicle of the present invention.

[0014] Figure 2 Schematic diagram of the robust constraint predictive control method for a quadrotor drone in an embodiment of the present invention.

[0015] Figure 3 It is a schematic diagram of the 3D trajectory tracking effect in the trajectory tracking effect of the quad-rotor drone in an embodiment of the present invention.

[0016] Figure 4 It is a schematic diagram of the yOz plane trajectory tracking effect in the trajectory tracking effect of the quad-rotor drone in an embodiment of the present invention.

[0017] Figure 5 Schematic diagram of the xOy plane trajectory tracking effect of the quad-rotor drone in the embodiment of the present invention.

[0018] Figure 6 Schematic diagram of the x-direction position change of the quad-rotor drone in an embodiment of the present invention.

[0019] Figure 7 Schematic diagram of the y-direction position change of the quad-rotor drone in an embodiment of the present invention.

[0020] Figure 8 Schematic diagram of the speed change in the x direction of the quad-rotor drone in an embodiment of the present invention.

[0021] Fig. 9 Schematic diagram of the speed change in the y direction of the quad-rotor drone in an embodiment of the present invention. DETAILED DESCRIPTION

[0022] Example

[0023] The technical solutions in the embodiments of the present invention will be described clearly and completely below in conjunction with the accompanying drawings in the embodiments of the present invention. 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.

[0024] As shown in this application and claims, unless the context clearly indicates an exception, the words "a", "an", "an kind" and / or "the" do not refer to the singular and may also include the plural. Generally speaking, the terms "include" and "comprise" only indicate the inclusion of the steps and elements that have been clearly identified, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements.

[0025] Unless otherwise specifically stated, the relative arrangement, numerical expressions and numerical values ​​of the parts and steps set forth in these embodiments do not limit the scope of the present application. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the accompanying drawings are not drawn according to the actual proportional relationship. The technology, method and equipment known to those of ordinary skill in the relevant field may not be discussed in detail, but in appropriate cases, the technology, method and equipment should be considered as a part of the authorization specification. In all examples shown and discussed here, any specific value should be interpreted as being merely exemplary, rather than as a limitation. Therefore, other examples of exemplary embodiments may have different values. It should be noted that similar reference numerals and letters represent similar items in the following drawings, so that once a certain item is defined in an accompanying drawing, it does not need to be further discussed in subsequent drawings.

[0026] Combination Figure 1 and Figure 2 , a robust constraint predictive control method for a quadrotor unmanned aerial vehicle, comprising the following steps:

[0027] Step 1: Build a dynamic model of the quadrotor drone:

[0028] Based on the principles of aerodynamics, the lift and torque model of the quadrotor drone is constructed according to the lift equation, the torque generated by the rotor, and the flight state. By adjusting the rotation speed of each rotor, the pitch, roll, and yaw are controlled to ensure the stable flight of the drone. Based on the Newton-Euler method, the linear and angular motion dynamics model of the quadrotor drone is constructed. Consider a symmetrical quadrotor drone with a mass of m and a moment of inertia of J:

[0029] (1)

[0030] in, The origin of the machine system The position coordinates relative to the world system, m is the mass of the quadrotor drone, J is the moment of inertia of the quadrotor drone, is the linear velocity of the quadrotor drone in the aircraft system, R is the coordinate transformation from the aircraft system to the inertial system, is the angular velocity of the machine system, is an antisymmetric matrix, is the torque, F is the resultant external force, T is the lift, is the acceleration due to gravity, and Represent the unit matrix in the quadrotor drone system and the world system respectively.

[0031] Step 2: Build a constraint predictive control model for the quadrotor drone and set constraint conditions;

[0032] When performing fixed-point hovering and path tracking operations of a quadrotor drone, the velocity loop can ensure that the speed of the quadrotor drone changes smoothly and reduce position errors. In order to make the quadrotor drone system more robust in dealing with uncertainty, interference and constraints, the forward Euler discretization method is used to discretize the drone kinematic equations in the x and y directions to design a robust constraint predictive control method for a quadrotor drone:

[0033] Define the system state as ,in, , and represents the expected trajectory position, and represents the desired trajectory speed; the input of the system is ,in , and represents the desired trajectory acceleration, and the output of the system is If environmental factors are considered in the system, air resistance, wind disturbance, etc. will affect the speed of the drone as uncertain interference items, causing the speed to decay with the time step, where the interference item is expressed as , the attenuation is , assuming that the interference term acts in the y direction, the nonlinear discrete state space model of the quadrotor drone is:

[0034] in , , is a fourth-order unit matrix, is the sampling time.

[0035] because is an unknown time-varying quantity within a certain range, so the system is an uncertain system. The characteristics of the system matrix The unknown time-varying, but its range of variation is limited, can be regarded as being in a set of matrices, so the uncertainty matrix of these quadrotor drone systems can be expressed in the following way using polytopic descriptions:

[0036] in, and The vertices of the set of known system matrices are called polytopic vertices. is the convex hull formed by all polytopic vertices, that is, for any time and All meet the following requirements:

[0037]

[0038] in, is the weight coefficient, satisfying the convex combination condition, that is, all The sum of is 1, and Non-negative. At this time, the matrix will always fall on L vertices The convex hull Inside, and the vertex It is given again and can be used to describe the uncertainty range of the quadrotor drone system.

[0039] Under the constraints of input and output variables of the quadrotor drone control, the system cost function is established using the robust model predictive control idea, and the control at time k is converted into solving the following infinite time domain "minimum-maximum" optimization problem, that is, in predictive control, when rolling optimization is performed, the system parameters will be in the range The performance index of the quadrotor UAV robust predictive control system in the infinite time domain is optimized by taking into account the system dynamics and constraints.

[0040]

[0041] Among them, G is the state weight matrix, U is the control input weight matrix, and the output of the quadrotor drone system is , is the output matrix, is the sampling time, and is the vertex of the known system matrix set A, B, called a polytopic vertex, is the convex hull formed by all polytopic vertices, is the attenuation amount, L represents the number of convex hulls, Umax is the control input constraint, Ymax is the output constraint, i represents the i-th convex hull, and k represents the k-th moment.

[0042] For this problem, we first give the upper bound of the maximum problem and transform the problem into a simple minimization problem. The quadratic form of X in the control system of the quadcopter is , V corresponding to the system requirements meets:

[0043]

[0044] Because the quadrotor UAV system is required to achieve trajectory tracking and closed-loop asymptotic stability, it must have ,Right now . Now calculate all the moments and we can get , thus obtaining the upper bound of the extremely large problem:

[0045]

[0046] The state feedback control law is used to control the state of the quadrotor UAV system in an invariant set, and the system output and control input constraints are considered.

[0047] First, we need to solve the problem of the infinite number of control variables of the quadcopter.

[0048]

[0049] Control the state of the quadrotor drone system within a constant set The following conditions need to be met:

[0050]

[0051] Among them, Q is a positive definite symmetric matrix that defines the shape and size of the ellipsoidal invariant set;

[0052] The essence of this condition is the constraint condition of the quadrotor drone system. In order to better describe the constraint content, this paper organizes the constraint transformation process of the quadrotor drone system and takes , using the Schur complement property of the linear matrix inequality LMI expression and the convex hull property of the polytopic description, we get the following constraints:

[0053] (1) The state of the quadrotor drone at time k Keep in the unchanged set In, meet:

[0054]

[0055] (2) In order to make the quadrotor UAV system asymptotically stable, the quadratic It needs to decrease and satisfy the condition of formula (6), then:

[0056]

[0057] It can be further expressed as:

[0058]

[0059] According to the Schur complement property of LMI, the above matrix inequality is transformed into the LMI inequality form:

[0060]

[0061] Due to the uncertainty of the parameters Satisfy the polyhedral conditions of the quadrotor drone system, which are the vertex parameters of the polyhedral model The above conditions can be reduced to the linear combination of each vertex parameter Conditions to be met:

[0062]

[0063] Under the state feedback control law, satisfying the above conditions can make the state of the quadrotor UAV system controlled within the invariant set. middle.

[0064] It is necessary to make the objective function of the robust constraint prediction system of the quadrotor drone have a maximum upper bound. and Available , then the upper bound of the objective function of the robust constrained predictive control problem of the quadrotor UAV exists.

[0065] (3) The output of the robust constraint prediction control system of the quadrotor UAV also needs to meet the constraint conditions. Consider the output constraint of the quadrotor UAV:

[0066]

[0067] Since X is in the invariant set , we can calculate and arrange the above formula to get:

[0068]

[0069] The above formula can be transformed into the model vertex parameters using the polyhedral condition , The LMI linear matrix inequality form is:

[0070]

[0071] Among them, H is the control gain matrix, which participates in weight coupling, is a scalar parameter that measures the system performance and represents the constraint boundary;

[0072] (4) Imposing constraints on the control input weight matrix:

[0073] Constraining and controlling the acceleration of a quadcopter drone during flight can ensure flight stability and rapid response. While satisfying the state feedback control law, it is necessary to satisfy the control input constraints in the robust constraint predictive control problem of the quadcopter drone and impose constraints on the acceleration control input. , and the linear matrix inequality LMI form that satisfies the control input constraints of the quadrotor drone is obtained:

[0074]

[0075] After the above analysis and derivation, the optimal solution of the robust constrained predictive control of the quadrotor drone at time k is transformed into solving the following optimization problem:

[0076]

[0077] Step 3: Solve the constraint predictive control model of the quadrotor UAV and complete the predictive control of the quadrotor UAV.

[0078] When the Q and Y values ​​are obtained, D can be obtained, and thus the specific form of the state feedback control law can be obtained. As long as the initial state of the quadcopter control system is in the invariant set In the Lyapunov function The closed-loop system obtained by the above-mentioned robust predictive control law for the quadrotor UAV must be asymptotically stable, and the optimal performance index can be obtained under the "worst" condition of model uncertainty. PID control is used to process the lifting and lowering state of the UAV, thereby realizing robust flight constraint control of the quadrotor UAV and improving the prediction speed of the system.

[0079] The present invention also provides a quad-rotor unmanned aerial vehicle robust constraint prediction control system, comprising the following modules:

[0080] Dynamics model building module: used to build the dynamics model of the quadrotor drone;

[0081] Constraint predictive control model building module: used to build the constraint predictive control model of the quadrotor drone and set the constraint conditions;

[0082] Control module: used to solve the constraint predictive control model of the quadrotor UAV and complete the predictive control of the quadrotor UAV.

[0083] The present invention also provides a computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the following steps when executing the computer program:

[0084] Step 1: Construct a dynamic model of the quadrotor drone;

[0085] Step 2: Build a constraint predictive control model for the quadrotor drone and set constraint conditions;

[0086] Step 3: Solve the constraint predictive control model of the quadrotor UAV and complete the predictive control of the quadrotor UAV.

[0087] The present invention also provides a computer storable medium having a computer program stored thereon, wherein when the computer program is executed by a processor, the following steps are implemented:

[0088] Step 1: Construct a dynamic model of the quadrotor drone;

[0089] Step 2: Build a constraint predictive control model for the quadrotor drone and set constraint conditions;

[0090] Step 3: Solve the constraint predictive control model of the quadrotor UAV and complete the predictive control of the quadrotor UAV.

[0091] In this embodiment, a DJI Phantom 4RTK quad-rotor drone is used as the simulation object, with a mass of 1391g, a wheelbase of 350mm, a maximum ascent speed of 5m / s, a maximum tilt angle of 25°, and a maximum rotation angular velocity of 150° / s. The quad-rotor drone dynamics model is established:

[0092]

[0093] The acceleration due to gravity is 9.8N / kg, and the moment of inertia matrix is , the force coefficient is 6.11×10 -8 N / r 2 , the moment coefficient is 10.5×10 -9 Nm / r 2 . Sampling period is 0.03s, the interference ratio A random time-varying variable between 0 and 1. Planning and The two vertex uncertain parameters of , use polytopes to describe the discretization model of this uncertain system:

[0094]

[0095] in, , , It is a fourth-order unit array.

[0096] The model is used for rolling optimization, taking the maximum control input of the quadrotor UAV system as 2m / s 2 , taking the maximum output of the quadrotor UAV system as 5m / s, the robust constrained predictive control problem of the quadrotor UAV considering the system dynamics and constraints can be described as:

[0097]

[0098] After converting the robust constrained predictive control problem of the quadrotor drone into a simple minimization problem, the system constraints are considered as follows:

[0099] 1) Set the quadcopter control state Keep in the unchanged set middle:

[0100]

[0101] 2) In order to make the quadrotor UAV system asymptotically stable, based on the stability principle of Lyapunov function, the quadratic form It needs to decrease and meet the upper bound condition. Based on the polyhedral condition, we can get:

[0102]

[0103] 3) Considering the output constraints of the quadcopter, the horizontal flight distance is required to be no more than 30m and the speed is no more than 5m / s. ,The polyhedral condition is used to obtain the linear matrix inequality LMI form that satisfies the control input constraints of the quadrotor drone:

[0104]

[0105] 4) Constraining and controlling the acceleration control input during the flight of a quadcopter can ensure flight stability and rapid response. While satisfying the state feedback control law, it is necessary to satisfy the control input constraints in the system and impose constraints on the acceleration based on actual flight experience. , and converted into linear matrix inequality LMI form:

[0106]

[0107] After the above analysis and derivation, the robust constraint predictive control problem of the quadrotor drone is transformed into the following optimization problem for solution:

[0108]

[0109] The desired trajectory is a spiral ascending trajectory with a radius of 4 m, an angular velocity of 0.4363 rad / s, and an ascending speed of 0.12 m / s. Figures 3 to 5 This is a quad-rotor drone trajectory tracking effect diagram. Figures 3 to 5 As shown, the blue is the expected trajectory of the quadrotor UAV, and the green is the actual trajectory of the quadrotor UAV. The robust constraint predictive control method for the quadrotor UAV of the present invention has a good real-time tracking effect.

[0110] Figure 6-9 is the change of the position and speed of the drone in the x and y directions. Figure 6-9 As shown, the blue is the expected trajectory of the quadrotor drone, and the red is the actual trajectory of the quadrotor drone. The robust constraint predictive control method for the quadrotor drone of the present invention has good robustness and stability to the interference in the uncertain system. In this method, the speed and position of the quadrotor drone are basically consistent with the expected data.

[0111] The above-mentioned embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the invention patent. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the attached claims.

Claims

1. A robust constraint predictive control method for a quadrotor drone, characterized in that: The following steps are involved: Step 1: Build a dynamic model of the quadrotor drone: The dynamic model of linear and angular motion of a quadrotor drone is constructed based on the Newton-Euler method: ； in, The origin of the machine system The position coordinates relative to the world system, m is the mass of the quadrotor drone, J is the moment of inertia of the quadrotor drone, is the linear velocity of the quadrotor drone in the aircraft system, R is the coordinate transformation from the aircraft system to the inertial system, is the angular velocity of the machine system, is an antisymmetric matrix, is the torque, F is the resultant external force, T is the lift, is the acceleration due to gravity, and Represent the unit matrix in the quadrotor drone system and the world system respectively; Step 2: Build a constraint predictive control model for the quadrotor drone and set the constraints: ； ； ； ； Among them, G is the state weight matrix, U is the control input weight matrix, is the state quantity of the quadrotor UAV system, where , and is the expected trajectory position of the quadrotor drone, and is the expected trajectory speed of the quadrotor drone, is the input quantity of the quadrotor UAV system, where , and is the expected trajectory acceleration of the quadrotor drone, and the output of the quadrotor drone system is , is the output matrix, is the sampling time, and is the vertex of the known system matrix set A, B, called a polytopic vertex, is the convex hull formed by all polytopic vertices, is the attenuation amount, L represents the number of convex hulls, Umax is the control input constraint, Ymax is the output constraint, i represents the i-th convex hull, and k represents the k-th moment; Step 3: Solve the constraint predictive control model of the quadrotor UAV and complete the predictive control of the quadrotor UAV.

2. The robust constraint predictive control method for a quadrotor drone according to claim 1, characterized in that: The constraint conditions of the constraint predictive control model of the quadrotor UAV are: (1) The state of the quadrotor drone at time k Keep in the unchanged set In, meet: ； ； Among them, Q is a positive definite symmetric matrix that defines the shape and size of the ellipsoidal invariant set; (2) In order to make the quadrotor UAV system asymptotically stable, based on the stability principle of the Lyapunov function: ； Among them, H is the control gain matrix, which participates in weight coupling, is a scalar parameter that measures the system performance and represents the constraint boundary; (3) Consider the output constraints of the quadrotor drone: ； (4) Imposing constraints on the control input weight matrix: 。 3. A robust constraint predictive control system for a quadrotor drone, characterized in that: Includes the following modules: Dynamics model building module: used to build the dynamics model of the quadrotor drone: The dynamic model of linear and angular motion of a quadrotor drone is constructed based on the Newton-Euler method: ； in, The origin of the machine system The position coordinates relative to the world system, m is the mass of the quadrotor drone, J is the moment of inertia of the quadrotor drone, is the linear velocity of the quadrotor drone in the aircraft system, R is the coordinate transformation from the aircraft system to the inertial system, is the angular velocity of the machine system, is an antisymmetric matrix, is the torque, F is the resultant external force, T is the lift, is the acceleration due to gravity, and Represent the unit matrix in the quadrotor drone system and the world system respectively; Constraint predictive control model building module: used to build a constraint predictive control model for a quadrotor drone and set constraints: ； ； ； ； Among them, G is the state weight matrix, U is the control input weight matrix, is the state quantity of the quadrotor UAV system, where , and is the expected trajectory position of the quadrotor drone, and is the expected trajectory speed of the quadrotor drone, is the input quantity of the quadrotor UAV system, where , and is the expected trajectory acceleration of the quadrotor drone, and the output of the quadrotor drone system is , is the output matrix, is the sampling time, and is the vertex of the known system matrix set A, B, called a polytopic vertex, is the convex hull formed by all polytopic vertices, is the attenuation amount, L represents the number of convex hulls, Umax is the control input constraint, Ymax is the output constraint, i represents the i-th convex hull, and k represents the k-th moment; Control module: used to solve the constraint predictive control model of the quadrotor UAV and complete the predictive control of the quadrotor UAV.

4. A computer device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 2 are implemented.

5. A computer storable medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 2 are implemented.

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