A smooth switching control method for an air-ground dual-purpose robot

Abstract

The application discloses a smooth switching control method for an air-ground dual-purpose robot, and belongs to the field of air-ground dual-purpose robots, and comprises the following steps: establishing kinematics and dynamics equations of air-ground modes; constructing a system model of the air-ground dual-purpose robot; establishing a first mathematical expression not considering a system state limitation and a second mathematical expression considering the system state limitation based on the system model; designing a first controller for stabilizing the system and a second controller for stabilizing the system under the system state limitation for the first mathematical expression and the second mathematical expression respectively; respectively solving and proving stability; and performing smooth switching control on the air-ground dual-purpose robot through the first controller or the second controller after solving. The smooth switching control method is suitable for attitude tracking control of the air-ground dual-purpose robot under the state limitation, and the stability and accuracy of the air-ground dual-purpose robot control are strengthened.

Description

Technical Field

[0001] This application relates to a smooth switching control method for air-ground dual-purpose robots, belonging to the field of air-ground dual-purpose robots. Background Technology

[0002] Dual-purpose robots possess both aerial flight and ground mobility capabilities, and can switch between air and ground modes depending on the mission scenario. Compared to ground robots, they offer higher spatial accessibility, stronger obstacle-crossing ability, and can operate in high-altitude environments. Compared to aerial robots, they consume less energy, have longer endurance, and often offer a higher safety factor. Therefore, dual-purpose robots have attracted widespread attention from scholars both domestically and internationally, and have broad development prospects and applications in areas such as underground space exploration, urban disaster search and rescue, and factory pipeline inspection.

[0003] Some existing air-to-ground amphibious robots already possess the ability to switch between air and ground modes quickly and without delay, such as the "rotor + passive wheel" configuration. However, current control methods for air-to-ground amphibious robots do not consider the multi-modal switching process, and cannot guarantee system stability during mode switching. Currently, the mainstream control method for air-to-ground amphibious robots is PID control. Some researchers completely refer to quadcopter control, using the same controller for both air and ground modes, i.e., a single PID control method; others use multi-PID control methods, setting PID parameters separately for air and ground modes. However, none of these methods consider system stability. In a few studies, although system stability in controller design has been addressed, the lack of a unified kinematic and dynamic model for both air and ground modes means that these control methods can only guarantee the stability of the amphibious robot when considering only a single mode of motion, which has significant limitations. Furthermore, to ensure that the actuators operate within a safe range, the state variables in the control system often have range limitations. For air-to-ground amphibious robots, the range limitations for state variables also differ due to the different dynamic equations for different modes. Currently, there is no control method that can guarantee the stability of the motion process of a dual-purpose air-ground robot and ensure that the state variables of the air-ground and dual-mode operations meet the range constraints. Summary of the Invention

[0004] The purpose of this application is to provide a smooth switching control method for air-ground dual-purpose robots, which solves the problems of existing control methods not considering the mode switching process of air-ground dual-purpose robots, failing to guarantee system stability at the moment of mode switching, and not considering the state constraints brought about by different modes. It can effectively realize the tracking control of air-ground dual-purpose robots under state constraints.

[0005] To achieve the above objectives, the first aspect of this application provides a smooth switching control method for an air-to-ground dual-purpose robot, comprising:

[0006] Establish the kinematic and dynamic equations for the air-to-ground mode;

[0007] A system model of the air-ground dual-purpose robot is constructed based on the aforementioned kinematic and dynamic equations;

[0008] Based on the system model, a mathematical expression is established to describe the control problem of the air-ground dual-purpose robot. The mathematical expression includes a first mathematical expression that does not consider the system state constraints and a second mathematical expression that considers the system state constraints.

[0009] A first controller is designed to stabilize the system based on the first mathematical expression. The first controller is solved to obtain the first controller gain, and the stability of the first controller gain is proved.

[0010] A second controller is designed to stabilize the system under constrained system state conditions based on the second mathematical expression. The second controller is solved and its gain is obtained. The stability of the second controller gain is then proven.

[0011] The air-ground dual-purpose robot is smoothly switched using the first or second controller after the solution is obtained.

[0012] In one implementation, establishing the kinematic and dynamic equations for the air-to-ground mode includes:

[0013] Define the coordinate system E, the inertial coordinate system I, and the body coordinate system B for the air-to-ground dual-purpose robot;

[0014] Derive the transformation relationships between the coordinate system E, the inertial coordinate system I, and the body coordinate system B;

[0015] Based on the transformation relationship, kinematic and dynamic equations for the air-to-ground mode are established, wherein the kinematic and dynamic equations include the kinematic and dynamic equations for the air mode and the kinematic and dynamic equations for the ground mode.

[0016] In one implementation, the system model for constructing the air-to-ground dual-use robot based on the kinematic and dynamic equations includes:

[0017] By combining the kinematic and dynamic equations of the air mode and the kinematic and dynamic equations of the ground mode, a generalized state-space expression consistent with the air-ground mode is established based on the generalized system model, thereby determining the system model;

[0018] The system model is specifically as follows:

[0019]

[0020] in, For system switching signals, each subsystem corresponds to an operating point (x). σ， uσ And a ground-to-air mode, the system attitude loop state variable x a =[φ θ ψ pqr] T φ, θ, and ψ represent the roll, pitch, and yaw angles of the amphibious robot, respectively; p, q, and r are the angular velocities defined in the body coordinate system; and the input variable u... a =[u φ u θ u ψ ] T The input torque provided to the rotor, E a，σ A a，σ B a，σ This is the system matrix.

[0021] In one implementation, establishing a mathematical expression based on the system model to describe the control problem of the air-to-ground dual-purpose robot includes:

[0022] A general switching system model is obtained by performing a matrix transformation on the system model. Based on the general switching system model, a mathematical expression is established to describe the control problem of the air-ground dual-purpose robot.

[0023] Wherein, for the system model, if rank(E) σ ) = rank(E σ， B σ ) = r σ If ≤n holds, then there exists a nonsingular matrix M. σ N σ , so that:

[0024]

[0025] Then based on the non-singular matrix M σ N σ For system matrix A σ By performing a matrix transformation on the state variable x, the general switching system model is obtained as follows:

[0026]

[0027] Meanwhile, due to the different equality constraints of the subsystems before and after the switch, the generalized system model may experience state transitions. For the switch time t, assume σ(t + )=i,σ(t - If ) = j, then:

[0028]

[0029]

[0030]

[0031]

[0032] In one implementation, establishing a mathematical expression based on the general switching system model to describe the control problem of the air-to-ground dual-purpose robot includes:

[0033] Based on the general switching system, the first mathematical expression is established as follows:

[0034]

[0035] In one embodiment, the step of solving for the first controller gain and proving the stability of the first controller gain includes:

[0036] For the first mathematical expression, let α > 0 be a given constant, μ > 1 be the ground friction coefficient, and the duration T and switching frequency f be given constants. For the dwell time τ, if there exists a symmetric positive definite matrix... With matrix W i This makes for The following inequalities hold:

[0037]

[0038]

[0039] in,

[0040]

[0041]

[0042] The switching logic in the system is represented by the PDT signal. The system is stable when the following switching logic is satisfied:

[0043]

[0044] The gain of the first controller is then:

[0045]

[0046] The stability of the first controller gain is proven using Lyapunov functions and Schur complement lemmas.

[0047] In one implementation, establishing a mathematical expression for the control problem of an air-to-ground robot based on the general switching system model further includes:

[0048] For a matrix C∈R m×n Given a constant b∈R, represent the k-th row of matrix C as Ck Then a restricted set of state variables x can be represented as: Ξ(C)≡{x∈R} n :|C k x|≤b,k∈Z [1,m]};

[0049] Based on the general switching system, the second mathematical expression is established as follows:

[0050]

[0051] In one embodiment, the step of solving for the second controller gain and proving the stability of the second controller gain includes:

[0052] For the second mathematical expression, let α > 0 be a given constant, μ > 1 be the ground friction coefficient, b > 0, and the duration T and switching frequency f be given constants. For the dwell time τ, if there exists a symmetric positive definite matrix... With matrix W i This makes for The following inequalities hold:

[0053]

[0054]

[0055]

[0056]

[0057] in,

[0058]

[0059]

[0060]

[0061] The switching logic in the system is described by the PDT signal. The system is stable when the following switching logic is satisfied, and x∈Ξ(C σ For any t∈[0,+∞), the following holds:

[0062]

[0063] The gain of the second controller is then:

[0064]

[0065] The stability of the second controller gain is proven using Lyapunov functions and Schur complement lemmas.

[0066] A second aspect of this application provides an electronic device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the first aspect or any embodiment of the first aspect.

[0067] A third aspect of this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the first aspect or any embodiment of the first aspect.

[0068] As can be seen from the above, this application provides a smooth switching control method for air-to-ground robots, solving the problems of existing control methods that do not consider the mode switching process of air-to-ground robots, cannot guarantee system stability at the moment of mode switching, and do not consider the state constraints brought about by different modes. Compared with existing control methods, the smooth switching control method provided in this application considers the mode switching problem in the controller design process and provides rigorous stability proof, while reducing trajectory tracking errors and improving the tracking performance of air-to-ground robots. In addition, it also considers the problem of different system state constraints under different modes in actual systems, and provides a design method for controllers that meet the system state constraints. This method is applicable to the attitude tracking control of air-to-ground robots under state constraints, enhances the stability and accuracy of air-to-ground robot control, and has high engineering application value. Attached Figure Description

[0069] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0070] Figure 1 A flowchart illustrating a smooth switching control method for an air-to-ground dual-purpose robot provided in an embodiment of this application;

[0071] Figure 2 This is a structural schematic diagram of an air-ground dual-purpose robot provided in an embodiment of this application;

[0072] Figure 3 This application provides a schematic diagram of the multimodal motion of an air-ground dual-purpose robot.

[0073] Figure 4 A schematic diagram of the switching logic of an air-to-ground dual-purpose robot provided in an embodiment of this application;

[0074] Figure 5(a) is a schematic diagram of the attitude angle curve of a smooth switching control method provided in an embodiment of this application without considering system state constraints;

[0075] Figure 5(b) is a schematic diagram of the attitude angular velocity curve of a smooth switching control method provided in an embodiment of this application without considering system state constraints;

[0076] Figure 6(a) is a schematic diagram of the attitude angle curve of a smooth switching control method under the condition of system state constraint provided in an embodiment of this application;

[0077] Figure 6(b) is a schematic diagram of the attitude angular velocity curve of a smooth switching control method under the condition of system state constraints provided in an embodiment of this application;

[0078] Figure 7 A schematic diagram illustrating the switching logic of another air-to-ground dual-purpose robot provided in this application embodiment;

[0079] Figure 8(a) is a schematic diagram of a desired attitude angle curve provided in an embodiment of this application;

[0080] Figure 8(b) is a schematic diagram of a desired attitude angular velocity curve provided in an embodiment of this application;

[0081] Figure 9(a) is a schematic diagram of the attitude angle curve of another smooth switching control method under the condition of system state constraint provided in the embodiment of this application;

[0082] Figure 9(b) is a schematic diagram of the attitude angular velocity curve of another smooth switching control method under the condition of system state constraint provided in the embodiment of this application;

[0083] Figure 10(a) is a schematic diagram of the attitude angle curve of a single PID control method in the prior art provided by an embodiment of this application;

[0084] Figure 10(b) is a schematic diagram of the attitude angle curve of a prior art multi-PID control method provided in an embodiment of this application;

[0085] Figure 11 This is a schematic diagram comparing the pitch angle error of a smooth switching control method considering system state constraints provided in this application embodiment with that of single-PID and multi-PID control methods in the prior art. Detailed Implementation

[0086] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0087] It should be understood that, when used in this specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0088] It should also be understood that the terminology used in this application specification is for the purpose of describing particular embodiments only and is not intended to limit the application. As used in this application specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0089] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0090] Many specific details are set forth in the following description in order to provide a full understanding of this application. However, this application may also be implemented in other ways different from those described herein. Those skilled in the art can make similar extensions without departing from the spirit of this application. Therefore, this application is not limited to the specific embodiments disclosed below.

[0091] Example 1

[0092] This application provides a smooth switching control method for dual-purpose air-ground robots, such as... Figure 1 As shown, the method includes:

[0093] Step 11: Establish the kinematic and dynamic equations for the air-to-ground mode;

[0094] Optionally, the kinematic and dynamic equations for establishing the air-to-ground mode include:

[0095] Define the coordinate system E, the inertial coordinate system I, and the body coordinate system B for the air-to-ground dual-purpose robot;

[0096] Derive the transformation relationships between the coordinate system E, the inertial coordinate system I, and the body coordinate system B;

[0097] Based on the transformation relationship, kinematic and dynamic equations for the air-to-ground mode are established, wherein the kinematic and dynamic equations include the kinematic and dynamic equations for the air mode and the kinematic and dynamic equations for the ground mode.

[0098] In one implementation, the coordinate system of the air-to-ground robot is first defined, and the transformation relationship between the coordinate systems is derived. An air-to-ground robot configuration is as follows: Figure 2 As shown, it features an embedded quadcopter structure, which can adjust the lift by changing the speed of the four motors, thereby altering the robot's attitude and position. External passive wheels on both sides assist the robot in ground movement; the axes of the passive wheels are in the same plane as the quadcopters. To describe the motion of the air-to-ground amphibious robot, I is defined as the inertial coordinate system; B is the body coordinate system, where... Perpendicular to the embedded quadcopter plane; coordinate system E origin O e Fixed to the center of the body, and coincide, and Parallel. Rotating in the ZYX order, the rotation matrix from the body coordinate system to the inertial coordinate system can be represented as:

[0099]

[0100] Wherein, φ, θ, and ψ are the roll angle, pitch angle, and yaw angle of the air-to-ground robot, respectively.

[0101] Based on formula (1), the kinematic and dynamic equations for the air-to-ground mode are established, where the multimodal motion forms of the air-to-ground dual-purpose robot are as follows: Figure 3 As shown, for the aerial mode, the kinematic and dynamic equations are as follows:

[0102]

[0103] Where ω=[pqr] T To define the angular velocity in the body coordinate system, J = diag(J x J y J z ) represents the moment of inertia matrix of the machine body, u φ u θ u ψ The input torque provided to the rotor.

[0104] When the amphibious robot moves close to the ground, assuming the ground is an absolute plane, the planar constraints are transformed into equality constraints on the state variables of the amphibious robot:

[0105]

[0106] Furthermore, when the amphibious robot is rolling on the ground, its body is affected by the frictional torque of the ground, and its kinematic and dynamic equations differ from those in the aerial mode, as shown below:

[0107]

[0108] Where μ is the ground friction coefficient, sgn(·) is the sign function, and d f Let be the ground friction torque. In rotational dynamics, the influence of ground modal rolling on angular velocity is discussed. Assuming the ground is flat, the amphibious robot always satisfies the following during its motion along the contact plane: From the coordinate system transformation relation, we can obtain p + r · tanθ = 0, so there is no need to expand and write d. φ The formulation is as follows: Assume the velocities of the passive wheels on both sides of the amphibious robot at their contact points with the ground are zero, meaning there is no relative slippage between the passive wheels and the ground. Also, assume the friction at the connection between the passive wheels and the rotor is negligible. Therefore, the difference between the dynamic solution for the angular velocity q and the aerial mode lies only in that the moment of inertia of the ground mode does not need to consider the passive wheels on both sides, i.e., J... y2 =J y -J 被动轮 And d θ =0; for angular velocity r, the effect of frictional torque needs to be considered separately. Where l is the distance between the centers of the passive wheel axles on both sides, m is the mass of the airframe, and F is the lift provided by the rotor.

[0109] Step 12: Construct a system model of the air-ground dual-purpose robot based on the aforementioned kinematic and dynamic equations;

[0110] Optionally, to perform attitude tracking control on the air-to-ground dual-purpose robot, a system model is first constructed for the continuous-time generalized switching system (also called the system). Specifically, the kinematic and dynamic equations of the air mode and the ground mode are combined, and a generalized state-space expression consistent between the air and ground modes is established based on the generalized system model. Simultaneously, based on the Jacobi linearization method, multiple operating points covering the parameter variation range are selected to determine the system model as follows:

[0111]

[0112] Where, σ(t): For system switching signals, each subsystem corresponds to an operating point (x). σ u σ And a ground-based mode, when the state variable x is used to describe the attitude loop state variable, the system attitude loop state variable x a=[φ θ ψ pqr] T Input variable u a =[u φ u θ u ψ ] T Furthermore, when state variable x is used to describe the position loop state variable, then the position loop state variable x is... p =[ENH v E v N v H ] T Input variable u p =[u x u y u z ] T E a，σ A a，σ B a，σ The system matrix is ​​represented as follows:

[0113] Airborne modal system matrix:

[0114] E a，σ =I6

[0115]

[0116]

[0117] Ground modal system matrix:

[0118]

[0119]

[0120]

[0121] Step 13: Based on the system model, establish a mathematical expression to describe the control problem of the air-ground dual-purpose robot, wherein the mathematical expression includes a first mathematical expression that does not consider the system state constraints and a second mathematical expression that considers the system state constraints;

[0122] In one implementation, to address the state-constrained situation caused by different modes in the prior art, this application embodiment needs to consider the establishment of a continuous-time generalized switching system control problem under state-constrained conditions. First, a matrix transformation is performed on the system model to obtain a general switching system model. Then, a mathematical expression for describing the control problem of the air-to-ground dual-purpose robot is established based on the general switching system model. Specifically, according to matrix theory, for a system model of the form of formula (5), if rank(E... σ ) = rank(E σB σ ) = r σ If ≤n holds, then there exists a nonsingular matrix M. σ N σ , so that:

[0123]

[0124] Then based on the non-singular matrix M σ N σ The system matrix A can be used. σ Transform with state variable x:

[0125]

[0126]

[0127] The transformed system model is as follows, also known as the generalized canonical form:

[0128]

[0129] Expanding the matrix, the above generalized canonical form can be written as follows. It can be seen that due to the equality constraints in the generalized system model, the transformed system state x2 can be represented by x1:

[0130]

[0131] Therefore, the system model can be transformed into a general switching system and an equality constraint as follows:

[0132]

[0133] Meanwhile, due to the different equality constraints of the subsystems before and after the switch, the generalized system model may experience state transitions. For the switch time t, assume σ(t + )=i,σ(t - If ) = j, then:

[0134]

[0135]

[0136]

[0137]

[0138] Furthermore, based on the constrained system state, for a matrix C∈R m×n Given a constant b∈R, represent the k-th row of matrix C as C k Then a restricted set of state variables x can be represented as: Ξ(C)≡{x∈R} n:|C k x|≤b,k∈Z [1，m]}

[0139] It is known that when a dual-purpose air-to-ground robot lands, its vertical velocity may not be zero, and the passive wheel structure itself has a certain degree of rigidity. Therefore, the impact at the moment of landing may cause a rapid switch between air-to-ground modes within a short period of time. To describe this phenomenon, embodiments of this application use PDT signals to represent the switching logic in the system.

[0140] In summary, the mathematical expression for the control problem of the air-to-ground dual-purpose robot is as follows:

[0141] The first mathematical expression is used to describe a continuous-time generalized switched system that does not consider system state constraints:

[0142]

[0143] The second mathematical expression is used to describe a continuous-time generalized switched system with constrained system states:

[0144]

[0145] Step 14: Design a first controller that makes the system stable based on the first mathematical expression, solve for the first controller gain to obtain the first controller gain, and prove the stability of the first controller gain.

[0146] Optionally, for the continuous-time generalized switching system expressed by the first mathematical expression, a first controller can be designed to stabilize the continuous-time generalized switching system, and the first controller with stability guarantee can be solved according to the following Theorem 1:

[0147] Theorem 1: Let α > 0 be a given constant, μ > 1 be the ground friction coefficient, and the duration T and switching frequency f be given constants. For the dwell time τ, if there exists a symmetric positive definite matrix... With matrix W i , making for The following inequalities hold:

[0148]

[0149]

[0150] in:

[0151]

[0152]

[0153] Then, for the PDT switching logic that satisfies the following formula:

[0154]

[0155] The system is stable, and its first controller gain is:

[0156]

[0157] In one implementation, proving the stability of the first controller gain includes: for The Lyapunov function is chosen to be of the following form:

[0158]

[0159] in:

[0160]

[0161] make but:

[0162]

[0163] By Schur's complement lemma, the above equation can be transformed into:

[0164]

[0165] For the switching time t, assume σ(t) + )=i,σ(t - If ) = j, then:

[0166]

[0167] when for available:

[0168]

[0169] Let γ p =T P (flnμ-α)+lnμ-ατ, ​​it can be seen that when flnμ-α<0 and At that time, γ p <0; when flnμ-α≥0 and At that time, γ p <0. That is, equation (22) yields γ. p <0. Therefore Therefore, the first controller gain obtained by solving the inequalities in Theorem 1 can stabilize the continuous-time generalized switching system.

[0170] Step 15: Design a second controller that stabilizes the system under constrained system state based on the second mathematical expression, solve for the second controller gain, and prove the stability of the second controller gain;

[0171] Optionally, for the continuous-time generalized switching system expressed by the second mathematical expression, a second controller can be designed to stabilize the continuous-time generalized switching system, and the second controller with stability guarantee and state constraint guarantee can be solved according to the following Theorem 2:

[0172] Theorem 2: Let α > 0, μ > 1, b > 0, and the duration T and switching frequency f be given constants. For the dwell time τ, if there exists a symmetric positive definite matrix... With matrix W i This makes for The following inequalities hold:

[0173]

[0174]

[0175]

[0176]

[0177] in,

[0178]

[0179]

[0180]

[0181] Then, for the PDT switching logic that satisfies the following formula:

[0182]

[0183] The system is stable, and x∈Ξ(C σ For any t∈[0,+∞), the second controller gain is:

[0184]

[0185] In one implementation, proving the stability of the second controller gain includes: for The Lyapunov function is selected in the following form:

[0186]

[0187] in,

[0188]

[0189] According to Theorem 1, the Lyapunov function is decreasing in t∈[0,+∞), and the state-constrained continuous-time generalized switching system is stable.

[0190] By Schul complement lemma and equation (27), the initial values ​​of the Lyapunov function satisfy:

[0191]

[0192] Therefore, V(t) < b 2 w at Established.

[0193] By Schul's complement lemma, equation (26) can be transformed into:

[0194]

[0195] therefore,

[0196]

[0197] That is, x∈Ξ(C) σ This holds true for any t∈[0,+∞).

[0198] In summary, the second controller gain obtained by solving the inequalities in Theorem 2 can stabilize the state-constrained continuous-time generalized switching system, and the system state variables satisfy x∈Ξ(C σ ).

[0199] Step 16: Perform smooth switching control on the air-ground dual-purpose robot using the first controller or the second controller after solving the problem.

[0200] Specifically, the corresponding controller parameters (i.e., the first controller gain) are obtained by solving Theorem 1, and the first controller can then be determined; the corresponding controller parameters (i.e., the second controller gain) are obtained by solving Theorem 2, and the second controller can then be determined. In practical applications, the appropriate first or second controller can be selected to smoothly switch between control of the air-to-ground dual-purpose robot according to different actual situations.

[0201] As can be seen from the above, the embodiments of this application provide a smooth switching control method for air-to-ground dual-purpose robots. The modal switching problem is considered in the controller design process, and rigorous stability proofs are provided. Simultaneously, trajectory tracking errors are reduced, improving the tracking performance of the air-to-ground dual-purpose robot. Furthermore, the problem of different system state constraints under different modes in actual systems is considered, and a controller design method that satisfies system state constraints is provided. This method is suitable for tracking and controlling the position and attitude of air-to-ground dual-purpose robots under state constraints, enhancing the stability and accuracy of air-to-ground robot control, and has high engineering application value.

[0202] Example 2

[0203] To facilitate understanding of the above technical solutions, the smooth switching control method provided in Embodiment 1 of this application will be described in detail below with reference to a specific implementation method.

[0204] In one implementation, when considering the stabilization problem of an air-to-ground robot in situations involving frequent switching between air and ground, the known system model has the following form:

[0205]

[0206] Pick σ(t) = 1 represents the aerial mode, σ(t) = 2 represents the ground mode, the mass of the dual-purpose robot is m = 0.5 kg, and the moment of inertia is J. x =0.319,J y =0.256,J z =0.352, air resistance coefficient, ground friction coefficient μ = 0.03, and weight acceleration is taken as g = 9.81 m / s². 2 To ensure the safe operation of the air-to-ground robot, its angular velocity is limited. The range of variation for the air mode p, q, r is [-1.5, 1.5] (rad / s), and the range of variation for the ground mode p, q, r is [-1, 1] (rad / s). The system switching signal conforms to the PDT form, with the parameters being a dwell time τ = 3s, a duration T = 1.8s, and a maximum switching frequency f = 2s. -1 For the above system, design the controller using Theorem 1 and Theorem 2 respectively. The corresponding controller parameters can be solved using Theorem 1:

[0207]

[0208]

[0209] Applying Theorem 2, the corresponding controller parameters can be solved as follows:

[0210]

[0211]

[0212] The initial state of the system is x0 = [0 1.22 0.17 0 0 0]. T σ(0) = 2, the switching logic signal is as follows Figure 4 As shown, at the initial moment, the amphibious robot rolls on the ground at a large pitch angle. To avoid obstacles, the robot decelerates and switches to flight mode at t=3s. After passing the obstacle, the robot lands at t=3.8s, bounces after landing, and frequently switches between air and ground modes, maintaining ground mode after t=5s.

[0213] The convergence of the corresponding controllers obtained by applying Theorem 1 and Theorem 2 is shown in Figure 5-6. It can be seen that both the controllers obtained by Theorem 1 and Theorem 2 can stabilize the system. The first controller obtained by Theorem 1 fails to satisfy the constrained constraints, as shown in Figure 5(b). When t = 0.8s, q... min = -1.2279 rad / s, far exceeding the constrained range. However, the second controller solved by Theorem 2 can satisfy the constrained constraints, as shown in Figure 6(b). When t = 0.78 s, q min = -0.4459 rad / s. Comparing the two controllers, it can be found that the first controller has a faster convergence speed in the initial stage than the second controller, but the amplitude of state jitter is also greater than that of the second controller. For some jitter-sensitive systems, the severity of state jitter is more important than the convergence speed.

[0214] In summary, when the system needs to meet constrained conditions or is sensitive to jitter, the second controller can be used as the preferred control method; when the system needs faster convergence speed, the first controller can be used as the preferred control method.

[0215] Example 3

[0216] To facilitate the demonstration of the effects of the above technical solutions, the smooth switching control method provided in Embodiment 1 of this application will be described in detail below with reference to a specific implementation method.

[0217] In one implementation, when considering the attitude tracking problem of an air-to-ground robot under large-angle maneuvering conditions, the known system model has the following form:

[0218]

[0219] Based on the actual operation of the air-to-ground dual-purpose robot, the ground mode θ exhibits a problem with large-angle rapid maneuvering. To improve trajectory tracking performance, the ground mode pitch angle θ is divided into multiple intervals: [-70, -50], [-50, -30], [-30, -10], [-10, 10], [10, 30], [30, 50], [50, 70] (deg). σ(t) = 1 represents the aerial mode, and 2 ≤ σ(t) ≤ 6 represents the ground mode. The mass of the dual-purpose aerial and ground robot is m = 0.5 kg, and the moment of inertia is J. x =0.319,J y =0.256,J z =0.352, air resistance coefficient, ground friction coefficient μ = 0.03, and weight acceleration is taken as g = 9.81 m / s². 2 To ensure the safe operation of the air-to-ground robot, its angular velocity is limited. The range of variation for the air mode p, q, r is [-1.5, 1.5] (rad / s), and the range of variation for the ground mode p, q, r is [-1, 1] (rad / s). The system switching signal conforms to the PDT form, with the parameters being a dwell time τ = 3s, a duration T = 1.8s, and a maximum switching frequency f = 2s. -1 For the above system, controllers are designed using Theorem 2, single PID, and multiple PID methods respectively. The corresponding controller parameters are solved using Theorem 2:

[0220]

[0221]

[0222]

[0223]

[0224]

[0225]

[0226]

[0227]

[0228] For the single PID method, after parameter tuning, the parameters for the angle loop and angular velocity loop are as follows:

[0229] PID φ，θ，ψ =[-4 -1 -0.1]

[0230] PID p,q,r =[-6 -5 -0]

[0231] For the multi-PID method, the parameters for the airborne modal angle loop and angular velocity loop are as follows:

[0232] PID φ，θ，ψ =[-4 -1 -0.1]

[0233] PID p,q,r =[-6 -5 -0.5]

[0234] The ground modal angle loop and angular velocity loop parameters are as follows:

[0235] PID φ，θ，ψ =[-6 -4 -0]

[0236] PID p,q,r =[-7.2 -2 0]

[0237] The initial state of the system is x0 = [0.03 0 0.785 0 0 0] r σ(0) = 1, the switching logic signal is as follows Figure 7 As shown in Figure 8, the desired attitude trajectory is as follows. Initially, the air-to-ground robot flies in the air. After landing at t=3s, the pitch angle rapidly increases to accelerate. From t=5-8s, it maintains a large-angle roll, then the pitch angle rapidly decreases, switching to a hovering state at t=10s. Applying the smooth switching control method provided in Example 1, the existing single-PID control method, and the air-to-ground multi-PID control method, the state convergence is shown in Figures 9-10. It can be seen that although all three methods can achieve trajectory tracking, due to the large-angle maneuvering at the pitch angle θ, different trajectory tracking errors exist. A comparison of the pitch angle tracking errors of the three methods is shown below. Figure 11 As shown, throughout the trajectory tracking process, the constrained switching controller (i.e., the second controller) significantly outperforms both the single-PID controller and the multi-PID controller.

[0238] In summary, the smooth switching control method provided in Embodiment 1 of this application not only solves the problems of existing control methods not considering the mode switching process of air-ground dual-purpose robots, which cannot guarantee the system stability at the moment of mode switching, but also does not consider the state constraints brought about by different modes. The provided second controller can also effectively reduce tracking errors under state constraints.

[0239] Example 4

[0240] This application provides an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor. The memory stores software programs and modules, and the processor executes various functional applications and data processing by running the software programs and modules stored in the memory. The memory and processor are connected via a bus. Specifically, the processor implements any of the steps in Embodiment 1 by running the computer program stored in the memory.

[0241] It should be understood that, in the embodiments of this application, the processor may be a Central Processing Unit (CPU), but it may also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0242] Memory may include read-only memory, flash memory, and random access memory, and provides instructions and data to the processor. Some or all of the memory may also include non-volatile random access memory.

[0243] As can be seen from the above, the electronic device provided in this application implements the smooth switching control method for air-to-ground dual-purpose robots described in Embodiment 1 by running a computer program. The controller design considers the modal switching problem and provides rigorous stability proofs, while reducing trajectory tracking errors and improving the tracking performance of the air-to-ground dual-purpose robot. Furthermore, it considers the problem of different system state constraints under different modes in actual systems, and provides a controller design method that satisfies system state constraints. This method is suitable for tracking and controlling the position and attitude of air-to-ground dual-purpose robots under state constraints, enhancing the stability and accuracy of air-to-ground robot control, and has high engineering application value.

[0244] It should be understood that if the integrated modules / units described above are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable storage medium can be appropriately increased or decreased according to the requirements of legislation and patent practice in the jurisdiction.

[0245] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0246] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the above device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0247] It should be noted that the methods and detailed examples provided in the above embodiments can be incorporated into the apparatus and devices provided in the embodiments, and can be referred to each other, without further elaboration.

[0248] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0249] In the embodiments provided in this application, it should be understood that the disclosed apparatus / terminal devices and methods can be implemented in other ways. For example, the apparatus / device embodiments described above are merely illustrative. For instance, the division of the modules or units described above is merely a logical functional division, and in actual implementation, it can be divided in other ways. For example, multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed.

[0250] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A smooth switching control method for air-to-ground dual-purpose robots, characterized in that, include: Establish the kinematic and dynamic equations for the air-to-ground mode; A system model of the air-ground dual-purpose robot is constructed based on the aforementioned kinematic and dynamic equations; Based on the system model, a mathematical expression is established to describe the control problem of the air-ground dual-purpose robot. The mathematical expression includes a first mathematical expression that does not consider the system state constraints and a second mathematical expression that considers the system state constraints. A first controller is designed to stabilize the system based on the first mathematical expression. The first controller is solved to obtain the first controller gain, and the stability of the first controller gain is proved. A second controller is designed to stabilize the system under constrained system state conditions based on the second mathematical expression. The second controller is solved and its gain is obtained. The stability of the second controller gain is then proven. The air-ground dual-purpose robot is smoothly switched using the first or second controller after the solution is obtained.

2. The smooth switching control method as described in claim 1, characterized in that, The kinematic and dynamic equations for establishing the air-to-ground mode include: Define the coordinate system E, the inertial coordinate system I, and the body coordinate system B for the air-to-ground dual-purpose robot; Derive the transformation relationships between the coordinate system E, the inertial coordinate system I, and the body coordinate system B; Based on the transformation relationship, kinematic and dynamic equations for the air-to-ground mode are established, wherein the kinematic and dynamic equations include the kinematic and dynamic equations for the air mode and the kinematic and dynamic equations for the ground mode.

3. The smooth switching control method as described in claim 2, characterized in that, The system model for constructing the air-ground dual-purpose robot based on the kinematic and dynamic equations includes: By combining the kinematic and dynamic equations of the air mode and the kinematic and dynamic equations of the ground mode, a generalized state-space expression consistent with the air-ground mode is established based on the generalized system model, thereby determining the system model; The system model is specifically as follows: in, For system switching signals, each subsystem corresponds to an operating point (x). σ u σ And a ground-to-air mode, the system attitude loop state variable x a =[φ θ ψ pqr] T φ, θ, and ψ represent the roll, pitch, and yaw angles of the amphibious robot, respectively; p, q, and r are the angular velocities defined in the body coordinate system; and the input variable u... a =[u φ u θ u ψ ] T The input torque provided to the rotor, E a，σ A a，σ B a，σ This is the system matrix.

4. The smooth switching control method as described in claim 3, characterized in that, The mathematical expression established based on the system model to describe the control problem of the air-ground dual-purpose robot includes: A general switching system model is obtained by performing a matrix transformation on the system model. Based on the general switching system model, a mathematical expression is established to describe the control problem of the air-ground dual-purpose robot. Wherein, for the system model, if rank(E) σ ) = rank(E σ B σ ) = r σ If ≤n holds, then there exists a nonsingular matrix M. σ N σ , so that: Then based on the non-singular matrix M σ N σ For system matrix A σ By performing a matrix transformation on the state variable x, the general switching system model is obtained as follows: Meanwhile, due to the different equality constraints of the subsystems before and after the switch, the generalized system model may experience state transitions. For the switch time t, assume σ(t + )=i,σ(t - If ) = j, then:

5. The smooth switching control method as described in claim 4, characterized in that, The mathematical expression for describing the control problem of the air-to-ground dual-purpose robot, based on the general switching system model, includes: Based on the general switching system, the first mathematical expression is established as follows:

6. The smooth switching control method as described in claim 5, characterized in that, The process of solving for the first controller gain and proving the stability of the first controller gain includes: For the first mathematical expression, let α > 0 be a given constant, μ > 1 be the ground friction coefficient, and the duration T and switching frequency f be given constants. For the dwell time τ, if there exists a symmetric positive definite matrix... With matrix Wi, such that for The following inequalities hold: in, The switching logic in the system is represented by the PDT signal. The system is stable when the following switching logic is satisfied: The gain of the first controller is then: The stability of the first controller gain is proven using Lyapunov functions and Schur complement lemmas.

7. The smooth switching control method as described in claim 4, characterized in that, The mathematical expression for describing the control problem of the air-to-ground dual-purpose robot, based on the general switching system model, also includes: For a matrix C∈R m×n Given a constant b∈R, represent the k-th row of matrix C as C k Then a restricted set of state variables x can be represented as: Ξ(C)≡{x∈R} n :|C k x|≤b,k∈Z [1,m] }; Based on the general switching system, the second mathematical expression is established as follows:

8. The smooth switching control method as described in claim 7, characterized in that, The process of solving for the second controller gain and proving its stability includes: For the second mathematical expression, let α > 0 be a given constant, μ > 1 be the ground friction coefficient, b > 0, and the duration T and switching frequency f be given constants. For the dwell time τ, if there exists a symmetric positive definite matrix... With matrix Wi, such that for The following inequalities hold: in, The switching logic in the system is described by the PDT signal. The system is stable when the following switching logic is satisfied, and x∈Ξ(C σ For any t∈[0,+∞), the following holds: The gain of the second controller is then: The stability of the second controller gain is proven using Lyapunov functions and Schur complement lemmas.

9. An electronic device, comprising: A memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor, when executing the computer program, implements the steps of the method as claimed in any one of claims 1 to 8.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1 to 8.

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