Air-ground cooperative system model prediction formation control method in underground pipe gallery environment

Abstract

The invention discloses an air-ground cooperative system model prediction formation control method in an underground pipe gallery environment, and the method comprises the steps: constructing an air-ground cooperative system nonlinear model, and constructing an underground pipe gallery model; designing a high-order interference observer to estimate current unknown external disturbance, and establishing an interference prediction model to estimate future unknown external disturbance; a rolling optimization control strategy based on state prediction is designed, control signals of all followers are optimized according to the current state of the system and the predicted future state in each control period, and the tracking precision is ensured while the tracking precision is improved. Collision between followers, collision between the followers and the wall of the pipe gallery and obstacle avoidance between the followers and static and dynamic obstacles in the pipe gallery are achieved; and solving is carried out based on a distributed model prediction formation control algorithm combined with a Lyapunov stability theory, so that each follower keeps an expected formation configuration while tracking a leader trajectory. And the driving safety of the formation in the underground pipe gallery environment is ensured.

Description

Technical Field

[0001] The present invention relates to a model prediction formation control method for an air-ground collaborative system in an underground pipe gallery environment, and belongs to the technical field of formation tracking control of an air-ground collaborative system. Background Art

[0002] With the rapid development of science and technology, drone and unmanned vehicle (UAV) technologies have become a hot topic in fields such as intelligent transportation, military reconnaissance, and disaster relief. Among the various types of drones and unmanned vehicles, quadcopters and two-wheel drive (2WD) unmanned vehicles (UAVs) have attracted considerable research attention due to their unique advantages. Quadcopters, with their simple structure, flexible control, and vertical takeoff and landing, offer broad application prospects in aerial photography, monitoring, and transportation. Two-wheel drive (2WD) unmanned vehicles, with their efficient energy utilization and strong environmental adaptability, are becoming a key development direction in smart mobility, logistics, and distribution. An air-ground collaborative system composed of these two types of vehicles can leverage their respective strengths in collaborative operations.

[0003] In complex and ever-changing environments, the impact of disturbances on unmanned systems is becoming increasingly prominent, undoubtedly posing a significant challenge to the stable operation of quadcopters and two-wheel-drive unmanned vehicles. Research has shown that disturbance estimation and compensation techniques are an effective and commonly used method for dealing with disturbances. However, because the disturbance compensation control term is a feedforward control term, the disturbance system needs to be divided into two parts when designing the controller. Consequently, the constraints imposed on the control input are also separated, increasing conservatism. More importantly, the control input obtained from the optimization problem may not be optimal. This can be avoided if future disturbance information can be included in the prediction model. Therefore, using disturbance foresight to obtain future disturbance estimates can achieve high-precision control in the presence of external disturbances.

[0004] In underground tunnel environments, how air-ground formations safely navigate through them while tracking the leader's trajectory and maintaining formation is a crucial consideration, primarily involving collision and obstacle avoidance control technologies. Current collision-free control technologies primarily include methods for designing artificial potential field functions and optimization-based approaches. Distributed model predictive control (DMPC) that combines these approaches and incorporates collision and obstacle avoidance potential field functions demonstrates outstanding structural flexibility, low computational cost, and minimal communication burden. However, the closed-loop stability of DMPC typically requires the design of appropriate terminal regions and control laws, which increases complexity. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: to provide a model prediction formation control method for an air-ground collaborative system in an underground pipeline corridor environment, to design an interference prediction model to estimate future external interference, to take the improved collision avoidance and obstacle avoidance function terms into account in the formation optimization problem, to design a Lyapunov-based model prediction control method to solve the formation tracking problem, and at the same time to ensure the safety of formation driving in the underground pipeline corridor environment.

[0006] The present invention adopts the following technical solutions to solve the above technical problems:

[0007] A model-predictive formation control method for an air-ground collaborative system in an underground tunnel environment, wherein the air-ground collaborative system includes multiple quadrotor drones and multiple two-wheel drive unmanned vehicles, includes the following steps:

[0008] Step 1: Select any UAV or any unmanned vehicle as the leader of the air-ground collaborative system, and the remaining UAVs and unmanned vehicles as followers to build a nonlinear model of the air-ground collaborative system; select any point on the underground corridor wall to construct the underground corridor model;

[0009] Step 2: Based on the nonlinear model of the air-ground collaborative system constructed in Step 1, a high-order interference observer is designed to estimate the current unknown external disturbance. Based on the designed high-order interference observer, an interference prediction model is established to estimate the future unknown external disturbance.

[0010] Step 3: Based on the interference prediction model established in Step 2, a rolling optimization control strategy based on state prediction is designed. In each control cycle, the control signal of each follower is optimized according to the current state of the system and the predicted future state. While ensuring tracking accuracy, collision avoidance between followers within the air-ground collaborative system, collision avoidance between followers and the tunnel wall, obstacle avoidance between followers and static obstacles within the tunnel, and obstacle avoidance between followers and dynamic obstacles within the tunnel are achieved.

[0011] In step 4, the rolling optimization control strategy designed in step 3 is solved using the distributed model predictive formation control algorithm combined with Lyapunov stability theory, so that each follower maintains the desired formation configuration while tracking the leader's trajectory.

[0012] Compared with the prior art, the present invention adopts the above technical solution and has the following technical effects:

[0013] 1. The present invention designs an interference prediction model to estimate future external interference, takes the improved collision and obstacle avoidance function into account in the formation optimization problem, and designs a Lyapunov-based model predictive control method to solve the formation tracking problem, while ensuring the safety of formation driving in the underground tunnel environment.

[0014] 2. The present invention designs a rolling optimization control method based on state prediction, which performs optimization according to the current system state and the predicted future state in each control cycle. While ensuring tracking accuracy, it constructs optimization problems with multiple objective functions, including collision avoidance between followers, obstacle avoidance between the formation and the tunnel wall, and obstacle avoidance between the formation and static and dynamic obstacles inside the tunnel, to achieve real-time optimization and control.

[0015] 3. This invention utilizes a distributed model predictive formation control algorithm incorporating Lyapunov stability theory, enabling followers to maintain the desired formation while tracking the leader's trajectory. This distributed model predictive formation control inherits the stability and robustness of the adaptive auxiliary control law and utilizes online optimization to improve the formation tracking performance of the air-ground collaborative system. The use of an adaptive auxiliary controller and the associated Lyapunov function stability constraints ensures the recursive feasibility of the distributed model predictive formation control algorithm and the closed-loop stability of the air-ground collaborative system. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 It is a schematic diagram of the principle of the air-ground collaborative system model prediction formation control method in the underground pipeline corridor environment of the present invention. DETAILED DESCRIPTION

[0017] The embodiments of the present invention are described in detail below, and examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be interpreted as limiting the present invention.

[0018] like Figure 1 As shown, the present invention proposes a model prediction formation control method for an air-ground collaborative system in an underground pipeline corridor environment, and the specific steps are as follows:

[0019] Step 1: Consider an air-ground collaborative system consisting of a quadrotor drone and a two-wheel drive unmanned vehicle. Due to differences in dynamic characteristics and spatial dimensionality between these two systems, a unified nonlinear model is developed to describe the behavior of the entire heterogeneous air-ground robotic system. The position loop models for the quadrotor drone and the two-wheel drive unmanned vehicle are presented below.

[0020] A. Quadrotor UAV

[0021] The position, control quantity, unknown external disturbance and system nonlinear term of the quadrotor drone are defined as p fi =[p fxi ,p fyi ,p fzi ] T 、u fi =[u fxi ,u fyi ,ufzi ] T d fi =[d fxi ,d fyi ,d fzi ] T 、 The position system of the quadrotor drone is represented as follows:

[0022]

[0023] where k 1i 、k 2i 、k 3i is the aerodynamic drag coefficient, and the control quantity contained in the above formula is expanded to be described as:

[0024]

[0025] Among them, φ fi ,θ fi , ψ fi are the roll angle, pitch angle and yaw angle of the i-th UAV respectively, M ai represents the mass of the i-th UAV, g is the acceleration of gravity, U i1 is the total thrust perpendicular to the direction of the fuselage. In the present invention, the attitude control of the UAV is not considered and it is assumed that the attitude control has been completed.

[0026] B. Two-wheel drive unmanned vehicle

[0027] Define the position information of the two-wheeled unmanned vehicle and the unknown external interference as p si =[p sxi ,p syi ] T d si =[d sxi ,d syi ] T , consider the two-wheeled unmanned vehicle performing pure rolling motion on a two-dimensional plane, without slipping between the vehicle and the ground. Combined with the analysis of nonholonomic constraints, the position system of the two-wheeled unmanned vehicle can be expressed as follows:

[0028]

[0029] Among them, the control input u in the above formula is si and the nonlinear term f si The details are as follows:

[0030]

[0031] Among them, v i is the linear velocity, θ si is the direction angle, ω i is the angular velocity.i Represents the distance between the front of the i-th two-wheeled unmanned vehicle and the midpoint of its two wheels.

[0032] The position system models of the quadcopter UAV and the two-wheel drive unmanned vehicle are combined into a unified form to describe it. Assuming that the air-ground collaborative system contains N>0 followers and one leader, the above position system can be summarized into a unified form and defined as follows: The position model of the follower is expressed as follows:

[0033]

[0034] Among them, p mi ,q mi Represent the position and velocity of the follower, u mi represents the control input, d mi represents unknown external interference, f mi is a known nonlinear term of the system, and m∈{f,s},

[0035] definition The leader's model can be represented as follows:

[0036]

[0037] where p0, q0, and u0 represent the position, velocity, and control input of the leader, respectively.

[0038] Since the formation problem is in the underground tunnel environment, a semicircular underground tunnel model is constructed by taking any point on the tunnel wall. The formation's forward direction is set to the X-axis direction, and a coordinate system is established with the starting point as the origin. Then the cross section in YOZ is a semicircle. Get any point on the tunnel wall (x t ,y t ,z t ) Establish the pipe radius as follows:

[0039]

[0040] Among them, ∈ t Indicates the offset of the pipe gallery.

[0041] The control objective of the present invention is to solve the problem of model predictive control of formation tracking in an air-ground collaborative system. In order to maintain a prescribed formation configuration and track the time-varying reference trajectory of the leader, the followers need to meet the following conditions:

[0042] (1) Tracking: d i0 is the formation configuration vector.

[0043] (2) Formation: d j0 represents the relative distance vector between follower j and the leader.

[0044] (3) Collision avoidance: ||p mi (t)-p mj (t)||≥2R, R is the selected safety radius.

[0045] (4) Obstacle avoidance: All followers do not collide with the underground tunnel wall during driving and avoid collision with unknown obstacles in the tunnel.

[0046] For the subsequent derivation, the following assumptions are made:

[0047] Assumption 1: Assume that the external disturbance and its derivative are bounded and satisfy ‖‖d mi ‖‖≤τ0,

[0048] Assumption 2: The leader state and its first-order and second-order derivatives are smooth and bounded, 0≤ζ min ≤‖‖ζ0‖‖ ∞ ≤ζ max <∞,

[0049] Assumption 3: The leader’s control input is bounded, satisfying ‖‖u0(t)‖‖≤c1, c1>0.

[0050] Assumption 4: After interference foresight, the future interference sequence is also bounded.

[0051] Step 2: Based on the vulnerability of the nonlinear air-ground heterogeneous robot model constructed in Step 1 to external disturbances in the underground tunnel environment, a control method based on a high-order disturbance observer and disturbance foresight is designed. The high-order disturbance observer is used to estimate unknown external disturbances and their derivatives. Based on the high-order disturbance observer, a disturbance foresight model is established. Information about future disturbances can be approximated using a Taylor expansion, and their impact on the follower is evaluated.

[0052] Model predictive control requires an accurate model to predict future states. In addition to the impact of current disturbances, the present invention attempts to embed the impact of the possible future behavior of disturbances into the prediction model to significantly improve the prediction accuracy and dynamic performance under time-varying disturbances. Interference prediction is used to obtain current and future disturbance estimates. Since the airflow disturbances in the underground pipeline corridor may change rapidly over time, interference prediction needs to rely on the expansion of multiple-order derivatives of the disturbance. Therefore, a high-order disturbance observer is considered to estimate the disturbance and its derivative, which is in the form of:

[0053]

[0054] in, is the interference term d mi The estimated value of s0...s n represents the observer variable, L s0 …L sn is the positive observer gain. The observation error can be designed as:

[0055]

[0056] Combining the systems (6) and (7) with the high-order disturbance observer (9), and taking the derivative of (10), the compact form of the observer error can be given as:

[0057]

[0058] in,

[0059] Therefore, for a given Q s > 0, we can always find a positive definite matrix D s , such that:

[0060]

[0061] Choose a Lyapunov function as:

[0062]

[0063] According to Young's inequality and (11)-(12), the derivative of the above equation can be obtained:

[0064]

[0065] in, ρ s ∈(0,1]. Then, integrating the above formula gives:

[0066]

[0067] Based on (14) and (15), e s The norm bounds of satisfy the following inequality:

[0068]

[0069] Therefore, based on the above estimation, the future disturbance information can be obtained through Taylor expansion. First, the actual disturbance at the future time t+η has the following expansion form:

[0070]

[0071] Among them, η∈(0,T] represents any future time, T>0 represents the prediction time domain, and R d (t+η) is an infinitesimal term and can be ignored below. Next, the future interference estimate can be approximated as:

[0072]

[0073] As can be seen from the above formula, increasing n can improve the accuracy of disturbance estimation. However, in practical applications, n cannot be selected too large, which is not only unnecessary but also increases the computational complexity. Therefore, n is determined by the trade-off between prediction accuracy and computational complexity. According to (17) and (18), the future disturbance estimation error is expressed as:

[0074]

[0075] and e s0 The norm bound of (t+η|t) is:

[0076]

[0077] Through the high-order disturbance observer (9) and Taylor expansion (18), current and future disturbance estimates can be obtained, thus achieving disturbance foresight.

[0078] Step 3: Based on the interference prediction model constructed in Step 2, a rolling optimization control method based on state prediction is designed. In each control cycle, optimization is performed according to the current system state and the predicted future state. While ensuring tracking accuracy, an optimization problem with multiple objective functions is constructed, including collision avoidance between followers, obstacle avoidance between the formation and the tunnel wall, and obstacle avoidance between the formation and static and dynamic obstacles inside the tunnel, to achieve real-time optimization and control.

[0079] The Lyapunov model predictive control strategy uses a receding optimization method to find a trade-off between formation error, system input, collision avoidance, and obstacle avoidance. By using a quadratic programming method to minimize the following objective function, the optimal control signal for the i-th follower can be obtained. The objective function is designed as follows:

[0080]

[0081] The following constraints are met:

[0082]

[0083] Where S(δ) is a piecewise function family with a sampling period of δ, and s∈[t k ,t k +T]. Weight matrix P i >0, R i >0. is the physical limit of the actuator, Indicates the auxiliary controller, is the relevant Lyapunov function. It should be noted that the role of the auxiliary controller is to handle the stability of the system, disturbance compensation and generate constraints, thereby assisting the actual controller to more effectively complete the formation tracking and obstacle avoidance tasks. Represents the predicted formation error, which is in the form of:

[0084]

[0085] Among them, d i0 is the fixed distance between follower i and the leader, d j0 is the fixed spacing between follower j and the leader, is the predicted position of follower i, is the assumed position of the j-th follower expressed as:

[0086]

[0087] In (21), represents the collision avoidance cost between followers, represents the obstacle avoidance cost between the follower and the tunnel wall, represents the obstacle avoidance cost of the follower and the static obstacles in the tunnel, Represents the obstacle avoidance cost of the followers and dynamic obstacles in the tunnel. In order to ensure the safety of the followers' platooning, an artificial potential field method is used to establish a suitable potential field function in the safe driving space. That is, the collision avoidance potential field function regards each follower as a high potential field. When the distance between follower i and follower j approaches a safe distance, a repulsive force will be generated between the two, which will make the followers move away from each other and ultimately achieve the collision avoidance goal. Collision avoidance cost The design is as follows:

[0088]

[0089] in, and is the Euclidean distance calculated based on the predicted state, λ>0 is a constant that determines the size of the repulsive potential field, k i >0 is the weight coefficient of the collision avoidance potential field, which can be adjusted by appropriately adjusting the parameters λ and k i , followers that are close to each other can be flexibly adjusted to avoid collisions.

[0090] Next, we consider the obstacle avoidance cost function and divide the obstacle avoidance function into three parts for discussion.

[0091] a. Obstacle avoidance on underground pipe gallery walls:

[0092] Since the internal environment of the tunnel will change, the formation needs to pass safely when the tunnel changes without colliding with the wall. Therefore, the potential field function of the follower and the wall obstacle avoidance is designed. as follows:

[0093]

[0094] in, Indicates the distance between the follower and the tunnel boundary measured by the sensor carried by the follower. is the angle between the UAV’s flight altitude and the tunnel radius, h 1i >0 obstacle avoidance potential field weight coefficient. When the distance between the follower and the tunnel boundary is less than the designed safety distance d res , the repulsive potential field function will become larger, causing the follower to move away from the tunnel wall.

[0095] b. Static obstacle avoidance:

[0096] However, it is not enough to only consider the collision with the tunnel wall. We also need to consider the problem of avoiding unknown static obstacles inside the tunnel. For static obstacles, we only need to consider the distance problem to solve it. We can design the obstacle avoidance potential function. as follows:

[0097]

[0098] Among them, h 2i >0 obstacle avoidance potential field weight coefficient, is the position of the static obstacle, R o is the influence radius of the static obstacle. The repulsion function is related to the distance between the follower and the static obstacle. The closer the distance, the greater the follower's repulsive potential energy. When the follower's potential energy reaches zero, it indicates that the follower has been freed from the influence of the static obstacle. The relationship between the distance between the follower position and the static obstacle position and the safe obstacle avoidance distance is analyzed to ensure that all followers can circumvent static obstacles and continue to track the leader's trajectory.

[0099] c. Dynamic obstacle avoidance:

[0100] In order to solve the dynamic obstacle avoidance problem during the follower's movement, the follower's relative velocity potential field and the dynamic obstacle's repulsion field function are introduced, so that the follower has the common function of relative distance and relative velocity repulsion potential field during the movement. as follows:

[0101]

[0102] Among them, h 3i >0 is the velocity repulsion gain, is the relative velocity between the follower and the dynamic obstacle, and are the measured current position and speed of the dynamic obstacle, l min is the safety distance set by the follower for collision, l d is the maximum distance at which the follower is affected by dynamic obstacles, is the angle between the relative speed and distance between the follower and the dynamic obstacle. , it means that the follower is far away from the obstacle or that the follower is not within the velocity potential field. At this time, there is no need to consider the influence of dynamic obstacles.

[0103] In order to construct the specific expression of the stability constraint in (25), it involves designing an appropriate state feedback controller and the corresponding Lyapunov function. For the formation tracking problem, first, the auxiliary controller based on the extended state observer is constructed using the backstepping method. Then, a distributed model predictive formation tracking controller for the air-ground collaborative system is proposed. Next, a distributed Lyapunov model predictive control algorithm is given. Finally, the recursive feasibility and stability of the air-ground collaborative system are analyzed.

[0104] First, define the coordinate transformation as follows:

[0105]

[0106] Among them, α q (t k ) represents the virtual controller, and the formation error e in the above coordinate transformation i (t k )The time derivative is:

[0107]

[0108] Construct the Lyapunov function as follows:

[0109]

[0110] The virtual controller is designed as follows:

[0111]

[0112] Among them, C i1 >0 is the control gain. Substituting the virtual controller into (34) yields:

[0113]

[0114] Next, for z in (32) i (t k ) and take the derivative:

[0115]

[0116] The Lyapunov function is established as:

[0117]

[0118] Based on disturbance foresight, the auxiliary controller can be designed as follows:

[0119]

[0120] Among them, C i2 >0 is the control gain. Consider the overall Lyapunov function:

[0121]

[0122] Based on the auxiliary control law (39) and the future disturbance estimate (18), the overall Lyapunov derivative can be written as:

[0123]

[0124] Therefore, we can get The convergence constraint (25) of Lyapunov model predictive control can be given as follows:

[0125]

[0126] Step 4: Design a distributed model predictive formation control algorithm that incorporates Lyapunov stability theory, enabling followers to maintain the desired formation while tracking the leader's trajectory. This distributed model predictive formation control inherits the stability and robustness of the adaptive auxiliary control law and utilizes online optimization to improve the formation tracking performance of the air-ground collaborative system. By utilizing the adaptive auxiliary controller and the associated Lyapunov function stability constraints, the recursive feasibility of the distributed model predictive formation control algorithm and the closed-loop stability of the air-ground collaborative system are ensured.

[0127] Based on the optimization problem (21), a distributed Lyapunov model prediction formation control algorithm is designed. The implementation process is as follows:

[0128] Offline process:

[0129] 1. Select a suitable observer gain matrix L s0 ,L s1 ,…,L sn ;

[0130] 2. For each follower i, select the sampling period δ and the weighting matrix P i 、R i , follower safety radius R, static obstacle influence radius R o , the safety distance d from the tunnel boundary res, and the relative velocity V of the dynamic obstacle im And other design parameters. Set t k =0;

[0131] Online Process:

[0132] 3. The i-th follower obtains the current state ζ i (t k );

[0133] 4. The i-th follower receives the status of neighbor follower j s∈[t k ,t k +T];

[0134] 5. Solve the optimization problem (21) and obtain the optimal control input sequence Take the first element in the sequence as the control input;

[0135] 6. Apply the optimal control input to predict the state sequence of follower i at the next moment;

[0136] 7. t k =t k +δ, return to step 3.

[0137] Input constraint analysis

[0138] In the recursive feasibility proof of model predictive control, the input of the auxiliary controller needs to be part of the candidate solution. If the constraints are not met, the candidate solution will fail. In order to ensure the safety of the system when the model predictive control fails, the auxiliary controller is required to meet

[0139] Lemma 1: Let Indicates the control gain C i2 For the air-ground collaborative dynamics models (6) and (7), based on the adaptive auxiliary controller, the following relationship holds:

[0140]

[0141] Proof: First define And (38) can be restated as Since Lemma 1 holds, we can get ||χ i ||≤||χ i (t0)||. In addition,||e i || ∞ ≤||e i ||≤||χ i ||,||z i || ∞ ≤||zi ||≤||χ i ||, we can deduce ||e i || ∞ ≤||χ i (t0)||,||z i || ∞ ≤||χ i (t0)||, and the communication topology satisfies Therefore, we have:

[0142]

[0143] From (32), it can be seen that all states in the global closed-loop tracking formation system are bounded, that is, and Since all states are bounded, the nonlinear term f mi Every element in is bounded, so there exists a known positive constant such that

[0144] Then, according to (35), we have:

[0145]

[0146] Among them, according to (41), and are all bounded, so there is So we have:

[0147]

[0148] Feasibility and stability analysis

[0149] Theorem 1: For the air-ground collaborative system described in (6) and (7), the distributed Lyapunov model predictive control algorithm determined by solving the tracking optimization problem ensures that each optimization problem has a solution in the receding horizon and that the system state converges asymptotically to the desired trajectory under the control. Using the distributed Lyapunov model predictive control algorithm, the formation tracking task specified by the air-ground collaborative system can be achieved.

[0150] Proof: The proof is divided into two parts. First, the recursive feasibility of the distributed Lyapunov model predictive control is proved. Then, the stability of the entire air-ground collaborative system is verified.

[0151] Part 1: Since Lemma 1 holds, we know that the Lyapunov-based adaptive auxiliary controller can always satisfy the input constraints. Therefore, for any sampling time, the input signal determined by the Lyapunov-based adaptive auxiliary controller is always applicable and can be used as the optimal input solution for distributed Lyapunov model predictive control. Therefore, the following formula is correct at all times:

[0152]

[0153] Auxiliary controller input is not only feasible, but also optimal at the current moment. In t k It is feasible to solve the distributed Lyapunov model predictive control at time t. k+1 , the feasible optimal input solution of distributed Lyapunov model predictive control can be selected as:

[0154]

[0155] A segmentation strategy is adopted, in the short term s∈[t k+1 ,t k+1 +δ), continue to use the auxiliary control input; in the mid-term s∈[t k+1 +δ,t k +T), inheriting the optimal solution of the previous moment; in the long term s∈[t k +T,t k+1 +T), and the terminal input of the previous moment is extended. Therefore, the tracking optimization problem always has a solution, which can ensure the recursive feasibility of distributed Lyapunov model predictive control.

[0156] Part 2: Due to the result of Lemma 1, the stability of the air-ground cooperative system (6) and (7) can be guaranteed. In the optimization problem, the constraint (25) requires that the energy decay rate of the actual controller does not exceed that of the auxiliary controller, that is, the distributed Lyapunov model predictive control derived by solving the tracking optimization problem inherits the stability of the Lyapunov-based adaptive auxiliary controller (39). In addition, the distributed Lyapunov model predictive control also improves the formation tracking performance through online optimization. Therefore, it can be obtained:

[0157]

[0158] If the optimized input reduces the error faster than the auxiliary controller, then If the optimization problem cannot find a feasible solution, directly using the input of the auxiliary controller also ensures that the system always meets

[0159] Based on the same inventive concept, an embodiment of the present application provides a computer device, including a memory, a processor, and a computer program stored in the memory and runnable on the processor. When the processor executes the computer program, it implements the steps of the aforementioned air-ground collaborative system model prediction formation control method in an underground tunnel environment.

[0160] Based on the same inventive concept, an embodiment of the present application provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the aforementioned air-ground collaborative system model prediction formation control method in an underground tunnel environment.

[0161] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0162] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0163] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0164] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0165] The above embodiments are only for illustrating the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the present invention.

Claims

1. A model-predictive formation control method for an air-ground collaborative system in an underground tunnel environment, wherein the air-ground collaborative system comprises multiple quadrotor drones and multiple two-wheel drive unmanned vehicles, characterized in that: The steps include: Step 1: Select any UAV or any unmanned vehicle as the leader of the air-ground collaborative system, and the remaining UAVs and unmanned vehicles as followers to build a nonlinear model of the air-ground collaborative system; select any point on the underground corridor wall to construct the underground corridor model; Step 2: Based on the nonlinear model of the air-ground collaborative system constructed in Step 1, a high-order interference observer is designed to estimate the current unknown external disturbance. Based on the designed high-order interference observer, an interference prediction model is established to estimate the future unknown external disturbance. Step 3: Based on the interference prediction model established in Step 2, a rolling optimization control strategy based on state prediction is designed. In each control cycle, the control signal of each follower is optimized according to the current state of the system and the predicted future state. While ensuring tracking accuracy, collision avoidance between followers within the air-ground collaborative system, collision avoidance between followers and the tunnel wall, obstacle avoidance between followers and static obstacles within the tunnel, and obstacle avoidance between followers and dynamic obstacles within the tunnel are achieved. In step 4, the rolling optimization control strategy designed in step 3 is solved using the distributed model predictive formation control algorithm combined with Lyapunov stability theory, so that each follower maintains the desired formation configuration while tracking the leader's trajectory.

2. The air-ground collaborative system model prediction formation control method in an underground pipeline corridor environment according to claim 1 is characterized in that: The specific process of step 1 is as follows: Defining Leader Status p0 and q0 represent the position and velocity of the leader respectively, and the position model of the leader is expressed as follows: Where u0 represents the control input of the leader, I3 is the third-order identity matrix, t represents time; Based on the position system of the remaining drones and unmanned vehicles, a unified nonlinear model is established to represent the position model of the follower and define the follower state. p mi ,q mi Represent the position and velocity of the i-th follower respectively, and the position model of the follower is expressed as follows: Among them, f mi represents the known nonlinear term of the system, u mi represents the control input of the follower, d mi represents unknown external interference, m∈{f,s}, f represents a UAV, s represents an unmanned vehicle, N is the number of followers, N>0; With the formation starting point as the origin and the formation moving direction as the X-axis, a three-dimensional coordinate system is established. The cross section of the underground corridor in the YOZ plane is a semicircle. The coordinate of any point (x t ,y t ,z t ) Establish the pipeline corridor radius as follows: Among them, ∈ t Indicates the offset of the corridor, R t Indicates the radius of the pipe gallery.

3. The air-ground collaborative system model prediction formation control method in an underground pipeline corridor environment according to claim 2 is characterized in that: The specific process of step 2 is as follows: Based on the nonlinear model of the air-ground collaborative system constructed in step 1, a high-order interference observer is designed. The high-order interference observer is designed as follows: in, is the unknown external interference d mi The estimated value of s0(t),...,s n (t) represents the observer variable, L s0 ,...,L sn is a positive definite observer gain, q mi The estimated value of , n is a coefficient determined by the trade-off between prediction accuracy and computational complexity; The observer error is designed as: Among them, e s0 (t) is the observation error of the interference itself, e sk (t) is the observation error of the k-th order derivative; Combining the air-ground cooperative system with the high-order disturbance observer and taking the derivative of the above observer error, the compact form of the observer error is obtained as follows: in, Based on the designed high-order interference observer, an interference prediction model is established, and the interference estimation at the future time t+η is approximately as follows: Where η represents any future time, η∈(0,T], T represents the prediction time domain, T>0; The future interference estimation error is expressed as: in, 4. The air-ground collaborative system model prediction formation control method in an underground pipeline corridor environment according to claim 3 is characterized in that: In step 3, a quadratic programming method is used to design the objective function corresponding to the rolling optimization control strategy based on state prediction, so as to obtain the optimal control signal of the i-th follower; the objective function is designed as follows: The constraints are as follows: in, represents the objective function, S(δ) represents the piecewise function family with a control period of δ, s∈[t k ,t k +T],P i 、R i are weight matrices, P i >0, R i >0, is the physical limit of the actuator, represents the Lyapunov function, Indicates t k Auxiliary controller at the moment; f mi (s|t k ) represents t k The nonlinear term designed at the moment acts on the future moment s; u mi (s|t k ) represents t k The control input designed at the moment acts on the future moment s; Indicates t k The interference estimate of the moment design acts on the future moment s; p mi (t k ),q mi (t k ) are the i-th follower t k The position and velocity at the moment, u mi (t k ) represents t k Control input at each moment; Represents the predicted formation error, which is in the form of: Among them, a ij is the Laplace matrix of the communication connection between followers, b i is the communication connection vector between the follower and the leader, d i0 is the fixed distance between the ith follower and the leader, d j0 is the fixed distance between the jth follower and the leader, is the predicted position of the ith follower, is the assumed position of the j-th follower, Expressed as: in, Indicates that the jth follower is at t k-1 The state value predicted at the future time s at the moment, Indicates that the jth follower is at t k-1 The state recursive value of the prediction time domain at each moment; represents the collision avoidance cost between followers and is designed as follows: Where λ is a constant that determines the size of the repulsive potential field, λ>0, k i is the weight coefficient of the potential field for collision avoidance, k i >0, is the Euclidean distance calculated based on the predicted state, and R is the follower safety radius; represents the obstacle avoidance cost between the follower and the tunnel wall, which is designed as follows: Among them, h 1i is the weight coefficient of the obstacle avoidance potential field between the follower and the tunnel wall, h 1i >0, T(t k ) represents the distance from the follower to the tunnel boundary measured by the sensor carried by the follower, is the angle between the UAV’s flight altitude and the tunnel radius, d res The safe distance from the corridor boundary; It represents the obstacle avoidance cost between the follower and the static obstacles in the tunnel, and is designed as follows: Among them, h 2i is the weight coefficient of the obstacle avoidance potential field between the follower and the static obstacles in the tunnel, h 2i >0, is the position of the static obstacle, R o is the influence radius of the static obstacle; It represents the obstacle avoidance cost between the follower and the dynamic obstacles in the tunnel, and is designed as follows: Among them, h 3i is the velocity repulsion gain, h 3i >0, V im (t k ) represents the relative velocity between the follower and the dynamic obstacle, and are the measured current position and speed of the dynamic obstacle, is the predicted speed of the i-th follower, l min The safety distance set for the follower to avoid collision, l d is the maximum distance at which the follower is affected by the dynamic obstacle, φ is the angle between the relative speed and distance between the follower and the dynamic obstacle, 5. The model prediction formation control method of the air-ground collaborative system in the underground pipeline corridor environment according to claim 4 is characterized in that: The auxiliary controller is constructed by backstepping method. The design is as follows: α q (t k ) indicates a virtual controller, which is expressed as follows: Among them, C i1 、C i2 are control gains, C i1 >0, C i2 >0,z i (t k )=q mi (t k )-α q (t k ), e i (t k ) is the formation error, Indicates that the jth follower is at t k The position at the moment, p0(t k ) indicates that the leader is at t k The position at the moment, p mi (t k ),q mi (t k ) represent the number of followers at t k Position and velocity at a given moment; Constraints of the objective function Translates to:

6. The model prediction formation control method for the air-ground collaborative system in the underground pipeline corridor environment according to claim 5 is characterized in that: In step 4, the optimal control input obtained by using the distributed model prediction formation control algorithm combined with Lyapunov stability theory is: in, Indicates t k The optimal control input of the i-th follower at time; In t k+1 At this moment, a segmentation strategy is adopted, in the short term s∈[t k+1 ,t k+1 +δ), continue to use the input of the auxiliary controller; in the medium term s∈[t k+1 +δ,t k +T), inheriting the optimal solution of the previous moment; in the long term s∈[t k +T,t k+1 +T), extend the input of the previous moment, as follows: in, Indicates t k+1 The optimal control input of the i-th follower at time δ is the control period, Indicates t k+1 Auxiliary controller at all times, Indicates t k The optimal control input for the prediction horizon at any moment.

7. A computer device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that: When the processor executes the computer program, the steps of the model prediction formation control method of the air-ground collaborative system in the underground pipeline corridor environment are implemented as described in any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the steps of the model prediction formation control method of the air-ground collaborative system in the underground pipeline corridor environment as described in any one of claims 1 to 6 are implemented.

Images