High-efficiency optimization control method and system for state dimension change and modal change moving body

Abstract

The invention discloses an efficient optimization control method and system for a state dimension change variable-mode moving body, relates to the field of robot control, and aims to solve the problem that an existing method is not suitable for a variable-mode and variable-dimension air-ground cross-domain robot moving body system with state dimension change and ground and air operation capacity. Comprising the steps of 1, constructing an air-ground cross-domain robot variable modal dimension generalized system model; step 2, fast-slow dynamic decomposition and splitting of the system model into a series of nonsingular subsystems are carried out, and an inter-modal variable dimension mapping operator is constructed for each subsystem model; 3, designing attitude control performance index parameters; step 4, calculating an upper bound judgment condition of the control performance of the air-ground cross-domain robot; 5, introducing a robust positive invariant set strategy, and establishing a numerical calculation linear inequality condition; step 6, constructing an air-ground cross-domain robot convex optimization problem and solving a matrix variable in the problem; and 7, solving a linear combination coefficient of the multi-point gain of the air-ground cross-domain robot on line.

Description

Technical Field

[0001] The present invention relates to the field of robot control technology, and in particular to a method and system for efficiently optimizing control of a state dimension-changing modal motion body. Background Art

[0002] Air-to-ground cross-domain robots can perform detection missions in complex, confined environments such as buildings and underground spaces. Equipped with sensors, they are also widely used in industrial scenarios such as equipment flaw detection and pipeline inspection, adapting to diverse mission requirements. Servo motors adjust the center of gravity or rotor tilt, enabling seamless transitions between aerial flight and ground rolling. Independent of satellite navigation, they utilize visual SLAM, inertial navigation, and sensor fusion technologies to achieve high-precision positioning and path planning in GPS-denied environments.

[0003] With the rapid development of computing platform computing power and optimization solution technology, the application field of optimization control methods has expanded from traditional industrial process control. The rolling time domain optimization control method has the ability to handle physical quantity constraints and ensure system safety during the control process, and has played an important role in the control application practice of moving body systems.

[0004] Due to the rapid dynamic response of moving systems such as robots, controllers generally require operating frequencies exceeding hundreds of hertz. Therefore, the real-time performance of online optimization control algorithms is crucial. To accelerate the online solution of rolling-horizon optimization problems, research institutions and industrial sectors at home and abroad have conducted extensive research over the past three decades, developing a series of efficient algorithms, including real-time rolling iteration, explicit solution, and offline-online hybrid solution. These algorithms have been successfully experimentally validated on moving platforms such as rotary-wing drones and quadruped robots, demonstrating their superior performance. However, existing efficient optimization control methods are primarily based on traditional non-singular system models, which inherently cannot describe the dynamic systems of air-to-ground cross-domain robots capable of both ground and air operations with varying state dimensions. During operation, the system mechanism or structure of such platforms may undergo significant changes, resulting in variable modes and dimensions in their dynamic models. Air-to-ground cross-domain robots possess full three-dimensional translational control degrees of freedom when in the air, but only two-dimensional control degrees of freedom on the contact plane when operating on the ground. Existing efficient optimization control methods cannot accurately model the dynamic characteristics of such cross-domain robots, and therefore cannot effectively optimize their control performance or ensure operational stability. It is necessary to consider the dynamics of moving bodies with random modal variations and design stochastic performance indicators that integrate multiple control objectives, such as rapidity and robustness. Furthermore, it is necessary to design a guaranteed cost controller and optimize closed-loop system performance. Furthermore, in the event of changes in the dimensionality of the control degrees of freedom due to sudden changes in the system's mechanism or structure, a variable-dimensional controller is required to ensure that physical constraints such as the system state and control input are satisfied, and that the online rolling horizon optimization remains continuously solvable. Summary of the Invention

[0005] The technical problems to be solved by the present invention are:

[0006] Existing efficient optimization control methods cannot describe variable-mode, variable-dimensional air-ground cross-domain robot motion systems with state dimension changes and the ability to operate on the ground and in the air.

[0007] The present invention is to solve the above technical problems using the following technical solutions:

[0008] The present invention provides a method for efficient optimization control of a variable-mode moving body with a changing state dimension, comprising the following steps:

[0009] Step 1: Construct a generalized system model of the air-ground cross-domain robot with variable modal dimension;

[0010] Step 2: Decompose the system model into a series of non-singular subsystems by fast-slow dynamic decomposition, and construct an inter-modal variable dimension mapping operator for each subsystem model;

[0011] Step 3: Design the performance index parameters of the air-ground cross-domain robot posture control;

[0012] Step 4: Calculate the upper bound of the control performance of the air-ground cross-domain robot based on the quadratic Lyapunov function;

[0013] Step 5: Introduce the robust positive invariant set strategy to establish numerically computable linear inequality conditions;

[0014] Step 6: Construct the convex optimization problem of the air-ground cross-domain robot and solve the matrix variables in the problem;

[0015] Step 7: Solve the linear combination coefficients of the multi-point gains of the air-ground cross-domain robot online.

[0016] Furthermore, step one includes the following steps:

[0017] The dynamic model of the air-ground cross-domain robot in the aerial mode is established as follows:

[0018]

[0019] in, represents the Euler angle, Indicates the angular velocity of the machine system's attitude motion, represents the moment of inertia matrix, represents the attitude torque provided by the rotor thrust, τ d represents the external disturbance torque; T(Φ) represents the angular velocity coordinate transformation matrix:

[0020]

[0021] The dynamic model of the air-ground cross-domain robot under the ground mode is constructed as follows:

[0022]

[0023] The moment of inertia matrix is expressed as and The coordinate transformation matrix is T roll (Φ)=[e rx ,0,0] T , whose first row vector is

[0024] Further introduce the mode-dependent singular matrix and The dynamic models of the air-ground cross-domain robot in the aerial mode and the ground mode are combined into:

[0025]

[0026] Select the state quantity as The control input is The combined dynamic model is transformed into the standard form of the generalized system model through Jacobi linearization and Euler discretization:

[0027] E σ(k) x(k+1)=A σ(k) x(k)+B σ(k) u(k)+G σ(k) d(k) (1)

[0028] Where x(k), u(k) and d(k) represent the system state, control input and disturbance input respectively, σ(k) represents the system mode; E σ(k) is a singular matrix; A σ(k) 、B σ(k) and G σ(k) is the system matrix of system state, control input and disturbance input. The physical constraints of the system are:

[0029]

[0030] Among them, x max 、u max Respectively represent the maximum limit of system state and control input, represents the admissible set of system states and control inputs, represents the real vector field of the corresponding dimension, (x) l 、(u) l represents the lth scalar element of the corresponding vector;

[0031] The random variation law of the system modal considered is:

[0032]

[0033] Among them, Prob{σ(k s +τ+1)=j|σ(k s +τ)=i} represents the probability of jumping from mode i to mode j, π ij is the probability parameter obtained by statistics, Represents a field of integers.

[0034] Furthermore, step 2 includes the following steps:

[0035] Perform fast-slow dynamic decomposition of the system:

[0036]

[0037] Among them, I i represents the identity matrix, and is a full rank matrix, and the rank of a singular matrix is

[0038] The transformed system state satisfies:

[0039]

[0040] Based on the state space mapping relationship given by formula (4), the generalized system model is rewritten as a set of non-singular differential-algebraic equations:

[0041]

[0042] Then the coordinate transformation relationship between the state spaces of each modal subsystem is: Calculate the inter-modal mapping operator Γ i，j :

[0043]

[0044] Among them, I j represents the identity matrix corresponding to mode j;

[0045] The system is further rewritten into a compact form:

[0046]

[0047] Furthermore, step three includes the following steps:

[0048] Based on the variable state dimension system model of formula (7), the robust optimization control problem is described as the minimization problem of the performance upper bound in the worst case:

[0049]

[0050] The expected cumulative cost of the object to be optimized in the infinite time domain is:

[0051]

[0052] Among them, l(k+i|k) is the stage cost:

[0053]

[0054] in, is a positive state and control input weight matrix, is a positive scalar describing the emphasis on robustness.

[0055] Furthermore, step four includes the following steps:

[0056] The modal dependent Lyapunov function is:

[0057]

[0058] in, It is the state component of the slow dynamic part of the subsystem introduced above;

[0059] If the quadratic function satisfies the following conditions:

[0060]

[0061] Then the following formula holds:

[0062]

[0063] get:

[0064]

[0065] The existence condition of the performance upper bound is further transformed into the form of linear inequality:

[0066]

[0067] in,

[0068]

[0069] Performance optimization is achieved by minimizing the upper bound of the cost corresponding to V(k|k).

[0070] Furthermore, step five includes the following steps:

[0071] structure The modal dependence ellipsoid set, the elements in the set satisfy: if the state Under the action of the controller and subsystem corresponding to the collective mode r, the state at the next moment still satisfies

[0072] structure The modal dependence of the quadratic function, ε r represents the corresponding modal-dependent level set, and its positive invariance condition is directly expressed as Considering the influence of bounded interference input, substituting into the system model of formula (7), the above positive invariance condition is further expressed as:

[0073]

[0074] Applying the S process to the above equation, we get the following linear inequality:

[0075]

[0076] in,

[0077]

[0078] M Tran ={(r, r′)∈M×M:π r，r′ >0}

[0079] The invariant set also satisfies the initial boundedness condition: This is equivalent to a linear inequality:

[0080]

[0081] Introduce the boundary constraint judgment conditions of the ellipsoid set:

[0082]

[0083] Combine formulas (13)-(16) to solve W that satisfies all inequality conditions simultaneously r , ensure that the constraints are met in infinite time domain The robust positive invariant set ε r .

[0084] Furthermore, step six includes the following steps:

[0085] Based on the inequality conditions obtained in steps 4 and 5, the following convex optimization problem for solving the variable-dimensional control law is established:

[0086]

[0087] in, represents the matrix variables in the optimization problem; the introduced matrix inequality condition is equivalent to

[0088] Given a representative state point x in the state space set，i，j , respectively solve the semi-positive programming problem to obtain The process includes the following:

[0089] ①Set performance weight parameters x max and u max ;

[0090] ② Given a set of initial conditions (x0, u0), solve the semi-positive definite programming problem to obtain a set of feasible regions ε0;

[0091] ③ Select a set of state points {x set，1，j :j∈M};

[0092] ④ Then select N-1 groups of state points {x set，i，j :j∈M};

[0093] ⑤ For all selected initial conditions (x0, u0), solve the semi-positive definite programming problem and store

[0094] Furthermore, step seven includes the following steps:

[0095] To solve the obtained As a basis, the reconstructed approximate solution space is obtained by its convex combination:

[0096]

[0097] Among them, V i，j It is a basic solution The combination coefficient of

[0098] The online optimization problem is of the form:

[0099]

[0100] in, and represents the controller parameters obtained by linear combination of basis matrices. When the system is running, the above optimization problem is solved and the control input is calculated based on real-time state feedback at each sampling time. The calculation process includes:

[0101] ① Obtain system feedback information x(k) and σ(k) and calculate the transformed slow dynamic component

[0102] ②Solve the optimization problem and obtain the linear combination coefficients

[0103] ③Calculate the combined control parameters and feedback gain

[0104] ④ Apply control signal to the controlled object

[0105] ⑤ Update the sampling time k = k + 1 and return to the process step ① rolling iterative calculation.

[0106] The present invention provides an efficient optimization control system for a variable-mode motion body with a change in state dimension. The system has a program module corresponding to the steps of the method described in any one of the above technical solutions, and executes the steps in the above-mentioned efficient optimization control method for a variable-mode motion body with a change in state dimension during operation.

[0107] The present invention also provides a computer-readable storage medium, which stores a computer program. The computer program is configured to implement the steps in the state dimension change variable mode motion body efficient optimization control method described in any one of the above technical solutions when called by a processor.

[0108] Compared with the prior art, the present invention has the following beneficial effects:

[0109] ① The present invention designs a variable-dimensional Lyapunov function and a corresponding optimization solution, which avoids the requirement of existing optimization control methods that subsystems in a multimodal robot system must be non-singular or have the same singularity. The resulting controller allows each modal dynamics to have different dimensions, can provide strict system performance guarantees, and ensure that constraints such as state / control inputs are met.

[0110] ② In optimizing the control law, this invention proposes a probability-weighted performance metric that considers the modal variations of the air-ground cross-domain robot. The resulting rolling optimization controller achieves improved control performance. Especially when there are large probabilistic differences in air-ground modal selection, the proposed performance metric optimizes system performance on average, effectively preventing the optimization design from overemphasizing low-probability events and thus impacting overall performance, resulting in better actual performance.

[0111] ③ The method proposed in this paper designs an optimization control scheme that combines offline and online solutions, significantly reducing the variable dimension and computational complexity of the online solution. This significantly reduces the number of variables and computational complexity required for the online solution, making it applicable to moving systems requiring higher sampling frequencies and faster control responses. Furthermore, the low computing power requirement further reduces the hardware cost of the embedded controllers used in the rolling optimization control algorithm, making it suitable for lightweight, low-cost platforms such as aerial photography drones. BRIEF DESCRIPTION OF THE DRAWINGS

[0112] Figure 1 This is a flow chart of a method for efficient optimization control of a variable-mode moving body with a change in state dimension according to an embodiment of the present invention;

[0113] Figure 2 Schematic diagram of a rotary-wing air-to-ground cross-domain robot in an embodiment of the present invention;

[0114] Figure 3 is a posture response curve diagram of the air-ground cross-domain robot in an embodiment of the present invention;

[0115] Figure 4 : is a torque command curve diagram of the air-ground cross-domain robot in an embodiment of the present invention;

[0116] Figure 5 : is a reference trajectory tracking curve diagram of the air-ground cross-domain robot in an embodiment of the present invention;

[0117] Figure 6 This is an online computational complexity analysis diagram in an embodiment of the present invention;

[0118] Figure 7 This is a diagram of the offline solution condition settings and feasible domain analysis in an embodiment of the present invention. DETAILED DESCRIPTION

[0119] In order to enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the present invention will be described below with reference to the accompanying drawings. Obviously, the described embodiments or examples are only some of the embodiments or examples of the present invention, and not all of them. Based on the embodiments or examples of the present invention, all other embodiments or examples obtained by those skilled in the art without creative work should fall within the scope of protection of the present invention.

[0120] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0121] Combine Figure 1 As shown, the present invention provides a method for efficient optimization control of a variable-mode moving body with a changing state dimension, comprising the following steps:

[0122] Step 1: Construct a generalized system model of the air-ground cross-domain robot with variable modal dimension;

[0123] Step 2: Decompose the system model into a series of non-singular subsystems by fast-slow dynamic decomposition, and construct an inter-modal variable dimension mapping operator for each subsystem model;

[0124] Step 3: Design the performance index parameters of the air-ground cross-domain robot posture control;

[0125] Step 4: Calculate the upper bound of the control performance of the air-ground cross-domain robot based on the quadratic Lyapunov function;

[0126] Step 5: Introduce the robust positive invariant set strategy to establish numerically computable linear inequality conditions;

[0127] Step 6: Construct the convex optimization problem of the air-ground cross-domain robot and solve the matrix variables in the problem;

[0128] Step 7: Solve the linear combination coefficients of the multi-point gains of the air-ground cross-domain robot online.

[0129] The present invention models the variable modal dynamics of an air-to-ground cross-domain robot in the form of a generalized system and decomposes it into a series of non-singular subsystems through fast-slow dynamic decomposition. A variable-dimensional modal-dependent feedback control law is established for each subsystem model, and the analytical expression of the upper bound of random performance is determined with the help of a quadratic Lyapunov function. To solve the constraint satisfaction problem in the infinite time domain, the concept of robust positive invariant sets is extended to the variable-dimensional state space, and numerically computable linear inequality conditions are established. Combining the results of both the upper bound of performance and the robust positive invariant sets, the present invention proposes design conditions for variable-dimensional control laws that optimize robust performance. Furthermore, by solving the matrix variables in the optimization problem offline and combining the matrix conditions of the optimal control law under multiple working conditions online, an efficient solution algorithm is constructed that can significantly reduce the complexity of online calculations.

[0130] Step 1 includes the following steps:

[0131] The hardware structure and coordinate system of the air-ground cross-domain robot in this embodiment are defined as follows: Figure 2 As shown, it includes an inertial system I fixed to the ground, a rolling system T fixed to the center of mass of the body with the xy plane parallel to the horizontal plane, and a machine system B fixed to the center of mass of the body with the xyz axes aligned with the direction of the body. Among them, the angle between the inertial system and the rolling system is the yaw angle ψ, and the angles between the rolling system and the machine system around the x and y axes are the roll angle φ and the pitch angle θ respectively. Due to the different air-ground motion characteristics, the dynamic models are established here separately. For the air mode, the dynamic model of the air-ground cross-domain robot under the air mode is established as:

[0132]

[0133] in, represents the Euler angle, Indicates the angular velocity of the machine system's attitude motion, represents the moment of inertia matrix, represents the attitude torque provided by the rotor thrust, τ d represents the external disturbance torque; T(Φ) represents the angular velocity coordinate transformation matrix:

[0134]

[0135] In the ground mode, the robot's motion is affected by the ground contact, and its roll attitude angle and angular velocity are limited. The dynamic model of the air-ground cross-domain robot in the ground mode is constructed as follows:

[0136]

[0137] The moment of inertia matrix is expressed as and The coordinate transformation matrix is T roll (Φ)=[e rx ,0,0] T , whose first row vector is

[0138] Further introduce the mode-dependent singular matrix and The dynamic models of the air-ground cross-domain robot in the aerial mode and the ground mode are combined into:

[0139]

[0140] Select the state quantity as The control input is The combined dynamic model is transformed into the standard form of the generalized system model through Jacobi linearization and Euler discretization:

[0141] E σ(k) x(k+1)=A σ(k) x(k)+B σ(k) u(k)+G σ(k) d(k) (1)

[0142] Where x(k), u(k) and d(k) represent the system state, control input and disturbance input respectively, σ(k) represents the system mode; E σ(k) is a singular matrix; it has different ranks in different modes, so the system presents a variable state dimension characteristic; A σ(k) 、B σ(k) and G σ(k) is the system matrix of system state, control input and disturbance input, which describes the evolution of system state over time. The physical constraints of the system are:

[0143]

[0144] Among them, x max 、u max Respectively represent the maximum limit of system state and control input, represents the admissible set of system states and control inputs, represents the real vector field of the corresponding dimension, (x) l 、(u) l represents the lth scalar element of the corresponding vector;

[0145] Furthermore, constraints can be set based on the actual mobility of the platform The switching law parameters can be obtained through statistical identification.

[0146] The random variation law of the system modal considered is:

[0147]

[0148] Among them, Prob{σ(k s +τ+1)=j|σ(k s +τ)=i} represents the probability of jumping from mode i to mode j, π ij is the probability parameter obtained by statistics, Represents a field of integers.

[0149] Step 2 includes the following steps:

[0150] Considering E σ(k) The singularity of the original system is transformed; the fast-slow dynamic decomposition of the system is performed:

[0151]

[0152] Among them, I i represents the identity matrix, and is a full rank matrix, and the rank of a singular matrix is

[0153] The transformed system state satisfies:

[0154]

[0155] Based on the state space mapping relationship given by formula (4), the variable mode generalized system model is rewritten as a non-singular differential-algebraic equation system:

[0156]

[0157] Then the coordinate transformation relationship between the state spaces of each modal subsystem is: Calculate the inter-modal mapping operator Γ i，j :

[0158]

[0159] Among them, I j represents the identity matrix corresponding to mode j;

[0160] The system is further rewritten into a compact form:

[0161]

[0162] The system matrix E obtained in the previous step σ(k) , A σ(k)Substitute into formula (3) to obtain the subsystem matrix after dynamic decomposition transformation And calculate the inter-modal mapping operator Γ according to formula (6) i，j .

[0163] Step three includes the following steps:

[0164] Based on the variable state dimension system model of formula (7), the robust optimization control problem is described as a problem of minimizing the upper bound of performance in the worst case, that is, the following minimization problem:

[0165]

[0166] The expected cumulative cost of the object to be optimized in the infinite time domain is:

[0167]

[0168] Here, l(k+i|k) describes the instantaneous performance of the control system at each step of operation, which is called the stage cost. In this invention, in order to counteract the interference caused by measurement noise, external environmental influences, modeling uncertainty, etc. of the moving body system, the stage cost with robust performance considerations is designed as follows:

[0169]

[0170] in, is a positive state and control input weight matrix, is a positive scalar describing the emphasis on robustness.

[0171] Adjust the weight parameters based on the robot's performance in terms of angle and angular velocity control accuracy, attitude torque control cost, and anti-interference ability of the three channels of roll / pitch / yaw. and

[0172] Step 4 includes the following steps:

[0173] Because J ∞ (k) describes the cumulative control cost of the system in the infinite time domain. It is the sum of an infinite number of terms and cannot be directly calculated numerically. Therefore, this step will combine the Lyapunov function to derive an analytical expression for its upper bound, and then use the upper bound expression to establish a numerically solvable optimization problem. The modal-dependent Lyapunov function is:

[0174]

[0175] in, It is the state component of the slow dynamic part of the subsystem introduced above;

[0176] If the quadratic function satisfies the following conditions:

[0177]

[0178] Then the following formula holds:

[0179]

[0180] get:

[0181]

[0182] That is, we get an upper bound J on the expected cost in infinite time domain ∞ (k)≤V(k|k). Then, the original cost function J ∞ The optimization of (k) can be transformed into the minimization of the performance upper bound V(k|k). The expression of the Lyapunov function designed in this step, where the state at the initial moment of the rolling time domain is To determine the value, the optimization of V(k|k) is to optimize the matrix P r To facilitate numerical solution, the existence condition of the performance upper bound is further transformed into the form of linear inequality:

[0183]

[0184] in,

[0185]

[0186]

[0187] The upper bound of the system performance index is obtained by numerically solving the above inequality; at the same time, by incorporating the above inequality into the optimization problem, performance optimization is achieved by minimizing the upper bound of the cost corresponding to V(k|k).

[0188] Step five includes the following steps:

[0189] The design requirements of rolling optimization control include not only the optimization of system performance, but also the optimization of state / control input. Constraints. To ensure that the regressing horizon controller can continuously output feasible control actions that meet the constraints, the constraints must not only be applied to the first step of the regressing horizon, but also to each step of the infinite horizon. In order to solve the constraint satisfaction problem of infinite state / control sequences, this step introduces the concept of robust positive invariant sets. Construction The modal dependence ellipsoid set, the elements in the set satisfy: if the state Under the action of the controller and subsystem corresponding to the collective mode r, the state at the next moment still satisfies If the modal-dependent robust positive invariant set εr of the generalized system with variable state dimension can be established, the constraint judgment on the infinite time domain state / control input can be transformed into the constraint judgment on the ellipsoid boundary, thereby achieving efficient solution of constrained optimization.

[0190] structure The modal dependence of the quadratic function, ε r represents the corresponding modal-dependent level set, and its positive invariance condition is directly expressed as Considering the influence of bounded interference input, substituting into the system model of formula (7), the above positive invariance condition is further expressed as:

[0191]

[0192] To facilitate numerical solution, the S process is applied to the above equation to obtain the following linear inequality:

[0193]

[0194] in,

[0195]

[0196] M Tran ={(r, r′)∈M×M:π r，r′ >0}

[0197] The above conditions ensure that the set ε r Convergence as the system runs. The invariant set also satisfies the initial boundedness condition: This is equivalent to a linear inequality:

[0198]

[0199] The above conditions determine a robust positive invariant set of the variable state dimension generalized system studied in this invention. To ensure that the states in the set all meet Constraints, introduce the ellipsoid set boundary constraint judgment conditions:

[0200]

[0201]

[0202] Combine formulas (13)-(16) to solve W that satisfies all inequality conditions simultaneously r , ensure that the constraints are met in infinite time domain The robust positive invariant set ε r .

[0203] Step six includes the following steps:

[0204] Based on the inequality conditions obtained in steps 4 and 5, the following convex optimization problem for solving the variable-dimensional control law is established:

[0205]

[0206] in, represents the matrix variables in the optimization problem; from Schur complement, the introduced matrix inequality condition is equivalent to Therefore, minimizing γ is equivalent to minimizing the upper bound of the cost function of the original optimization problem, which can achieve system performance optimization.

[0207] Although the above optimization problem is a semi-definite programming problem that can be solved numerically, there are many matrix parameters in the optimization and the dimension of the decision variables to be solved is high. Its online calculation speed is still not ideal for the moving body system. In order to further reduce the computational complexity of the online solution, this step proposes to decompose the optimization problem into two steps: offline solution and online solution. The matrix variable solution part with high parameter dimension and large computational amount is completed offline, and fast online calculation is achieved based on the offline calculation results. Considering that the control laws obtained by the rolling optimization control method under different initial states are different, the design idea of the offline solution part is to give a representative state point x in the state space. set，i，j , respectively solve the semi-positive programming problem to obtain These solutions are used as the basis of the control law parameter space for actual online solution.

[0208] Given a representative state point x in the state space set，i，j , respectively solve the semi-positive programming problem to obtain The process includes the following:

[0209] ①Set performance weight parameters x max and u max ;

[0210] ② Given a set of initial conditions (x0, u0), solve the semi-positive definite programming problem to obtain a set of feasible regions ε0;

[0211] ③ Select a set of state points {x set,1，j :j∈M};

[0212] ④ Then select N-1 groups of state points {x set,i，j :j∈M};

[0213] ⑤ For all selected initial conditions (x0, u0), solve the semi-positive definite programming problem and store

[0214] Step seven includes the following steps:

[0215] To solve the obtained As a basis, the reconstructed approximate solution space is obtained by its convex combination:

[0216]

[0217] Among them, v i，j It is a basic solution The combination coefficients of ; then, the online optimization problem is transformed from solving the complete matrix variable group υ to solving a small number of combination coefficients v i，j .

[0218] The online optimization problem is of the form:

[0219]

[0220] in, and represents the controller parameters obtained by linear combination of basis matrices; since the constraints of the original semidefinite programming problem are all linear inequalities, the parameters obtained by linear combination here also satisfy all constraints, that is, they also have the performance guarantees established in the previous steps. When the system is running, the above optimization problem is solved based on real-time state feedback at each sampling time and the control input is calculated. The calculation process includes:

[0221] ① Obtain the system feedback current state x(k) and modal σ(k), and calculate the transformed slow dynamic component

[0222] ② Solve the optimization problem of formula (19) and obtain the linear combination coefficient

[0223] ③Calculate the combined control parameters and feedback gain

[0224] ④ Apply control signal to the controlled object

[0225] ⑤ Update the sampling time k = k + 1 and return to the process step ① rolling iterative calculation.

[0226] This step obtains the robot's current state x(k) and modal state σ(k) in real time online, and substitutes the feedback information and the matrix parameters given in step 6 into the online optimization problem (19), calling the Mosek solver to solve in real time. Calculate the posture control instructions This step should be deployed in the onboard computer of the air-ground cross-domain robot, responding to the system's state / modal feedback information in real time in a loop iterative manner to provide the robot with a control strategy.

[0227] This embodiment uses a rotary-wing air-to-ground cross-domain robot to verify the application of the technical method proposed in this invention. The robot's attitude angle response curve, torque command curve, and trajectory tracking curve are obtained as follows: Figure 3 、 Figure 4 and Figure 5 As shown in the figure, the proposed optimization control method can ensure the stability of the state-variable dimensional posture dynamics in the air-ground variable modal motion of the robot while satisfying the constraints. In the process of implementing the algorithm for the air-ground cross-domain robot controlled object, the relationship between the number of different offline reference points and the dimension of the decision variables and the calculation time of the online solution is summarized as follows: Figure 6 , it can be seen that when the reference points are selected no more than 15 points, the maximum online calculation time of the algorithm is less than 10ms, which meets the 100Hz attitude control frequency requirement, and the calculation efficiency can meet the real-time requirements of the control algorithm. In addition, the reference point selection strategy and feasible domain in the offline solution are shown as follows Figure 7 As shown in Figure 1, by selecting reference points near the equilibrium point and the boundary of the maximizing ellipsoid, the function space of the control law obtained by online solution can effectively balance optimal control performance and maximize the feasible state range. The above experimental results verify the effectiveness of the method described in the patent.

[0228] The present invention proposes an efficient optimization control method (algorithm) for a variable-mode moving body with a changing state dimension, which is the underlying technical core of the present invention. Various products can be derived based on the algorithm.

[0229] Based on the method proposed in the present invention, a high-efficiency optimization control system for a variable-mode motion body with a changing state dimension is developed using a programming language. The system has a program module corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned high-efficiency optimization control method for a variable-mode motion body with a changing state dimension during operation.

[0230] The developed system (software) computer program is stored on a computer-readable storage medium. The computer program is configured to implement the steps of the above-mentioned method for efficient optimization control of a state dimension-changing variable-mode moving body when called by a processor. This materializes the present invention on a carrier, becoming a computer program product.

[0231] Various implementations of the systems and techniques described herein can be realized in digital electronic circuitry, integrated circuitry, dedicated ASICs (application specific integrated circuits), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include being implemented in one or more computer programs that are executable and / or interpreted on a programmable system comprising at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0232] The computer programs (also referred to as programs, software, software applications, or code) of the present invention include machine instructions for a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., a magnetic disk, an optical disk, a memory, a programmable logic device (PLD)) for providing machine instructions and / or data to a programmable processor, including a machine-readable medium that receives machine instructions as a machine-readable signal. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0233] Although the present invention is disclosed as above, the scope of protection disclosed by the present invention is not limited thereto. Those skilled in the art of the present invention may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for efficient optimization control of a variable-mode moving body with varying state dimension, characterized in that: The steps include: Step 1: Construct a generalized system model of the air-ground cross-domain robot with variable modal dimension; Step 2: Decompose the system model into a series of non-singular subsystems by fast-slow dynamic decomposition, and construct an inter-modal variable dimension mapping operator for each subsystem model; Step 3: Design the performance index parameters of the air-ground cross-domain robot posture control; Step 4: Calculate the upper bound of the control performance of the air-ground cross-domain robot based on the quadratic Lyapunov function; Step 5: Introduce the robust positive invariant set strategy to establish numerically computable linear inequality conditions; Step 6: Construct the convex optimization problem of the air-ground cross-domain robot and solve the matrix variables in the problem; Step 7: Solve the linear combination coefficients of the multi-point gains of the air-ground cross-domain robot online.

2. The method for efficient optimization control of a variable-mode moving body with state dimension change according to claim 1, characterized in that: Step 1 includes the following steps: The dynamic model of the air-ground cross-domain robot in the aerial mode is established as follows: in, represents the Euler angle, Indicates the angular velocity of the machine system's attitude motion, represents the moment of inertia matrix, represents the attitude torque provided by the rotor thrust, τ d represents the external disturbance torque; T(Φ) represents the angular velocity coordinate transformation matrix: The dynamic model of the air-ground cross-domain robot under the ground mode is constructed as follows: The moment of inertia matrix is expressed as and The coordinate transformation matrix is T roll (Φ)=[e rx , 0, 0] T , whose first row vector is Further introduce the mode-dependent singular matrix and The dynamic models of the air-ground cross-domain robot in the aerial mode and the ground mode are combined into: Select the state quantity as The control input is The combined dynamic model is transformed into the standard form of the generalized system model through Jacobi linearization and Euler discretization: E σ(k) x(k+1)=A σ(k) x(k)+B σ(k) u(k)+G σ(k) d(k) (1) Where x(k), u(k) and d(k) represent the system state, control input and disturbance input respectively, σ(k) represents the system mode; E σ(k) is a singular matrix; A σ(k) 、B σ(k) and G σ(k) is the system matrix of system state, control input and disturbance input. The physical constraints of the system are: Among them, x max 、u max Respectively represent the maximum limit of system state and control input, represents the admissible set of system states and control inputs, represents the real vector field of the corresponding dimension, (x) l 、(u) l represents the lth scalar element of the corresponding vector; The random variation law of the system modal considered is: Among them, Prob{σ(k s +τ+1)=j|σ(k s +τ)=i} represents the probability of jumping from mode i to mode j, π ij is the probability parameter obtained by statistics, Represents a field of integers.

3. The efficient optimization control method for a variable-mode moving body with a state dimension change according to claim 2, characterized in that: Step 2 includes the following steps: Perform fast-slow dynamic decomposition of the system: Among them, I i represents the identity matrix, and is a full rank matrix, and the rank of a singular matrix is The transformed system state satisfies: Based on the state space mapping relationship given by formula (4), the generalized system model is rewritten as a set of non-singular differential-algebraic equations: Then the coordinate transformation relationship between the state spaces of each modal subsystem is: Calculate the inter-modal mapping operator Γ i，j : Among them, I j represents the identity matrix corresponding to mode j; The system is further rewritten into a compact form:

4. The method for efficient optimization control of a state dimension-changing modal moving body according to claim 3, characterized in that: Step three includes the following steps: Based on the variable state dimension system model of formula (7), the robust optimization control problem is described as the minimization problem of the performance upper bound in the worst case: The expected cumulative cost of the object to be optimized in the infinite time domain is: Among them, l(k+i|k) is the stage cost: in, is a positive state and control input weight matrix, is a positive scalar describing the emphasis on robustness.

5. The efficient optimization control method for a variable-mode moving body with a state dimension change according to claim 4 is characterized in that: Step 4 includes the following steps: The modal dependent Lyapunov function is: in, It is the state component of the slow dynamic part of the subsystem introduced above; If the quadratic function satisfies the following conditions: Then the following formula holds: get: The existence condition of the performance upper bound is further transformed into the form of linear inequality: in, Performance optimization is achieved by minimizing the upper bound of the cost corresponding to V(k|k).

6. The method for efficient optimization control of a variable-mode moving body with state dimension change according to claim 5, characterized in that: Step five includes the following steps: structure The modal dependence ellipsoid set, the elements in the set satisfy: if the state Under the action of the controller and subsystem corresponding to the collective mode r, the state at the next moment still satisfies structure The modal dependence of the quadratic function, ε r represents the corresponding modal-dependent level set, and its positive invariance condition is directly expressed as Considering the influence of bounded interference input, substituting into the system model of formula (7), the above positive invariance condition is further expressed as: Applying the S process to the above equation, we get the following linear inequality: in, M Tran ={(r,r′)∈M×M:π r，r′ >0} The invariant set also satisfies the initial boundedness condition: This is equivalent to a linear inequality: Introduce the boundary constraint judgment conditions of the ellipsoid set: Combine formulas (13)-(16) to solve W that satisfies all inequality conditions simultaneously r , ensure that the constraints are met in infinite time domain The robust positive invariant set ε r .

7. The method for efficient optimization control of a variable-mode moving body with state dimension change according to claim 6, characterized in that: Step six includes the following steps: Based on the inequality conditions obtained in steps 4 and 5, the following convex optimization problem for solving the variable-dimensional control law is established: in, represents the matrix variables in the optimization problem; the introduced matrix inequality condition is equivalent to Given a representative state point x in the state space set，i，j , respectively solve the semi-positive programming problem to obtain The process includes the following: ①Set performance weight parameters x max and u max ; ② Given a set of initial conditions (x0, u0), solve the semi-positive definite programming problem to obtain a set of feasible regions ε0; ③ Select a set of state points {x set，1，j :j∈M}; ④ Then select N-1 groups of state points {x set，i，j :j∈M}; ⑤ For all selected initial conditions (x0, u0), solve the semi-positive definite programming problem and store 8. The efficient optimization control method for a variable-mode moving body with a state dimension change according to claim 7, characterized in that: Step seven includes the following steps: To solve the As a basis, the reconstructed approximate solution space is obtained by its convex combination: Among them, v i，j It is a basic solution The combination coefficient of The online optimization problem is of the form: in, and represents the controller parameters obtained by linear combination of basis matrices. When the system is running, the above optimization problem is solved and the control input is calculated based on real-time state feedback at each sampling time. The calculation process includes: ① Obtain system feedback information x(k) and σ(k) and calculate the transformed slow dynamic component ②Solve the optimization problem and obtain the linear combination coefficients ③Calculate the combined control parameters and feedback gain ④ Apply control signal to the controlled object ⑤ Update the sampling time k = k + 1 and return to the process step ① rolling iterative calculation.

9. An efficient optimization control system for a variable-mode moving body with varying state dimension, characterized in that: The system has a program module corresponding to the steps of the method described in any one of claims 1 to 8, and executes the steps of the state dimension change variable mode motion body efficient optimization control method during operation.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, and the computer program is configured to implement the steps of the state dimension change and variable mode motion body efficient optimization control method according to any one of claims 1 to 9 when called by a processor.

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