A robust control method and system for an air-ground dual-purpose platform-manipulator composite robot

Abstract

The present invention provides a robust control method and system for an air-ground dual-purpose platform-robotic arm composite robot, belonging to the field of switching system control. The method aims to solve the problem that when designing a switching controller for a switching generalized system, the modal dependence characteristics of the norm-bounded nonlinear terms in the system are not considered in advance, resulting in the obtained robust controller being unable to meet the system stability and interference suppression performance requirements. The method includes constructing a multi-modal dynamic equation of the air-ground dual-purpose platform-robotic arm composite robot, establishing a state space expression of the air-ground dual-purpose platform-robotic arm composite robot, designing a feedback controller that can stabilize the air-ground dual-purpose platform-robotic arm composite robot switching system, selecting appropriate system performance indicators, and designing a robust controller for the air-ground dual-purpose platform-robotic arm composite robot. The method enables the air-ground dual-purpose platform-robotic arm composite robot to maintain stability and robustness in both air and ground modes, reduces design conservatism, and has a wide range of applications.

Description

Technical Field

[0001] The present invention relates to the technical field of switching system control, and in particular to a robust control method and system for an air-ground dual-purpose platform-mechanical arm composite robot. Background Art

[0002] Arm-carrying drones, typically consisting of a multirotor aircraft and a robotic arm, excel at maneuvering and transporting objects in inaccessible locations, attracting widespread attention from industry and researchers. However, when operating close to the ground, the collision risk of arm-carrying drones is significantly increased compared to ground-based robots. To address this, hybrid air-ground platform-robotic arm robots capable of both aerial and ground mobility have been proposed in recent years. However, existing research on the motion control of such robots often employs separate designs for aerial and ground controllers, ignoring the inevitable switching between motion modes, resulting in degraded system performance and even instability.

[0003] A generalized system is a system that contains implicit state variables in its state-space model. It is often used to describe dynamic systems with constraints or that rely on certain algebraic equations. It can effectively cover both the aerial and terrestrial motion modes of an air-ground dual-purpose platform-manipulator hybrid robot. Due to their unique structural characteristics, generalized systems face significant challenges in analysis and control design. Within the framework of switching systems, the main challenge in controlling generalized switching systems lies in designing switching rules and control strategies to ensure good dynamic performance and stability during and after switching. Existing research rarely considers the modal dependence of norm-bounded nonlinear terms in the system, resulting in high conservatism and design difficulties when dealing with such complex systems. Therefore, the study of control methods for switching generalized systems with mode-dependent norm-bounded nonlinear terms has important theoretical significance and practical application value.

[0004] Therefore, the present invention will take the air-ground dual-purpose platform-manipulator composite robot, a typical switching generalized system containing modally dependent norm-bounded nonlinear terms, as the research object, and propose a robust control method that takes into account both steady-state performance and transient performance. It solves the problem that some existing switching generalized systems do not consider the modal dependence characteristics of the norm-bounded nonlinear terms in the system in advance when designing the switching controller, resulting in the obtained robust controller being unable to meet the system stability and interference suppression performance requirements. Summary of the Invention

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

[0006] In order to solve the problem that the modal dependence characteristics of the norm-bounded nonlinear terms in the system are not considered in advance when designing the switching controller of the existing switched generalized system, resulting in the obtained robust controller being unable to meet the requirements of system stability and disturbance suppression performance.

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

[0008] The present invention provides a robust control method for an air-ground dual-purpose platform-manipulator composite robot, comprising the following steps:

[0009] S100, for the air-ground dual-purpose platform - the robot arm is in accordance with the robot to establish a right-hand coordinate system {I: I -x I ,y I ,z I}、Body coordinate system {B:O B -x B ,y B ,z B} and the manipulator coordinate system of the i-th link on the manipulator {D i :O i -x i ,y i ,z i Then, the aerial dynamic equations and ground dynamic equations of the air-ground dual-purpose platform-manipulator composite robot are established;

[0010] S200, based on the dynamic equations obtained in step S100, establish a state space expression for the air-ground dual-purpose platform-manipulator composite robot, design a position controller and a posture controller, and establish a generalized switching control system;

[0011] S300, establishing a feedback controller capable of stabilizing the air-ground dual-purpose platform-manipulator composite robot switching system, including setting a triangular nonlinear coupling term of the air-ground dual-purpose platform-manipulator composite robot to be subject to a bounded boundary constraint of a modular correlation norm, and determining the exponential stability of the closed-loop system;

[0012] S400, establish a robust controller for the air-ground dual-purpose platform-manipulator composite robot, so that the system has H ∞ and H2 performance.

[0013] Furthermore, in step S100, it includes:

[0014] S110, establish a right-handed coordinate system {I:O I -x I ,y I ,z I}、Body coordinate system {B:O B -x B ,y B ,z B} and the manipulator coordinate system of the i-th link on the manipulator {D i :O i -x i ,yi ,z i};

[0015] S120. Establish the aerial dynamics equations of the air-ground dual-purpose platform-manipulator composite robot:

[0016]

[0017] Where m is the total mass of the air-ground dual-purpose platform-manipulator composite robot; ω = [p, q, r] T , T, τ, and J represent the angular velocity of the body in the body coordinate system B, the torque generated by the rotor, the disturbance torque generated by the manipulator, and the moment of inertia, respectively; S = S(Φ) is the transformation matrix that converts the angular velocity into the Euler angular velocity; g = [0, 0, g] T 、 and f represent the gravitational acceleration, linear velocity, force generated by the rotor, and disturbance force generated by the manipulator, respectively, expressed in the inertial coordinate system I. z =[0,0,1] T and is the rotation matrix from the body coordinate system B to the inertial coordinate system I; variable ξ=[x,y,z] T and They represent the position and roll-pitch-yaw angles of the body coordinate system B relative to the inertial coordinate system I respectively; p, q, and r are the three components of the angular velocity;

[0018] S130. Establish the ground dynamics equation of the air-ground dual-purpose platform-manipulator composite robot. The following dynamics equation is valid when i = {1, 2} and j = {2, 3}:

[0019]

[0020] Among them, f r and τ r They are rolling resistance and resistance torque:

[0021]

[0022] Wherein, L represents the half width of the passive wheel; μ represents the friction coefficient;

[0023] S140. Nonholonomic constraints for the air-ground dual-purpose platform-manipulator composite robot in ground mode with continuous contact with the ground:

[0024]

[0025] The values ​​of the disturbance force f and the disturbance torque τ caused by the manipulator in formula (1) and formula (2) are calculated based on the spatial relationship of the connecting rod using the iterative Newton-Euler dynamics formula, for i = 0, 1, 2, 3, 4:

[0026]

[0027] in, It is from D i to D i+1 The rotation matrix of Indicates O i+1 Relative to D i The position of θ i and m i denote the joint angle and mass of the i-th link respectively; ω i 、v i 、F i 、T i 、 and J i In D i In the coordinate system, the angular velocity of the i-th connecting rod, the velocity of the origin, the force and torque acting on the center of mass, the position of the center of mass, the velocity of the center of mass, and the moment of inertia of the i-th connecting rod are represented respectively;

[0028] After the forward iteration, for i=4,3,2,1,0, reverse iteration is performed using formula (6):

[0029]

[0030] Among them, f i and τ i are the force and torque exerted by link i-1 on link i; for a light grasping target, f5 and τ5 are approximately The estimated force acting on the base link is obtained by iterative calculation and torque in, and denote the estimation errors of the base disturbance force and moment, respectively.

[0031] Furthermore, in step S200, it includes:

[0032] S210: Establish a position controller according to the dynamic equation obtained in step S100, including:

[0033] S211. Combining formula (1) and formula (2), the translational dynamics and rotational dynamics of the air-ground dual-purpose platform-manipulator composite robot are expressed as Mutual coupling; introduction of pseudo control vector A continuously differentiable pattern vector function h1:R4 →R 3 :

[0034]

[0035] in, is the expected Euler angle value; E 1σ and f rσ are the modally dependent generalized matrix and friction force, E 1σ and f rσ The value of depends on the switching signal σ∈{1,2}: In the air subsystem (σ=1), E 11 =I3 and f r1 =0 3×1 ; In the ground subsystem (σ=2), E 12 =diag{1,1,0} and f r2 =f r ;

[0036] Combining formula (7) with formula (1) and formula (2), the position controller of the air-ground dual-purpose platform-manipulator composite robot is linearized as:

[0037]

[0038] S212. For the aerial subsystem, the desired yaw angle ψ d Set to ψ obtained from the upper-level motion planner * value, simplify h1 to

[0039]

[0040] Among them, c * and s * Represent the cosine and sine values ​​respectively;

[0041] Its Jacobian determinant is:

[0042]

[0043] According to the inverse function theorem, except Outside the nearby points, h 11 is locally reversible; for any pseudo control vector v1, by the inverse function Derive the corresponding F, and for:

[0044]

[0045] S213. For the ground subsystem, the roll angle is fixed to ψd ≠ψ * , F = λmg, where λ∈R is a variable;

[0046] ψ d and The values ​​are:

[0047]

[0048] S220, design the attitude controller and introduce the pseudo control vector v2∈R of the attitude controller 3 And the corresponding modal correlation vector function h2:

[0049]

[0050] Among them, in the air subsystem (σ=1), E 21 =I3 and τ r1 =0 3×1 ; In the ground subsystem (σ=2), E 22 =diag{0,1,1} and τ r2 =τ r ;

[0051] According to formula (13), formula (1) and formula (2), the air-ground attitude controller is linearized as:

[0052]

[0053] The T values ​​in the air subsystem and the ground subsystem are obtained by inversely solving formula (15):

[0054]

[0055] S230, define the status separately enter and disturbances for:

[0056]

[0057] in, variable ξ d =ξ * Given by the upper-level motion planner; Φ d Given by the inverse solver formula (11) and formula (12);

[0058] The air-ground dual-purpose platform-manipulator composite robot is represented as a switching generalized control system:

[0059]

[0060] Among them, σ(t) takes the value of M = {1, 2} and controls the switching of the control system; and They are respectively ∞ and the output controlled by the H2 controller; represents a nonlinear term with modal dependence and norm-bounded properties;

[0061] For the ground subsystem, the upper-level planner ensures that According to formula (4), Combining the position controller and the attitude controller, the state space matrix of the system is expressed as:

[0062]

[0063] Among them, k f and k t All are constant coefficients;

[0064] By finding a suitable auxiliary matrix P i and Q i , perform generalized matrix transformation on the system, and the transformed matrix is The system state after transformation is

[0065]

[0066] Furthermore, in step S300, it includes: limiting the boundedness and mode of the nonlinear terms in the system according to Theorem 1 and Theorem 2,

[0067] S310, Theorem 1, for Existence matrix Ξ i , so that the triangular nonlinear coupling term ∈ of the air-ground dual-purpose platform-manipulator composite robot is bounded by the module-related norm Constraints, where:

[0068]

[0069] Among them, c i is the modal-related coefficient, which takes different values ​​in airborne and ground modes;

[0070] S320, Theorem 2, Consider a switched generalized system with bounded nonlinear modal dependence norm, given a scalar and If there exists a positive definite matrix X under the condition Δ(t)≡0 i , matrix W i and scalars Make The following conditions hold:

[0071]

[0072] in,

[0073]

[0074] Then when Δ(t)≡0, Under the ADT switching signal, the system is globally consistent exponentially stable; where the mode-dependent state feedback controller is u=K i x,

[0075] Furthermore, in step S400, it is included to determine whether the system has H by Theorem 3. ∞ and H2 performance,

[0076] Theorem 3. Consider a switched generalized system with modally dependent norm-bounded nonlinearity. Given a scalar and If there exists a positive definite matrix X i , matrix W i , and scalar Make The following conditions hold:

[0077]

[0078] in,

[0079]

[0080] in, is defined by the following initial set of system states:

[0081]

[0082] The system satisfies Under the ADT switching signal, the system is globally consistent exponentially stable and has a guaranteed α-weighted H ∞ Performance γ and guaranteed H2 performance ρ, and the state feedback controller is u=K i x, where

[0083] The present invention provides a robust control system for an air-ground dual-purpose platform-mechanical arm composite robot. The system has a program module corresponding to the above steps and executes the steps in the above robust control method for an air-ground dual-purpose platform-mechanical arm composite robot during operation.

[0084] The present invention provides a computer-readable storage medium storing a computer program. The computer program is configured to implement steps of a robust control method for an air-ground dual-purpose platform-manipulator composite robot when called by a processor.

[0085] Compared with the prior art, the present invention has the following beneficial effects:

[0086] Improving system stability - By introducing a switching generalized system model containing norm-bounded nonlinear terms, this invention can more comprehensively and accurately describe the complex dynamics of the air-ground dual-purpose platform-manipulator composite robot in the air-ground mode. This allows the controller design to fully consider the system's stabilization methods in various sub-modes, thereby solving the system instability problem caused by ignoring these factors in traditional methods.

[0087] Enhanced robustness - Aiming at the external disturbance caused by the uncertainty of the mass of the object grasped by the air-ground dual-purpose platform-manipulator composite robot, the present invention adopts a hybrid H2-H ∞ The control method is to optimize the H2 performance index that measures the transient performance of the system and the H performance index that measures the disturbance suppression ability of the system. ∞ performance indicators, realized the robust control of the composite robot, effectively suppressed the impact of external interference on system performance, and enhanced the robustness and reliability of the system.

[0088] Reduced design conservatism – Traditional controller design methods model the norm-bounded nonlinear terms of switching generalized systems as being independent of the system's mode. This requires a high degree of conservatism to ensure stability, leading to performance degradation. This present invention reduces conservatism in the design process by modeling the norm-bounded nonlinear terms as modally dependent and deriving numerically testable criteria for the responses to verify controller stability and performance. These criteria make controller design more precise and efficient, avoiding performance degradation of the air-ground dual-purpose platform-manipulator hybrid robot.

[0089] Wide Range of Applications – While this invention primarily addresses the control of dual-use air-ground platform-manipulator hybrid robots, the proposed control method and theoretical framework are equally applicable to other generalized switching systems, including various multimodal robots. Therefore, this invention can provide a reference and inspiration for the control of such systems, demonstrating high application value and potential for widespread adoption. BRIEF DESCRIPTION OF THE DRAWINGS

[0090] Figure 1 Flowchart of a robust control method for an air-ground dual-purpose platform-manipulator composite robot according to an embodiment of the present invention;

[0091] Figure 2 Schematic diagram of air-ground mode switching of the air-ground dual-purpose platform-manipulator arm composite robot in an embodiment of the present invention;

[0092] Figure 3Schematic diagram of the reference coordinate system of the air-ground dual-purpose platform-manipulator composite robot in an embodiment of the present invention, wherein { I -x I ,y I ,z I} represents the right-handed inertial coordinate system, with the origin O I is any point in the world coordinate system; B -x B ,y B ,z B} represents the body coordinate system of the air-ground dual-purpose platform-manipulator composite robot, and the origin O of the body coordinate system B is B Coincident with the geometric center of the air-ground dual-purpose platform-manipulator composite robot; {D i :O i -x i ,y i ,z i} represents the manipulator coordinate system of the i-th link of the manipulator, i = 0, 1, 2, 3, 4, 5 represents the link number of the manipulator; variable ξ = [x, y, z] T ∈R 3 and They represent the position and roll-pitch-yaw angles of the body coordinate system B relative to the inertial coordinate system I respectively;

[0093] Figure 4 For the mixed H2-H in the embodiment of the present invention ∞ Schematic diagram comparing the transient performance of the robust controller and the traditional controller without H2 performance optimization in tracking a given trajectory, where Theorem 3 is the hybrid H2-H ∞ Robust controller, Corollary 3 is a traditional controller without H2 performance optimization, and reference is to track a given trajectory;

[0094] Figure 5 The mixed H2-H considering the norm-bounded nonlinear term in the embodiment of the present invention ∞ Schematic diagram comparing the control effects of the robust controller and the traditional controller that does not consider the modal dependence characteristics, where: Figure 5 The figure above is the control effect diagram of the robust controller considering the modal dependence characteristics of the norm-bounded nonlinear term. Figure 5 The figure below shows the control effect of a traditional controller that does not consider the modal dependence characteristics. The colors represent the maximum expected rotor speed under different parameter combinations. With physical cap The blue color indicates feasible rotor speed and the red color indicates infeasible rotor speed. The darker the color, the higher the degree of feasibility / infeasibility. DETAILED DESCRIPTION

[0095] In the description of the present invention, it should be noted that the terms "first," "second," and "third" mentioned in the embodiments of the present invention are used for descriptive purposes only and are not to be understood as indicating or implying relative importance or implicitly specifying the number of the technical features indicated. Therefore, a feature specified as "first," "second," or "third" may explicitly or implicitly include one or more of such features.

[0096] 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.

[0097] Specific implementation plan 1: Combined Figures 1 to 5 As shown, the present invention provides a robust control method for an air-ground dual-purpose platform-manipulator composite robot, comprising the following steps:

[0098] S100, for the air-ground dual-purpose platform - the robot arm is in accordance with the robot to establish a right-hand coordinate system {I: I -x I ,y I ,z I}、Body coordinate system {B:O B -x B ,y B ,z B} and the body coordinate system of the i-th link on the robot arm {D i :O i -x i ,y i ,z i}, then establish the multimodal dynamic equations of the air-ground dual-purpose platform-manipulator composite robot, including the air dynamic equations and the ground dynamic equations, including:

[0099] S110, combined Figure 1 The air-ground dual-purpose platform-manipulator composite robot Chat-PM of the configuration shown is established as follows Figure 2 The reference coordinate system shown; let {I:O I -x I ,y I ,z I} represents the right-handed inertial coordinate system, {B:O B -x B ,y B ,z B} represents the body coordinate system of the air-ground dual-purpose platform-manipulator composite robot, where the geometric center of the air-ground dual-purpose platform-manipulator composite robot is B overlap; {D i :O i -x i ,y i,z i} represents the manipulator coordinate system of the i-th link of the manipulator, where the subscript i = 0, 1, 2, 3, 4, 5 represents the link number of the manipulator. The number of link numbers is not necessarily five and needs to be determined according to the robot model; the variable ξ = [x, y, z] T and They represent the position and roll-pitch-yaw angles of the body coordinate system B relative to the inertial coordinate system I (obtained by rotating in the order of Z-Y-X axis of the world coordinate system);

[0100] S120. Establish the aerial dynamics equations of the air-ground dual-purpose platform-manipulator composite robot:

[0101]

[0102] Where m is the total mass of the air-ground dual-purpose platform-manipulator composite robot; ω = [p, q, r] T , T, τ, and J represent the angular velocity, torque generated by the rotor, disturbance torque generated by the manipulator, and moment of inertia of the air-ground dual-purpose platform-manipulator composite robot expressed in the collective coordinate system B, respectively. Here, p, q, and r are the three components of the angular velocity; S = S(Φ) is the transformation matrix that converts the angular velocity into the Euler angular velocity; g = [0, 0, g] T 、 and f represent the gravitational acceleration, linear velocity, force generated by the rotor, and disturbance force generated by the manipulator expressed in the inertial coordinate system I, respectively. z =[0,0,1] T and are all rotation matrices from the collective coordinate system B to the inertial coordinate system I;

[0103] S130. Establish the ground dynamics equation of the air-ground dual-purpose platform-manipulator composite robot. The following dynamics equation is valid when i = {1, 2} and j = {2, 3}:

[0104]

[0105] Among them, f r and τ r They are rolling resistance and resistance torque:

[0106]

[0107] Wherein, L represents the half width of the passive wheel; μ represents the friction coefficient;

[0108] S140. Due to the continuous contact with the ground, the following nonholonomic constraints of the air-ground dual-purpose platform-manipulator hybrid robot in ground mode are considered:

[0109]

[0110] The values ​​of the disturbance force f and the disturbance torque τ caused by the manipulator in formulas (1) and (2) are calculated based on the spatial relationship of the connecting rods using the iterative Newton–Euler dynamics formula, for i = 0, 1, 2, 3, 4:

[0111]

[0112] in, From the robot coordinate system D i To the robot arm coordinate system D i+1 The rotation matrix of Indicates O i+1 Relative to D i The position of θ i and m i denote the joint angle and mass of the i-th link respectively; ω i 、v i 、F i 、T i 、 and J i In the robot arm coordinate system D i where represent the angular velocity, origin velocity, force and torque acting on the center of mass, position of the center of mass, velocity of the center of mass, and moment of inertia of the i-th connecting rod respectively;

[0113] It should be noted that, in addition to the setting for considering the movement of the connection point and the effect of gravity, In addition, all quantities in the forward recursion are initialized to zero;

[0114] After the forward iteration, for i=4,3,2,1,0, the reverse iteration is performed using the following equation:

[0115]

[0116] Among them, f i and τ i are the force and torque applied by link i-1 on link i, respectively. It should be noted that f5 and τ5 represent the force and torque applied by the end effector on the environment, respectively, and their values ​​are difficult to obtain without prior information about the grasping target. For a grasping target with a lighter mass, f5 and τ5 are approximated as With this approximation, the estimated forces acting on the base link can be obtained by iterative calculation and torque in, and denote the estimation errors of the base disturbance force and moment, respectively;

[0117] S200: Based on the dynamic equations obtained in step S100, establish a state space expression for the air-ground dual-purpose platform-manipulator composite robot, specifically including:

[0118] S210, based on the dynamic equation obtained in step S100, first design a position controller, including:

[0119] S211. As shown in formula (1) and formula (2), the translational dynamics and rotational dynamics of the air-ground dual-purpose platform-manipulator composite robot are expressed by Mutual coupling; in order to reduce the impact of nonlinear and coupling effects on the position controller, a pseudo control vector is introduced A continuously differentiable pattern vector function h1:R 4 →R 3 , which is defined as follows:

[0120]

[0121] in, is the expected Euler angle value; E 1σ and f rσ are the modally dependent generalized matrix and friction force, E 1σ and f rσ The values ​​of E and E are dependent on the switching signal σ∈{1,2}: In the air subsystem (σ=1), E 11 =I3 and f r1 =0 3×1 ; In the ground subsystem (σ=2), E 12 =diag{1,1,0} and f r2 =f r ;

[0122] Combining formula (7) with formula (1) and formula (2), the position controller of the air-ground dual-purpose platform-manipulator composite robot is linearized as:

[0123]

[0124] S212. For the aerial subsystem, the desired yaw angle ψ d Set to ψ obtained from the upper-level motion planner * value, in this case h1 simplifies to

[0125]

[0126] Among them, c * and s * Represent the cosine and sine values ​​respectively;

[0127] Its Jacobian determinant is:

[0128]

[0129] According to the inverse function theorem, except Nearby points, h 11 is locally invertible; therefore, for any pseudo control vector v1, it can be obtained by the inverse function Derive the corresponding F, and Its algebraic expression is:

[0130]

[0131] S213. For the ground subsystem, the roll angle is fixed to ψ d is no longer set equal to ψ * , to avoid numerical instability and overflow when deriving actual input; ψ d is selected as one of the variables of the inverse solution, and the value of F is fixed to F = λmg, where λ∈R is a variable; in this case, ψ d and The values ​​are:

[0132]

[0133] S220, design a posture controller, similar to the position controller, and introduce a pseudo control vector v2∈R of the posture controller 3 And the corresponding modal correlation vector function h2, which is defined as follows:

[0134]

[0135] Among them, in the air subsystem (σ=1), E 21 =I3 and τ r1 =0 3×1 ; In the ground subsystem (σ=2), E 22＝ diag{0,1,1} and τ r2 =τ r ;

[0136] According to (13), (1) and (2), the air-ground attitude controller is linearized as:

[0137]

[0138] The T values ​​in the air and ground subsystems can be obtained by the following inverse solutions:

[0139]

[0140] S230 is based on all content, by defining the status separately enter and disturbances for:

[0141]

[0142] in, variable ξ d =ξ * Given by the upper-level motion planner; Φ d Given by the inverse solver formula (11) and formula (12);

[0143] The air-ground dual-purpose platform-manipulator composite robot can be represented as the following switching generalized control system:

[0144]

[0145] Among them, σ(t) takes the value of M = {1, 2} and controls the switching of the control system; and They are respectively ∞ and the output controlled by the H2 controller; represents a nonlinear term with modal dependence and norm-bounded properties;

[0146] For the ground subsystem, the upper-level planner ensures that According to formula (4), we can deduce Combining the position controller and the attitude controller, the state space matrix of the system can be expressed as:

[0147]

[0148] Among them, k f and k t All are constant coefficients;

[0149] By finding a suitable auxiliary matrix P i and Q i , this system can be transformed into a generalized matrix, and the transformed matrix is The system state after transformation is

[0150]

[0151] S300: Design a feedback controller that can stabilize the air-ground dual-purpose platform-manipulator composite robot switching system, specifically including:

[0152] According to step S100 and step S200, a state feedback controller is designed to stabilize the generalized switching system. To execute the subsequent steps, the boundedness and modal correlation characteristics of the nonlinear terms in the system are first explained according to Theorem 1 and Theorem 2:

[0153] S310, Theorem 1: For There exists a matrix Ξ i , so that the triangular nonlinear coupling term ∈ of the air-ground dual-purpose platform-manipulator composite robot is bounded by the module-related norm Constraints, where:

[0154]

[0155] Among them, c i is the modal-related coefficient, which takes different values ​​in airborne and ground modes;

[0156] Proof: Define ξ=ξ(Φ,Φ d )=[ζ x ,ζ y ,ζ z ] T =(R B，d -R B )i z , since Φ=Φ d +e Φ , for each Euler angle

[0157] By utilizing the following trigonometric identities:

[0158]

[0159] in,

[0160]

[0161] In the air subsystem, the first component ζ x is transformed into:

[0162]

[0163] Among them, c * and s * Represent the cosine and sine values ​​respectively;

[0164] Since |sin(Φ i )|,|cos(Φ i )|≤1, so For all have:

[0165]

[0166] By means of the inequality |sin(a)|<|a|, and For any |a|,|b|,|c|≤1, we have:

[0167]

[0168] By a similar method, the boundary conditions of the other two components of ζ in the air subsystem are and Therefore, in the air subsystem, ζ satisfies the following constraints:

[0169]

[0170] For the ground subsystem, due to the nonholonomic constraints , we can use the same method as above to calculate ζ to satisfy the following constraints:

[0171]

[0172] Based on the above information, the modal dependence constraint relationship of the nonlinear term ε can be derived as follows:

[0173]

[0174] Among them, c1=15.90, c2=4.25; is the upper bound of F in subsystem i, and the proof of Theorem 1 ends here;

[0175] The exponential stability of the closed-loop system is determined by Theorem 2;

[0176] S320, Theorem 2: Consider a switched generalized system with bounded nonlinearity of modal correlation norm; given a scalar and If there exists a positive definite matrix X under the condition Δ(t)≡0 i , matrix W i and scalars Make The following conditions hold:

[0177]

[0178] in,

[0179]

[0180] Then when Δ(t)≡0, Under the ADT switching signal, the system is globally consistent exponentially stable; where the mode-dependent state feedback controller is u=K i x,

[0181] Proof: Consider the Lyapunov candidate function V(t,σ(t)), which has the form:

[0182]

[0183] in,

[0184]

[0185] and is positive definite, then the derivative of V(t) is:

[0186]

[0187] in,

[0188] Based on Theorem 1, the nonlinear terms in the system are eliminated by the following inequality:

[0189]

[0190] Then we can get:

[0191]

[0192] in,

[0193] Then, by taking the Schur complement and substituting and You can get:

[0194]

[0195] By multiplying the above formula by M 1i , when Δ(t)≡0, we can get:

[0196]

[0197] At the switching time t k , the equivalent system from arrive The state jump can be achieved by mapping To describe, that is:

[0198]

[0199] By taking Schur's complement, we can deduce that All switching times t k , the following inequality holds:

[0200]

[0201] Therefore, it can be concluded that:

[0202]

[0203] Assume t k+1It is t k At the next switching moment, Integrating up to t gives:

[0204]

[0205] in,

[0206] Then, by recursively using formula (38) and formula (39), we can get:

[0207]

[0208] Therefore, it can be clearly seen that if Then, when Δ≡0, the system is globally asymptotically stable, thus completing the proof of Theorem 2;

[0209] S400. Select appropriate system performance indicators and design a robust controller for the air-ground dual-purpose platform-manipulator hybrid robot, specifically including:

[0210] Give the guarantee that the system has a given H ∞ The criteria for H2 performance are as follows:

[0211] Theorem 3: Consider a switched generalized system with modally dependent norm-bounded nonlinearity, given a scalar

[0212] and If there exists a positive definite matrix X i , matrix W i , and scalar Make The following conditions hold:

[0213]

[0214] in,

[0215]

[0216] in, is defined by the following initial set of system states:

[0217]

[0218] The system satisfies Under the ADT switching signal, the system is globally consistent exponentially stable and has a guaranteed α-weighted H ∞ Performance γ and guaranteed H2 performance ρ, and the state feedback controller is u=K i x, where

[0219] Proof: For the system H ∞ Performance, considering the function Σ i (t), which has the form:

[0220]

[0221] By taking the Schur complement of Equation 2 in Equation (42), and then substituting and You can get:

[0222]

[0223] in,

[0224] for from Integrating the above formula up to t, we get:

[0225]

[0226] Through iterative calculation, we can get:

[0227]

[0228] Under zero initial conditions, the above formula becomes:

[0229]

[0230] Multiply the above formula by It is known that When 0≤N(t0,s)lnβ≤αs, then:

[0231]

[0232] Then, integrating the above equation from t0 to t0, we get:

[0233]

[0234] Take t0 = 0, and we can know that the system has α-weighted H ∞ performance γ;

[0235] For the H2 performance of the system, according to the Schur complement, it can be deduced from Equation (42) (3) Then when Δ=0, we have:

[0236]

[0237] Integrating the above inequality in [0,∞) and combining V(∞)=0, we can obtain:

[0238]

[0239] Then, by rewriting the initial state set into the following equivalent form:

[0240]

[0241] in, It can be deduced from formula (53) and formula (54):

[0242]

[0243] According to Schur's complement, Equation 4 in Equation (42) is equivalent to

[0244] therefore This means that the system has H2 performance ρ, and the proof of Theorem 3 is complete.

[0245] Specific embodiment 2: The present invention provides a robust control system for an air-ground dual-purpose platform-robotic arm composite robot. The system has a program module corresponding to the above steps, and executes the steps in the above-mentioned robust control method for an air-ground dual-purpose platform-robotic arm composite robot during operation.

[0246] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0247] Specific embodiment three: The present invention provides a computer-readable storage medium, which stores a computer program. The computer program is configured to implement the steps of a robust control method for an air-ground dual-purpose platform-manipulator composite robot when called by a processor.

[0248] The other combinations and connection relationships of this embodiment are the same as those of the first embodiment.

[0249] Example 1

[0250] The transient performance test verifies that the hybrid H2-H ∞ Compared with traditional H ∞ The task of setting up the air-ground dual-purpose platform-manipulator composite robot is to carry a load of 30g and guide the air-ground platform and the manipulator to move along a pre-specified reference trajectory with an initial position error of e ξ =[-0.8,0.5,0.7] T , the yaw error is e ψ =-0.6. By applying the results from Theorem 3 and the traditional H ∞ The two types of controllers obtained in the method are respectively obtained, and the state response of the system is as follows Figure 4As shown in Figure 3, it is clear that the controller derived from Theorem 3 exhibits better stability performance, characterized by faster convergence speed, less oscillation and smaller overshoot.

[0251] Example 2

[0252] Assume that at a certain moment, the actual posture of the air-ground dual-purpose platform-manipulator composite robot in the ground subsystem deviates from the expected posture, and the error is e Φ =[e φ =0,e θ ,e ψ ] T , and in different tests Φ The state feedback gain matrix of the air-ground dual-purpose platform-manipulator composite robot is obtained by modeling the system as a norm-bounded nonlinear term with modal dependence and a traditional modal-independent method, where the parameter β is taken between 1.5 and 5.0 to test different average dwell times. For each e θ 、e ψ and β, the maximum desired rotor speed is derived With physical cap The ratio of Figure 5 As shown, it can be concluded that the proposed method considering the mode-dependent norm bounded nonlinearity is less conservative than the mode-independent method, which helps to control the gain within a reasonable range.

[0253] 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 robust control method for an air-ground dual-purpose platform-manipulator composite robot, characterized in that: The following steps are involved: S100, establish a right-hand coordinate system {I:O I -x I ,y I ,z I }、Body coordinate system {B:O B -x B ,y B ,z B } and the manipulator coordinate system of the i-th link on the manipulator {D i :O i -x i ,y i ,z i Then, the aerial dynamic equations and the ground dynamic equations of the air-ground dual-purpose platform-manipulator composite robot are established; S200, based on the dynamic equations obtained in step S100, establish a state space expression for the air-ground dual-purpose platform-manipulator composite robot, design a position controller and a posture controller, and establish a generalized switching control system; S300, establishing a feedback controller capable of stabilizing the air-ground dual-purpose platform-manipulator composite robot switching system, including setting a triangular nonlinear coupling term of the air-ground dual-purpose platform-manipulator composite robot to be subject to a bounded boundary constraint of a modular correlation norm, and determining the exponential stability of the closed-loop system; S400, establish a robust controller for the air-ground dual-purpose platform-manipulator composite robot, so that the system has H ∞ and H2 performance.

2. The robust control method of the air-ground dual-purpose platform-manipulator composite robot according to claim 1 is characterized in that: In step S100, it includes: S110, establish a right-handed coordinate system {I:O I -x I ,y I ,z I }、Body coordinate system {B:O B -x B ,y B ,z B } and the manipulator coordinate system of the i-th link on the manipulator {D i :O i -x i ,y i ,z i }; S120. Establish the aerial dynamics equations of the air-ground dual-purpose platform-manipulator composite robot: Where m is the total mass of the air-ground dual-purpose platform-manipulator composite robot; ω = [p, q, r] T , T, τ, and J represent the angular velocity of the body in the body coordinate system B, the torque generated by the rotor, the disturbance torque generated by the manipulator, and the moment of inertia, respectively; S = S(Φ) is the transformation matrix that converts the angular velocity into the Euler angular velocity; g = [0, 0, g] T 、 and f represent the gravitational acceleration, linear velocity, force generated by the rotor, and disturbance force generated by the manipulator, respectively, expressed in the inertial coordinate system I. z =[0,0,1] T , is the rotation matrix from the body coordinate system B to the inertial coordinate system I; variable ξ=[x,y,z] T and They represent the position and roll-pitch-yaw angles of the body coordinate system B relative to the inertial coordinate system I respectively; p, q, r are the three components of the angular velocity; S130. Establish the ground dynamics equation of the air-ground dual-purpose platform-manipulator composite robot. The following dynamics equation is valid when i = {1, 2} and j = {2, 3}: Among them, f r and τ r They are rolling resistance and resistance torque: Wherein, L represents the half width of the passive wheel; μ represents the friction coefficient; S140. Nonholonomic constraints for the air-ground dual-purpose platform-manipulator composite robot in ground mode with continuous contact with the ground: The values ​​of the disturbance force f and the disturbance torque τ caused by the manipulator in formula (1) and formula (2) are calculated based on the spatial relationship of the connecting rod using the iterative Newton-Euler dynamics formula, for i = 0, 1, 2, 3, 4: in, It is from D i to D i+1 The rotation matrix of Indicates O i+1 Relative to D i The position of θ i and m i denote the joint angle and mass of the i-th link respectively; ω i 、v i 、F i 、T i 、 and J i In D i In the coordinate system, the angular velocity of the i-th connecting rod, the velocity of the origin, the force and torque acting on the center of mass, the position of the center of mass, the velocity of the center of mass, and the moment of inertia of the i-th connecting rod are represented respectively; After the forward iteration, for i=4,3,2,1,0, reverse iteration is performed using formula (6): Among them, f i and τ i are the force and torque exerted by link i-1 on link i; for a light grasping target, f5 and τ5 are approximately The estimated force acting on the base link is obtained by iterative calculation and torque in, and denote the estimation errors of the base disturbance force and moment, respectively.

3. The robust control method of the air-ground dual-purpose platform-manipulator composite robot according to claim 2 is characterized in that: In step S200, it includes: S210: Establish a position controller according to the dynamic equation obtained in step S100, including: S211. Combining formula (1) and formula (2), the translational dynamics and rotational dynamics of the air-ground dual-purpose platform-manipulator composite robot are expressed as Mutual coupling; introduction of pseudo control vector A continuously differentiable pattern vector function h1:R 4 →R 3 : in, is the expected Euler angle value; E 1σ and f rσ are the modally dependent generalized matrix and friction force, E 1σ and f rσ The value of depends on the switching signal σ∈{1,2}: In the air subsystem (σ=1), E 11 =I3 and f r1 =0 3×1 ; In the ground subsystem (σ=2), E 12 =diag{1,1,0} and f r2 =f r ; Combining formula (7) with formula (1) and formula (2), the position controller of the air-ground dual-purpose platform-manipulator composite robot is linearized as: S212. For the aerial subsystem, the desired yaw angle ψ d Set to ψ obtained from the upper-level motion planner * value, simplify h1 to Among them, c * and s * Represent the cosine and sine values ​​respectively; Its Jacobian determinant is: According to the inverse function theorem, except Outside the nearby points, h 11 is locally reversible; for any pseudo-control vector ν1, by the inverse function Derive the corresponding F, and for: S213. For the ground subsystem, the roll angle is fixed to ψ d ≠ψ * , F = λmg, where λ∈R is a variable; ψ d and The values ​​are: S220, design the attitude controller and introduce the pseudo control vector v2∈R of the attitude controller 3 And the corresponding modal correlation vector function h2: Among them, in the air subsystem (σ=1), E 21 =I3 and τ r1 =0 3×1 ; In the ground subsystem (σ=2), E 22 =diag{0,1,1} and τ r2 =τ r ; According to formula (13), formula (1) and formula (2), the air-ground attitude controller is linearized as: The T values ​​in the air subsystem and the ground subsystem are obtained by inversely solving formula (15): S230, define the status separately enter and disturbances for: in, variable ξ d =ξ * Given by the upper-level motion planner; Φ d Given by the inverse solver formula (11) and formula (12); The air-ground dual-purpose platform-manipulator composite robot is represented as a switching generalized control system: Among them, σ(t) takes the value of M = {1, 2} and controls the switching of the control system; and They are respectively ∞ and the output controlled by the H2 controller; represents a nonlinear term with modal dependence and norm-bounded properties; For the ground subsystem, the upper-level planner ensures that According to formula (4), Combining the position controller and the attitude controller, the state space matrix of the system is expressed as: Among them, k f and k t All are constant coefficients; By finding a suitable auxiliary matrix P i and Q i , perform generalized matrix transformation on the system, and the transformed matrix is The system state after transformation is 4. The robust control method of the air-ground dual-purpose platform-manipulator composite robot according to claim 3 is characterized in that: In step S300, it includes: limiting the boundedness and mode of the nonlinear terms in the system according to Theorem 1 and Theorem 2, S310, Theorem 1, for Existence matrix Ξ i , so that the triangular nonlinear coupling term ∈ of the air-ground dual-purpose platform-manipulator composite robot is bounded by the module-related norm Constraints, where: Among them, c i is the modal-related coefficient, which takes different values ​​in airborne and ground modes; S320, Theorem 2, Consider a switched generalized system with bounded nonlinear modal dependence norm, given a scalar and If there exists a positive definite matrix X under the condition Δ(t)≡0 i , matrix W i and scalars Make The following conditions hold: in, Then when Δ(t)≡0, Under the ADT switching signal, the system is globally consistent exponentially stable; where the mode-dependent state feedback controller is u=K i x, 5. The robust control method of the air-ground dual-purpose platform-manipulator composite robot according to claim 4 is characterized in that: In step S400, it includes: judging that the system has H by Theorem 3 ∞ and H2 performance, Theorem 3. Consider a switched generalized system with modally dependent norm-bounded nonlinearity. Given a scalar and If there exists a positive definite matrix X i , matrix W i , and scalar Make The following conditions hold: in, in, is defined by the following initial set of system states: The system satisfies Under the ADT switching signal, the system is globally consistent exponentially stable and has a guaranteed α-weighted H ∞ Performance γ and guaranteed H2 performance ρ, and the state feedback controller is u=K i x, where 6. A robust control system for an air-ground dual-purpose platform-manipulator composite robot, characterized by: The system has the steps of the robust control method of an air-ground dual-purpose platform-mechanical arm composite robot as described in any one of claims 1 to 5 above.

7. 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 robust control method of an air-ground dual-purpose platform-robotic arm composite robot according to any one of claims 1 to 5 when called by a processor.

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