Robust adaptive control method for ugv

Abstract

The application relates to a robust adaptive control method of an UGV, a dynamic model of a ground unmanned vehicle is established without considering a small-angle approximation assumption, a steering angle is taken as a state variable, controllability conditions of the UGV system are relaxed by using existence of some auxiliary matrices, and a controller is designed. In the application, the UGV is modeled without the small-angle approximation assumption, and the front wheel steering angle is taken as the state variable of the system instead of being taken as a control input signal. In order to further relax the controllability conditions of the UGV system, a robust adaptive strategy of introducing auxiliary matrices is provided. In addition, by designing an adaptive controller, asymptotic tracking of an output to a reference output is realized.

Description

Technical Field

[0001] This invention relates to the field of unmanned ground vehicle (UGV) control technology, and in particular to a robust adaptive control method for UGVs. Background Technology

[0002] In recent years, unmanned ground vehicles (UGVs) have attracted increasing attention across various fields, from industry and academia to the military. Consequently, UGVs have garnered widespread interest from researchers and scholars. However, as a nonlinear system subject to external disturbances, the design of its trajectory tracking control has become a popular and challenging research topic.

[0003] Currently, although extensive research has been conducted on trajectory tracking control of unmanned ground vehicles, including PID control, model predictive control (MPC), fuzzy modeling control, sliding mode control (SMC), and adaptive control, some unresolved issues remain in this field. For example, PID control exhibits significant limitations when handling complex and highly nonlinear systems.

[0004] Currently, robust adaptive control methods are widely used to overcome parameter uncertainties and unknown external disturbances in UGVs. While this control method is powerful, some challenges remain in establishing vehicle dynamic models and designing controllers. In most existing UGV trajectory tracking control methods, the established dynamic models are insufficient to fully describe the vehicle's motion due to the assumption of small-angle approximations. Furthermore, the front wheel steering angle is typically used as the control input signal, resulting in a non-affine vehicle dynamic model, which complicates controller design and stability analysis.

[0005] Meanwhile, for MIMO systems like UGV, since the gain matrix of the control input is usually complex, time-varying, or even unknown, it is difficult to guarantee the controllability of the system. Therefore, it is necessary to relax the controllability conditions. Summary of the Invention

[0006] The purpose of this invention is to provide a robust adaptive control method for UGVs to solve the above-mentioned problems existing in the prior art.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: a robust adaptive control method for UGVs, comprising the following steps:

[0008] The dynamic model of UGV is constructed as follows:

[0009]

[0010] The state of the dynamic model is The input vector of the dynamic model is The output vector of the dynamic model is It is a nonlinear equation, defined as y c This indicates the lateral displacement of the driverless vehicle. This represents a three-dimensional column vector, where γ1, γ2, and γ3 are all intermediate variables with no actual meaning.

[0011]

[0012]

[0013]

[0014] d(·)=[d1(·),d2(·),d3(·)] T Let d1(·), d2(·), and d3(·) represent unknown but bounded external disturbances as follows:

[0015]

[0016] g(x1,t) is the matrix that controls the input gain, represented as follows:

[0017]

[0018] The controller designed is as follows:

[0019]

[0020] Where ω>0 and σ>0 are design parameters, for η=η1||Φ||+η2||s||+η1,v(t)>0 obeys η1 and η2 are both design parameters with no practical meaning. ν(t) is a function of t. Φ is a defined function with no actual physical meaning. s represents the filtering error. This represents the adaptive parameters of the design.

[0021] Preferably, the controller must simultaneously satisfy the following:

[0022] Condition 1: The expected output y of the system d And its first derivative is known and bounded, and its second derivative is... Bounded, that is Where y l <∞ represents an unknown constant, and x1 and x2 both represent state variables;

[0023] Condition 2: There exists an unknown symmetric positive definite matrix α(x1,t) that is differentiable with respect to x1 and t, such that αg+g T α is uniformly positive definite, that is Where β>0 is an unknown constant.

[0024] Condition 3: Choose an auxiliary matrix such that Let be the identity matrix, and let α(x1,t) be the auxiliary matrix.

[0025]

[0026] in:

[0027]

[0028] a2 = 0

[0029]

[0030] a4 = J f

[0031]

[0032]

[0033] p6=2lsin(δ f (mR+2J) f sin(δ f ))(ml+I z sin(δ f ))

[0034]

[0035] Among them, a1, a2, a3, a4, a5, a6, n6 and p6 represent intermediate variables and have no practical meaning.

[0036] Compared with the prior art, the present invention has at least the following advantages:

[0037] In this invention, the UGV is modeled without making approximate assumptions about small angles, and the front wheel steering angle is treated as a state variable of the system rather than as a control input signal. To further relax the controllability conditions of the UGV system, a robust adaptive strategy incorporating an auxiliary matrix is ​​proposed. Furthermore, by designing an adaptive controller, asymptotic tracking of the output to the reference output is achieved. Attached Figure Description

[0038] Figure 1 This is a UGV vehicle model.

[0039] Figure 2 This is a diagram of tire slip angle.

[0040] Figure 3 This is a diagram of the trajectory and attitude tracking process.

[0041] Figure 4 This is a tracking error graph.

[0042] Figure 5 This is the input signal.

[0043] Figure 6 To adjust parameters Detailed Implementation

[0044] The present invention will now be described in further detail.

[0045] In this invention, the UGV is modeled without making approximate assumptions about small angles, and the front wheel steering angle is treated as a state variable of the system rather than as a control input signal. To further relax the controllability conditions of the UGV system, a robust adaptive strategy incorporating an auxiliary matrix is ​​proposed. Furthermore, by designing an adaptive controller, asymptotic tracking of the output to the reference output is achieved.

[0046] A robust adaptive control method for UGVs includes the following steps:

[0047] S1: Constructing a dynamic model of UGV:

[0048] We consider a two-wheel steering, four-wheel drive vehicle where the two front wheels can steer, and each wheel can be driven independently. We consider a vehicle with bilateral symmetry. The vehicle dynamics are represented by a four-wheel model, such as... Figure 1 As shown,

[0049] In the vehicle model, V represents the vehicle's speed. Let m be the yaw angle, m be the vehicle mass, and l be the yaw angle. f and l r These represent the distances from the front and rear axles to the center of gravity, respectively, while l represents the distance from the wheel to the longitudinal centerline of the vehicle.

[0050] To establish a more practical vehicle dynamics model, it is necessary to examine the total lateral force of the front and rear wheels, denoted by F. yf F yr Indicate. Consider as follows: Figure 2 The tire shown is a top view. θ vf It is the speed angle of the front wheel, δ f Represents the front steering angle.

[0051]

[0052] Similar to θ vf The definition, that is, the velocity angle of the rear tire, can be written as:

[0053]

[0054] From (1) and (2), we can obtain:

[0055]

[0056]

[0057] In the formula C f and C r ... x v represents the longitudinal velocity of the autonomous vehicle. y This indicates the lateral speed of the autonomous vehicle.

[0058] The longitudinal force on the front and rear wheels is represented by F. xf and F xr They can be represented by the following equations.

[0059]

[0060]

[0061] Where R represents the radius of the wheel, T wf and T wr These represent the drive torque of the front and rear wheels, respectively. and This represents an uncertain but bounded disturbance torque acting on the front and rear wheels, caused by uncertain road conditions.

[0062] Therefore, under the action of the aforementioned forces, yaw, steering, and lateral motion can be established, such as...

[0063]

[0064]

[0065]

[0066] In the above formula, where T f J represents the steering torque of the front tires. f It is the moment inertia of the front steering axle, f f k represents the coefficient of viscous friction of the front steering wheel. f This is the torque coefficient of the front steering motor, D is the width of the wheel-road contact surface, and I... z It is the vehicle's moment of inertia about its yaw axis. This refers to the external disturbances encountered when the front wheels of the autonomous vehicle are turning. f represents the external disturbances encountered by the autonomous vehicle when it turns. y (·) indicates external disturbances encountered when the autonomous vehicle moves laterally. f y(·) represents an external disturbance or torque acting on the system; it is unknown but bounded. z The value represents the moment of inertia of the autonomous vehicle's center of gravity about an axis perpendicular to the xoy plane, and l represents half the distance between the axles of the left and right wheels of the autonomous vehicle.

[0067] Formula F yf ,F yr ,F xf and F xr Substituting the expressions into equations (5a), (5b), and (5c), the dynamic model of the vehicle can be established without assuming small-angle approximations, as follows:

[0068]

[0069] The state of the dynamic model is The input vector of the dynamic model is The output vector of the dynamic model is It is a nonlinear equation, defined as y c This indicates the lateral displacement of the driverless vehicle. This represents a three-dimensional column vector, where γ1, γ2, and γ3 are intermediate variables with no actual meaning.

[0070]

[0071]

[0072]

[0073] d(·)=[d1(·),d2(·),d3(·)] T Let d1(·), d2(·), and d3(·) represent unknown but bounded external disturbances as follows:

[0074]

[0075] g(x1,t) is the matrix that controls the input gain, represented as follows:

[0076]

[0077] S2: Controller Design:

[0078] To design the control scheme, the filtering error s(t) is first defined as:

[0079]

[0080] Where λ is the positive design parameter, e(t) = y(t) - y d(t) represents the tracking error. It is the first derivative of the tracking error, and the time derivative of s(t) along the return.

[0081]

[0082] Then the controller is:

[0083]

[0084] Where ω>0 and σ>0 are design parameters, for η=η1||Φ||+η2||s||+η1,v(t)>0 obeys η1 and η2 are both design parameters with no practical meaning. v(t) is a function of t. Φ is a defined function with no actual physical meaning. s represents the filtering error. These represent the adaptive parameters designed by the designer.

[0085] Specifically, the controller must simultaneously satisfy the following:

[0086] Condition 1: The expected output y of the system d And its first derivative is known and bounded, and its second derivative is... Bounded, that is Where y l <∞ represents an unknown constant, and x1 and x2 both represent state variables;

[0087] Condition 2: There exists an unknown symmetric positive definite matrix α(x1,t) that is differentiable with respect to x1 and t, such that αg+g T α is uniformly positive definite, that is Where β>0 is an unknown constant.

[0088] Condition 3: To relax the controllability conditions of the above system, we can choose an auxiliary matrix such that... Let be the identity matrix, and let α(x1,t) be the auxiliary matrix.

[0089]

[0090] in:

[0091]

[0092] a2 = 0

[0093]

[0094] a4 = J f

[0095]

[0096]

[0097] p6=2lsin(δ f (mR+2J) f sin(δ f ))(ml+I z sin(δ f ))

[0098]

[0099] Among them, a1, a2, a3, a4, a5, a6, n6 and p6 represent intermediate variables and have no practical meaning.

[0100] 1. Stability analysis of the method of this invention:

[0101] Lemma 1: For any obeying any And for any v(t) > 0, Established.

[0102] Since ν(t)≥0, we can obtain

[0103]

[0104] Lemma 2: Considering the filtering error s(t) = λ1e1(t) + λ2e2(t) + ... + λ n-1 e n-1 (t)+e n (t), where e1 = e represents the tracking error of the uncertain nonlinear system. and λ i (i = 1, ..., n-1) are all constants, such that the polynomial z n-1 +λ n-1 z n-2 +…+λ1 is the Holwitz polynomial. Because as t→∞, s(t)→0. m Therefore, as t→∞, the tracking error e and its nth derivative e (m) (m=1,…,n) asymptotically converges to zero. Furthermore, e and e (m) The convergence rate is the same as that of s(t).

[0105] Stability analysis of robust adaptive control method for UGV:

[0106] All internal signals are globally eventually uniformly bounded (GUUB), and the system's trajectory tracking error is guaranteed to converge asymptotically to zero.

[0107] Choose from the following Lyapunov functions:

[0108]

[0109] Differentiating both sides of (11), we get:

[0110]

[0111] Where α is a symmetric positive definite matrix such that:

[0112]

[0113] Substitute (9) into (13), This can be further expressed as:

[0114]

[0115] Considering conditions 1 and 3, we can directly deduce that:

[0116]

[0117] Then using (15), we can obtain:

[0118]

[0119] in:

[0120]

[0121] Substituting (16) into (14), we can obtain

[0122]

[0123] Substituting controller (10) into (18), we have Lemma 1.

[0124]

[0125] From condition 2, we know αg+g T α is a symmetric matrix, αg-g T If α is a skew-symmetric matrix, then the following equation holds:

[0126]

[0127] Substituting (20) into (19) yields:

[0128]

[0129] set up Consider the following Lyapunov function:

[0130]

[0131] Using equation (21), the derivative with respect to V2 can be expressed as:

[0132]

[0133] Combining the definition of the adaptive law in equation (10), equation (23) can be further expressed as:

[0134]

[0135] Integrating both sides of (24) yields:

[0136]

[0137] Based on Lemma 1, the definition of V2 in equation (22), and equation (25), we obtain and By Lemma 2 and the definition of s(t), show and According to e = x1 - y d and It can be further obtained and Next, through assumption 3 From formula (10), we can obtain Finally, we can obtain from formula (9) This proves that all signals in a closed-loop system are GUUB. More importantly, by applying Barbalat's introduction, we obtain lim t→∞ s(t)=0 m ,because and The tracking error e and its first derivative can be obtained. As t→∞, it asymptotically converges to zero with the same decreasing rate as s(t).

[0138] 2. Simulation Verification

[0139] To verify the effectiveness and flexibility of the proposed method, we conducted a numerical simulation of a vehicle using the parameters listed in Table 1. Simulation results for the attitude trajectory tracking process, tracking error, and control input signals are presented.

[0140] The purpose of the simulation is to verify whether, under the aforementioned vehicle model and the proposed control scheme, the output can asymptotically track the desired output, and to ensure that all signals are GUUB. The adaptive control parameters are selected as: ω = 150, λ = 10, σ = 0.01, and the desired trajectory signal is set as y d(t)=[0.2+0.1sin(t),0.2+0.1sin(t),0.2+0.2sin(t)] T The initial condition is chosen as x1(0) = [0.1, 0.1, 0.1]. T x2(0) = [0,0,0] T , The interference input signal is given as d(t) = [0.002sin(t), 0.002cos(t), 0.002sin(t)]. T The integrable function is set as v(t) = 1.5e (-1.5t) And nonnegative scalar functions η1(x1) and η2(x2). The choices are η1(x1) = ||x1||, η2(x2) = ||x2||. Simulation results are as follows Figures 3 to 5 As shown.

[0141] Table 1 Vehicle Parameters

[0142] parameter value parameter value m(kg) 10 l(m) 0.4 <![CDATA[l f (m)]]> 0.3 <![CDATA[J f ]]> 10 <![CDATA[l r (m)]]> 0.5 <![CDATA[f f ]]> 10 <![CDATA[I z (kg / m 2 )]]> 10 <![CDATA[k f ]]> 10 <![CDATA[C f (N / rad)]]> 10 <![CDATA[v x (m / s)]]> 3 <![CDATA[C r (N / rad)]]> 10 R(m) 0.3 D(m) 0.05

[0143] like Figure 3 As shown, the system output y will track the desired trajectory y. d .from Figure 4 It can be seen that the tracking error asymptotically converges to zero. (See diagrams below.) Figure 5 and Figure 6 The control input signal u(t) and parameters shown are... The boundedness guarantee is GUUB.

[0144] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A robust adaptive control method for UGVs, characterized in that, Includes the following steps: The dynamic model of UGV is constructed as follows: The state of the dynamic model is , , The input vector of the dynamic model is The output vector of the dynamic model is , It is a nonlinear equation, defined as , This indicates the lateral displacement of the driverless vehicle. Represents a three-dimensional column vector. All three are intermediate variables and have no real meaning. This represents an unknown but bounded external disturbance. It is expressed as follows: It is a matrix that controls the input gain, represented as follows: Filtering errors Defined as: in These are positive design parameters. Indicates tracking error. It is the first derivative of the tracking error, taken along the rate of return. The time derivative; The controller designed is as follows: in and For design parameters, Obey , , Both are design parameters and have no practical significance. , It is a function of t. This represents a defined function, which has no actual physical meaning. This represents the adaptive parameters of the design.

2. The robust adaptive control method for UGV as described in claim 1, characterized in that: The controller must simultaneously satisfy: Condition 1: The system's expected output And its first derivative is known and bounded, and its second derivative is... Bounded, that is ,in For unknown constants, and Both represent state variables; Condition 2: There exists an unknown symmetric positive definite matrix. It is for And t are differentiable, such that It is uniformly positive definite, that is ,in It is an unknown constant. Condition 3: Choose an auxiliary matrix such that The identity matrix is ​​and the auxiliary matrix is ​​. : in: in, , , , , , , and These represent intermediate variables and have no practical meaning.

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