A method for optimizing the geometric parameters of an unmanned bicycle

Abstract

The application discloses a kind of unmanned bicycle geometric structure parameter optimization method, first establish linear variable parameter (linear variable parameter, LPV) mechanics model, and write as the form of state equation, the eigenvalue of state transition matrix is obtained, with the maximum as target then the balance stable speed range of unmanned bicycle, the relationship between the negative real part of state transition matrix eigenvalue and the value of parameter to be optimized is analyzed, and the optimal parameter under target is obtained.Unmanned bicycle wheelbase, handlebar rake, rear offset, wheel radius and other various geometric structure parameters are taken as examples, in zero dynamic and under the control of PD controller, the corresponding optimization result is obtained, and finally the reliability of the optimization result is verified by combining data and image comparison.The application fully considers the influence of unmanned bicycle geometric structure parameters on its balance stable speed range, and under the same conditions, the optimization result of the application can effectively improve the balance stable speed range of unmanned bicycle, i.e., the optimization of unmanned bicycle geometric structure parameters is realized.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of unmanned bicycle, in particular to a kind of unmanned bicycle geometric structure parameter optimization method. BACKGROUND

[0002] Unmanned bicycle is a new type of intelligent driving vehicle that can realize balance motion autonomously on narrow road. Balance stability speed range is an important indicator of bicycle performance evaluation, which is influenced by controller on one hand and closely related to wheelbase, handlebar rake angle, rear offset, wheel radius and other geometric structure parameters on the other hand. At present, there is still lack of a theoretical method for reasonable optimization of geometric structure parameters of unmanned bicycle in the field of unmanned bicycle research. Therefore, it is of great theoretical significance and practical value to give a dynamic model quantitatively describing the influence of geometric structure parameters of unmanned bicycle on system balance characteristics in principle and use it for optimization of key structural parameters in engineering practice. Existing literature research shows that linear variable parameter (LPV) mechanical model is a classic unmanned bicycle model, which can more simply and effectively explain the second-order dynamic response relationship between geometric structure parameters of unmanned bicycle and real-time motion parameters, and is widely used in the field of unmanned bicycle research, especially in system characteristic analysis and balance controller design. However, so far, few researchers have noticed that the model can be used to reasonably select and optimize the hidden geometric structure parameters. SUMMARY

[0003] The present application provides a kind of unmanned bicycle geometric structure parameter optimization method, for optimizing the mechanical structure of unmanned bicycle, so as to improve its balance stability speed range.

[0004] To solve the above problems, the present application is realized by the following technical scheme:

[0005] A kind of unmanned bicycle geometric structure parameter optimization method, comprising the following steps:

[0006] Step 1, establish LPV model of unmanned bicycle:

[0007]

[0008] Select state variable, write LPV model expression as state equation form, get state transition matrix:

[0009]

[0010] 1) When unmanned bicycle is in zero dynamic, take matrix A as state transition matrix;

[0011] 2) When unmanned bicycle is in PD controller control, take matrix A* is the state transition matrix;

[0012] Step 2, determine the geometric structure parameters to be optimized and the constraint conditions, solve the eigenvalues of the state transition matrix, and take the maximum balance stable speed range of the unmanned bicycle as the target;

[0013] Step 3a, when the unmanned bicycle is in zero dynamics, the optimal parameters under the target are obtained by analyzing the relationship between the negative real part of the eigenvalue of the state transition matrix A and the value of the parameter to be optimized;

[0014] Step 3b, when the unmanned bicycle is in PD controller control, the optimal parameters under the target are obtained by analyzing the relationship between the negative real part of the eigenvalue of the state transition matrix A * and the value of the parameter to be optimized;

[0015] Step 4, verify the reliability of the optimization result.

[0016] In the above step 1, M is the mass matrix; C is the "damping" matrix; K is the stiffness matrix;

[0017] delta is the roll angle of the frame and the steering angle of the handlebar, respectively; is the first order derivative and the second order derivative of q in the time domain, respectively; f=[0 τ] T , and tau is the handlebar torque.

[0018] State variable is the first order derivative of the state variable x in the time domain; the input variable u=tau (tau=0 when in zero dynamics, tau=-kx when in PD controller control, and k is the PD controller parameter); the matrix The matrix

[0019] In the above step 2, according to the control engineering principle, when the real part of the eigenvalue of the state transition matrix in the state equation is less than zero, it is considered that the system is stable, and the speed range corresponding to the real part of the eigenvalue of the state transition matrix less than zero is the balance stable speed range of the unmanned bicycle.

[0020] Compared with the prior art, the present application has the following characteristics:

[0021] 1. The present application quantitatively characterizes the internal relationship between the geometric structure parameters of the unmanned bicycle and its balance stable speed range by analyzing the eigenvalues of the state transition matrix of the unmanned bicycle through the LPV model, and has a rigorous and reliable theoretical basis.

[0022] 2. By taking the maximum balance stability speed range of the unmanned bicycle as the target, the relationship between the negative real part of the eigenvalue of the state transition matrix and the value of the to-be-optimized parameter is analyzed, the optimal parameter under the target is obtained, the optimization target of the geometric structure parameters of the unmanned bicycle is realized, and the engineering significance is obvious. BRIEF DESCRIPTION OF DRAWINGS

[0023] Figure 1 is a flowchart of the present application.

[0024] Figure 2 is a mechanical structure diagram of the unmanned bicycle, wherein H, B, R and F are four rigid bodies of the unmanned bicycle, which are respectively handlebar, frame, rear wheel and front wheel; w is the wheelbase, α is the handlebar rake angle, c is the rear offset, and r is the wheel radius.

[0025] Figure 3 Figs. (a) and (b) are respectively the non-optimal wheelbase w and the optimal wheelbase w under the target of the maximum balance stability speed range of the unmanned bicycle at zero dynamic in example one. * The corresponding balance stability speed range (the shaded part in the figure) of the unmanned bicycle; the solid line in the figure is the real part Re(λ) curve of the eigenvalue, and the dotted line is the imaginary part Im(λ) curve of the eigenvalue, and the same below.

[0026] Figure 4 Figs. (a) and (b) are respectively the non-optimal handlebar rake angle α and the optimal handlebar rake angle α under the target of the maximum balance stability speed range of the unmanned bicycle at zero dynamic in example one. * The corresponding balance stability speed range of the unmanned bicycle.

[0027] Figure 5 Figs. (a) and (b) are respectively the non-optimal rear offset c and the optimal rear offset c under the target of the maximum balance stability speed range of the unmanned bicycle at zero dynamic in example one. * The corresponding balance stability speed range of the unmanned bicycle.

[0028] Figure 6 Figs. (a) and (b) are respectively the non-optimal wheel radius r and the optimal wheel radius r under the target of the maximum balance stability speed range of the unmanned bicycle at zero dynamic in example one. * The corresponding balance stability speed range of the unmanned bicycle.

[0029] Figure 7 Figs. (a) and (b) are respectively the non-optimal wheelbase w and the optimal wheelbase w under the target of the maximum balance stability speed range of the unmanned bicycle at zero dynamic in example two. * The corresponding balance stability speed range of the unmanned bicycle.

[0030] Figure 8Figures (a) and (b) are respectively the non-optimal handlebar rake angle a and the optimal handlebar rake angle a of the example two under the target of the maximum balance and stability speed range of the unmanned bicycle when controlled by the PD controller * The corresponding balance and stability speed range diagram of the unmanned bicycle.

[0031] Figure 9 Figures (a) and (b) are respectively the non-optimal trail c and the optimal trail c of the example two under the target of the maximum balance and stability speed range of the unmanned bicycle when controlled by the PD controller * The corresponding balance and stability speed range diagram of the unmanned bicycle.

[0032] Figure 10 Figures (a) and (b) are respectively the non-optimal wheel radius r and the optimal wheel radius r of the example two under the target of the maximum balance and stability speed range of the unmanned bicycle when controlled by the PD controller * The corresponding balance and stability speed range diagram of the unmanned bicycle. DETAILED DESCRIPTION

[0033] In order to make the purpose, technical solutions and advantages of the present application more clear, the present application is further described in detail below with the wheelbase w, the handlebar rake angle a, the trail c and the wheel radius r of the unmanned bicycle as the optimization objects and in combination with specific examples under various conditions.

[0034] Example one: when the unmanned bicycle is in zero dynamics, the wheelbase w, the handlebar rake angle a, the trail c and the wheel radius r of the unmanned bicycle are optimized.

[0035] First, the wheelbase is optimized, and the steps are as follows:

[0036] Step 1, establish the LPV model of the unmanned bicycle:

[0037]

[0038] In the formula, m 11 , m 12 , m 21 , m 22 , c 11 , c 12 , c 21 , c 22 , k 11 , k 12 , k 21 , k 22 are constant coefficients related to the LPV model parameters of the unmanned bicycle and containing the to-be-optimized parameters.

[0039] The frame roll angle The handlebar rotation angle d, the frame roll angle speed and the handlebar rotation angle speed For state variables, the LPV model is written in the form of state equation, and the state transition matrix A containing the optimized parameter wheelbase w is obtained:

[0040]

[0041] In the formula, the state variable The input variable u = τ, the system input τ = 0 when the zero dynamic; the state transition matrix The input matrix

[0042] Step 2, taking the wheelbase of the unmanned bicycle as the optimization object, considering that the wheelbase should be greater than the sum of the front wheel radius and the rear wheel radius, and the wheelbase should not be too long, the wheelbase optimization range w = 0.6m ~ 2m is taken, and the maximum balance stable speed range of the unmanned bicycle is taken as the target.

[0043] Let the wheelbase w and the speed v of the unmanned bicycle change uniformly in the range of w min ~ w max and v min ~ v max , and the step length is Δw, Δv. The eigenvalues of the state transition matrix A are solved, and then the maximum balance stable speed range of the unmanned bicycle is solved. The specific steps are as follows:

[0044] 1) Let the wheelbase and the speed change in the range of w min ~ w max and v min ~ v max with a fixed step length, respectively in the array w and the array v;

[0045] 2) The eigenvalues of the state transition matrix A are solved, and the real parts of the four eigenvalues are taken out and exist in the array rRn(n = 1 ~ 4);

[0046] 3) Find the position index of the four eigenvalues of the state transition matrix A whose real parts are less than zero and exist in the array num;

[0047] 4) Find the position index of the wheelbase and the speed corresponding to the four eigenvalues whose real parts are less than zero, and exist in the array p and the array q respectively:

[0048] Each element p(i) in the array p is obtained by rounding up num(i) / l, and each element q(i) in the array q = num(i)-(p(i)-1)*l, where i = 1 ~ j, j is the number of elements in the array num, is the number of elements in the speed v array;

[0049] 5) Find the number of each wheelbase position index in the array p and exist in the array aa;

[0050] 6) Find the maximum value in array aa and denote it as aa. max ;

[0051] 7) Find the maximum value aa in the array aa. max The index of the value is stored in the array Vrow, and the maximum value in the array Vrow is recorded as Vrow. max ;

[0052] 8) Find the first Vrow of array aa. max The sum of -1 elements is denoted as bb;

[0053] 9) Find the position values ​​corresponding to the maximum and minimum speeds within the maximum equilibrium stable speed range of the unmanned bicycle, and denote them as q1 and q2 respectively:

[0054] q1 is the (bb+aa)th element in array q. max There are 10 elements, where q2 is the (bb+1)th element in array q;

[0055] 10) Take the q1th and q2th elements in the velocity array v and denote them as v1 and v2 respectively. vf = v1 - v2 is the maximum stable speed range of the unmanned bicycle.

[0056] In the above, w min w max They are 0.6m and 2m respectively; v min v max The speeds are 0 m / s and 10 m / s respectively; Δw and Δv are both 0.01.

[0057] Step 3: Based on the analysis of the relationship between the negative real parts of the eigenvalues ​​of the state transition matrix A and the wheelbase values ​​in Step 2, calculate the wheelbase corresponding to the maximum equilibrium stable speed range. Let w be the Vrowth element in the wheelbase w array. * This is the optimal wheelbase for that objective. For this example, w... * =0.78m.

[0058] Step 4, as attached Figure 3 As shown in Figure (a), the shaded area represents the stable speed range for the unmanned bicycle with a non-optimal wheelbase w. The shaded area in Figure (b) represents the speed range with the optimal wheelbase w. * The corresponding stable speed range for unmanned bicycles. See the table below for details:

[0059] Speed w = 0.64 m w = 0.71 m w * = 0.78 m w = 0.85 m w = 0.92 m [v1 (m / s)] 10 10 10 5.74 4.21 [v2 (m / s)] 5.09 4.41 3.95 3.63 3.91 vf(m / s) 4.91 5.59 6.05 2.11 0.30

[0060] Note: v1 and v2 are the maximum and minimum stable speeds of the autonomous bicycle for each wheelbase, respectively; vf = v1 - v2 is the range of stable speeds of the autonomous bicycle for each wheelbase, i.e., the speed range corresponding to the shaded area in the figure.

[0061] To make the above step 2 and step 3 more clear, now take an example as follows:

[0062] Let w min = 0.8, w max = 0.9; v min = 3.6 m / s, v max = 3.7 m / s; Δw = 0.01 m, Δv = 0.05 m / s, the wheelbase of the unmanned bicycle is optimized in this range, as follows:

[0063] In step 2, the maximum balanced stable speed range of the unmanned bicycle is solved, as follows:

[0064] 1) The eigenvalues of the state transition matrix A are solved:

[0065] Wheelbase w / m:

[0066] Value 0.80 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.90 Bit 1 2 3 4 5 6 7 8 9 10 11

[0067] Speed v / (m / s):

[0068] Value 3.60 3.65 6.70 Bit 1 2 3

[0069] Real part rR1 of the first eigenvalue:

[0070] Value -9.0062 -9.1180 -9.2299 -8.9303 -9.0408 -9.1514 -8.8401 -8.9492 Bit 1 2 3 4 5 6 7 8 -9.0583 -8.7353 -8.8427 -8.9502 -8.6158 -8.7215 -8.8272 -8.4819 -8.5857 9 10 11 12 13 14 15 16 17 -8.6896 -8.3347 -8.4364 -8.5383 -8.1752 -8.2749 -8.3745 -8.0054 -8.1028 18 19 20 21 22 23 24 25 26 -8.2002 -7.8273 -7.9223 -8.0173 -7.6435 -7.7361 -7.8286 27 28 29 30 31 32 33

[0071] Real part rR2 of the second eigenvalue:

[0072]

[0073]

[0074] Real part rR3 of the third eigenvalue:

[0075] Value 0.1722 0.1286 0.0883 0.1345 0.0928 0.054 0.0997 0.0598 Bit 1 2 3 4 5 6 7 8 0.0227 0.0684 0.0304 -0.0049 0.0415 0.0055 -0.028 0.0199 -0.0141 9 10 11 12 13 14 15 16 17 -0.0458 0.0046 -0.0273 -0.0571 -0.0035 -0.0332 -0.0611 -0.0032 -0.0308 18 19 20 21 22 23 24 25 26 -0.0567 0.0062 -0.0192 -0.0430 0.0256 0.0025 -0.0192 27 28 29 30 31 32 33

[0076] Real part rR4 of the fourth eigenvalue:

[0077] Value -0.8625 -0.7959 -0.7356 -0.8009 -0.7383 -0.6816 -0.7399 -0.6812 Bit 1 2 3 4 5 6 7 8 -0.6283 -0.6796 -0.6249 -0.5756 -0.6201 -0.5694 -0.5237 -0.5615 -0.5147 9 10 11 12 13 14 15 16 17 -0.4725 -0.5040 -0.4610 -0.4222 -0.4475 -0.4082 -0.3726 -0.3921 -0.3563 18 19 20 21 22 23 24 25 26 -0.3239 -0.3378 -0.3053 -0.2758 -0.2845 -0.2551 -0.2286 27 28 29 30 31 32 33

[0078] 2) The index array num when the real parts of the four eigenvalues are all negative:

[0079] Value 12 15 17 18 20 21 22 23 24 25 26 27 29 30 33 Bit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

[0080] 3) The wheelbase index array p when the real parts of the four eigenvalues are all negative:

[0081] Array 4 5 6 6 7 7 8 8 8 9 9 9 10 10 11 Bit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

[0082] The speed position array q when the four eigenvalues are negative:

[0083] Value 3 3 2 3 2 3 1 2 3 1 2 3 2 3 3 Bit 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

[0084] 4) Find the number of each axis distance position in array p and put it in array aa:

[0085] Axle distance bit 1 2 3 4 5 6 7 8 9 10 11 aa 0 0 0 1 1 2 2 3 3 2 1

[0086] 5) The maximum value aa in array aa is: max = 3.

[0087] 6) The maximum value aa in array aa is: max The corresponding axis distance position is in array Vrow:

[0088] Vrow 8 9

[0089] The maximum value Vrow in array Vrow is: max = 9.

[0090] 7) Sum the first Vrow max -1 elements in array aa and record it as bb, bb = 9.

[0091] 8) q1 is the bb+aa max th element in array q, and q2 is the bb+1 th element in array q, then q1 = 3 and q2 = 1.

[0092] 9) Take the q1 th and q2 th elements in array v as v1 and v2 respectively, and vf = v1-v2 is the maximum balance stable speed range, then v1 = 3.7 m / s, v2 = 3.6 m / s, and vf = v1-v2 = 3.7-3.6 = 0.1 m / s.

[0093] In step 3, take the Vrow th element in array w, which is the axis distance corresponding to the maximum balance stable speed range of the unmanned bicycle, and record it as w * .

[0094] w 0.87m 0.88m

[0095] Similarly, the handlebar rake angle α, rear offset c, and wheel radius r of the unmanned bicycle can be optimized, and the conditions and results are as follows:

[0096] (1) Optimize the handlebar rake angle α.

[0097] Conditions: α min = 5°, α max = 35°; v min = 0 m / s, v max= 10 m / s; Δα = 1°, Δv = 0.01 m / s.

[0098] Result: α * = 20°. The optimal handlebar rake α * and the non-optimal handlebar rake α correspond to the balanceable and stable speed range of the unmanned bicycle, which is shown in Figs. (a) and (b) of Fig. 6, and the specific values are shown in the following table: Figure 4

[0099] Speed α＝12° α＝16° * = 20° ​ α＝24° α＝28° [v1 (m / s)] 4.33 4.87 5.39 5.88 6.37 [v2 (m / s)] 3.85 3.61 4.02 4.62 5.41 vf(m / s) 0.48 1.26 1.37 1.26 0.96

[0100] Note: v1 and v2 are the maximum and minimum values of the balanceable and stable speed of the unmanned bicycle corresponding to each handlebar rake, respectively; vf = v1-v2 is the balanceable and stable speed range of the unmanned bicycle corresponding to each handlebar rake, i.e. the speed range corresponding to the shaded part in the figure.

[0101] (2) Optimization of the rear offset c.

[0102] Condition: c min = 0 m, c max = 0.25 m; v min = 0 m / s, v max = 10 m / s; Δc = 0.01 m, Δv = 0.01 m / s.

[0103] Result: The optimization of the rear offset has two optimal solutions, c * = 0.24 m and c * = 0.25 m, and the balanceable and stable speed range of the unmanned bicycle corresponding to the two solutions is consistent. The optimal rear offset c * and the non-optimal rear offset c correspond to the balanceable and stable speed range of the unmanned bicycle, which is shown in Figs. (a) and (b) of Fig. 7, and the specific values are shown in the following table: Figure 5

[0104] Speed c = 0.04 m c = 0.09 m c = 0.14 m c = 0.19 m c * = 0.24 m c * = 0.25 m [v1 (m / s)] 4.08 5.17 6.84 10 10 10 [v2 (m / s)] 3.88 3.56 3.42 3.34 3.28 3.28 vf(m / s) 0.20 1.61 3.42 6.66 6.72 6.72

[0105] Note: v1 and v2 are the maximum and minimum values of the balanceable and stable speed of the unmanned bicycle corresponding to each rear offset, respectively; vf = v1-v2 is the balanceable and stable speed range of the unmanned bicycle corresponding to each rear offset, i.e. the speed range corresponding to the shaded part in the figure.

[0106] From the above table, it can be seen that when the rear offset is in the range of 0.19 m-0.25 m, the balanceable and stable speed range of the unmanned bicycle has little difference, so a suitable value in this range can be selected as the final optimal solution according to the assembly conditions and other requirements.

[0107] (3) Optimization of the wheel radius r.

[0108] Condition: r min = 0 m, r​​max =0.8m; v min =0m / s, v max =10m / s; Δr=0.01m, Δv=0.01m / s.

[0109] Result: There are two optimal solutions for optimizing the wheel radius, namely r * =0.52m and r * =0.53m, and the corresponding stable speed ranges for the two unmanned bicycles are slightly different. Their optimal wheel radius r * A comparison of the stable speed range of unmanned bicycles corresponding to non-optimal wheel radii r is shown in the figure below. Figure 6 As shown in Figures (a) and (b), see the table below for details:

[0110] Speed r＝0.23m r＝0.33m r＝0.43m r * = 0.52 m r * = 0.53 m r＝0.63m [v1 (m / s)] 4.16 5.28 5.25 7.34 7.45 8.53 [v2 (m / s)] 3.24 3.83 3.70 5.33 5.44 7.19 vf(m / s) 0.92 1.45 1.55 2.01 2.01 1.34

[0111] Note: v1 and v2 are the maximum and minimum stable speeds of the unmanned bicycle corresponding to each wheel radius, respectively; vf = v1 - v2 is the range of stable speeds of the unmanned bicycle corresponding to each wheel radius, that is, the speed range corresponding to the shaded area in the figure.

[0112] Example 2: When the unmanned bicycle is under the control of the PD controller, the wheelbase w, handlebar tilt angle α, rear offset c, and wheel radius r of the unmanned bicycle are optimized.

[0113] First, optimize the wheelbase, following these steps:

[0114] Step 1: Establish an unmanned bicycle LPV model:

[0115]

[0116] In the formula, m 11 m 12 m 21 m 22 c 11 c 12 c 21 c 22 k 11 k 12 k 21 k 22 These are constant coefficients related to the parameters of the unmanned bicycle LPV model and contain parameters to be optimized.

[0117] Similarly, the frame roll angle Handlebar angle δ, frame roll rate and handlebar angular velocity As state variables, the LPV model is written in the form of state equations, yielding the state transition matrix A containing the axis distance w to be optimized.* :

[0118]

[0119] where state variable input variable u = τ, system input τ = -kx under the control of PD controller, select appropriate PD controller parameters, in this example k = [-20 0 8 0]; matrix matrix

[0120] Step 2, taking the wheelbase of the unmanned bicycle as the optimization object, and taking w = 0.6m ~ 2m as the wheelbase optimization range, construct the target of taking the maximum balance stable speed range under the control of the PD controller as the goal.

[0121] Let the wheelbase w and the speed v of the unmanned bicycle change uniformly in the range of w min ~ w max and v min ~ v max , with a step size of Δw, Δv. Find the eigenvalues of matrix A * , and then find the maximum balance stable speed range of the unmanned bicycle. The specific steps are as follows:

[0122] 1) Let the wheelbase and speed change with a fixed step size in the range of w min ~ w max and v min ~ v max , respectively, in arrays w and v;

[0123] 2) Find the eigenvalues of matrix A * , and take the real parts of the four eigenvalues and put them into arrays rRn(n = 1 ~ 4), respectively;

[0124] 3) Find the index of the four eigenvalues of matrix A * whose real parts are all less than zero and put it into array num;

[0125]

[0126] The remaining steps are the same as in Example 1, which will not be repeated here.

[0127] In the above, w min , w max are 0.6m and 2m respectively; v min , v max are 0m / s and 10m / s respectively; Δw, Δv are all 0.01.

[0128] Step 3, based on step 2, the state transition matrix A *The analysis of the relationship between the negative real part of the eigenvalue and the wheelbase value, and the wheelbase corresponding to the maximum balance stability speed range is obtained. The Vrow element in the wheelbase w array is denoted as w * , which is the optimal wheelbase under the target. For this example, w * = 0.95 m.

[0129] Step 4, as shown in FIG. (a) of the accompanying drawings, the speed range corresponding to the shaded part in the figure is the non-optimal wheelbase w * balance stability speed range of the unmanned bicycle. The speed range corresponding to the shaded part in FIG. (b) is the optimal wheelbase w * balance stability speed range of the unmanned bicycle. See the following table for details:

[0130] Speed w = 0.65 m w = 0.75 m w = 0.85 m w * = 0.95 m w = 0.97 m [v1 (m / s)] 10 10 10 10 0.97 [v2 (m / s)] 0.85 0.70 0.55 0.36 0.33 vf(m / s) 9.15 9.30 9.45 9.64 0.64

[0131] Note: v1 and v2 are the maximum and minimum values of the balance stability speed of the unmanned bicycle corresponding to each wheelbase, respectively; vf = v1-v2 is the balance stability speed range of the unmanned bicycle corresponding to each wheelbase, i.e. the speed range corresponding to the shaded part in the figure.

[0132] Similarly, the handlebar rake angle a, the rear offset c, and the wheel radius r of the unmanned bicycle can be optimized, and the optimization conditions and results are as follows:

[0133] (1) Optimize the handlebar rake angle a.

[0134] Conditions: a min = 5°, a max = 35°; v min = 0 m / s, v max = 10 m / s; Δa = 1°, Δv = 0.01 m / s.

[0135] Results: a * = 16°. The comparison chart of the optimal handlebar rake angle a * and the non-optimal handlebar rake angle a corresponding to the balance stability speed range of the unmanned bicycle is shown in FIG. (a) and (b) of the accompanying drawings, and the details are shown in the following table: Figure 8

[0136] Speed α＝6° α＝11° * = 16° ​ α＝21° α＝26° [v1 (m / s)] 0.50 10 10 10 10 [v2 (m / s)] 0.47 0.51 0.48 0.77 1.23 vf(m / s) 0.03 9.49 9.52 9.23 8.77

[0137] Note: v1 and v2 are the maximum and minimum values of the balance stability speed of the unmanned bicycle corresponding to each handlebar rake angle, respectively; vf = v1-v2 is the balance stability speed range of the unmanned bicycle corresponding to each handlebar rake angle, i.e. the speed range corresponding to the shaded part in the figure.

[0138] (2) Optimize the rear offset c.

[0139] Conditions: c min ​= 0 m, c max = 0.25 m; v min = 0 m / s, v max = 10 m / s; Δc = 0.01 m, Δv = 0.01 m / s.

[0140] Result: optimal rear offset c * It is preferable to take 0.01 m, 0.02 m, 0.03 m, 0.04 m multiple values, and they correspond to the same range of balance and stable speed of the unmanned bicycle. The optimal rear offset c * The comparison chart of the balance and stable speed range of the unmanned bicycle corresponding to the optimal rear offset c and the non-optimal rear offset c is shown in Figs. (a) and (b) of Figure 9 , and the specific values are shown in the following table:

[0141] Speed c = 0 m c c = 0.11 m c = 0.18 m c = 0.25 m [v1 (m / s)] 4.02 10 10 10 10 [v2 (m / s)] 0.47 0.45 0.54 0.68 0.82 vf(m / s) 3.55 9.55 9.46 9.32 9.18

[0142] Note: v1 and v2 are the maximum and minimum values of the balance and stable speed of the unmanned bicycle corresponding to each rear offset, respectively; vf = v1-v2 is the balance and stable speed range of the unmanned bicycle corresponding to each rear offset, i.e. the speed range corresponding to the shaded part in the figure.

[0143] (3) Optimization of the wheel radius r.

[0144] Condition: r min = 0 m, r max = 0.8 m; v min = 0 m / s, v max = 10 m / s; Δr = 0.01 m, Δv = 0.01 m / s.

[0145] Result: the balance and stable speed range of the unmanned bicycle tends to decrease slowly within the range of 0.1 m to 0.8 m of the wheel radius. The comparison chart of the balance and stable speed range of the unmanned bicycle corresponding to each wheel radius is shown in Figs. (a) and (b) of Figure 10 , and the specific values are shown in the following table:

[0146] Speed r＝0.1m r＝0.2m r＝0.3m r＝0.4m r＝0.5m r＝0.6m r＝0.7m r＝0.8m [v1 (m / s)] 10 10 10 10 10 10 10 10 [v2 (m / s)] 0.45 0.47 0.48 0.53 0.58 0.65 0.73 0.85 vf(m / s) 9.55 9.53 9.52 9.47 9.42 9.35 9.27 9.15

[0147] Note: v1 and v2 are the maximum and minimum values of the balance and stable speed of the unmanned bicycle corresponding to each wheel radius, respectively; vf = v1-v2 is the balance and stable speed range of the unmanned bicycle corresponding to each wheel radius, i.e. the speed range corresponding to the shaded part in the figure.

[0148] The parameters of the LPV model of the unmanned bicycle in the above example come from a physical prototype of an existing unmanned bicycle, and the specific values are shown in Table 1.

[0149] Table 1: Parameter values of the LPV model of the research object in the example

[0150]

[0151] In the above two examples, the LPV model is used to control the zero dynamic and PD controller for two cases, with the maximum balance speed range of the unmanned bicycle as the target, and the state transition matrix A, A * The analysis of the relationship between the negative real part of the eigenvalue and the value of the parameter to be optimized obtains the optimal parameter under the target, and realizes the optimization of various geometric structure parameters such as the wheelbase w, the handlebar rake angle α, the rear offset c and the wheel radius r. The results show that under the same conditions, the geometric structure parameter optimization result of the application can effectively improve the balance speed range of the unmanned bicycle, that is, the target of optimizing the geometric structure parameters of the unmanned bicycle is achieved, which has important engineering significance.

[0152] The above examples are only specific examples for further detailing the purposes, technical solutions and the like of the application, but the application is not limited to this. Any modification, equivalent replacement, improvement and the like within the scope disclosed by the application are included in the protection scope of the application.

Claims

1. A method for optimizing the geometry parameters of an unmanned bicycle, characterized in that, The steps include the following: Step 1, establishing the LPV model of the unmanned bicycle: where M is the mass matrix; C is the "damping" matrix; K is the stiffness matrix; δ are the roll angle of the vehicle frame and the handlebar angle, respectively; are the first and second order derivatives of q in the time domain, respectively; f = [0 τ] T τ is the handlebar torque: Selecting state variables, expressing the LPV model expression in the form of state equation, and obtaining the state transition matrix: wherein, is the first order derivative of the state variable x over the time domain; the input variable u = τ, τ = 0 when the zero dynamics, τ = -kx when the PD controller controls, k is the PD controller parameter, A, B are the state transition matrix; 1) When the unmanned bicycle is in zero dynamics, the matrix A is the state transition matrix; 2) When the unicycle is under the control of the PD controller, the state transition matrix is A * A = [0 1 0 0; 0 0 1 0; 0 0 0 1 ; 0 -k p -k d 1 0] Step 2, determining the geometric structure parameters to be optimized and the constraint conditions, solving the eigenvalues of the state transition matrix, and taking the maximum range of the balance stable speed of the unmanned bicycle as the target; Step 3a, when the self-balancing bicycle is in zero dynamics, traverse in a fixed step within the given range of parameters, for each set of parameters and speed combination, solve the eigenvalues of the state transition matrix A, when the real part of the four eigenvalues is less than zero, consider that the self-balancing bicycle system is stable, for each parameter value, statistics its corresponding stable speed range v f1 v1-v2, wherein v1 is the maximum stable speed, v2 is the minimum stable speed, and the parameter value that maximizes the stable speed range is selected as the optimal parameter; Step 3b, when the self-balancing bicycle is in the control of the PD controller, traverse in a fixed step within the given range of parameters, for each set of parameters and speed combination, solve the eigenvalue of the state transition matrix A * , when the real part of the four eigenvalues is less than zero, it is considered that the self-balancing bicycle system is stable, for each parameter value, the corresponding stable speed range v f2 =v1-v2 is calculated, where v1 is the maximum stable speed and v2 is the minimum stable speed, and the parameter value that maximizes the stable speed range is selected as the optimal parameter; Step 4, verifying the reliability of the optimization result.

2. The method of claim 1, wherein the method further comprises: In step 1, the LPV model is used to analyze the influence of various geometric structure parameters on the balance stable speed range of the unmanned bicycle.

3. The method of claim 1, wherein the method further comprises: In step 1, the LPV model is written in the form of state equation, and then in step 2, the matrix A, A * The real part of the eigenvalue is analyzed to determine whether the self-balancing motion of the unmanned bicycle can be achieved under the corresponding parameters.

4. The method of claim 1, wherein the method further comprises: In step 2, the matrix A, A * The relationship between the negative real part of the eigenvalue and the value of the parameter to be optimized is as follows: 1) Let the parameters to be optimized and the velocities vary in fixed steps in the ranges o min ~ o max and v min ~ v max respectively, in arrays o and arrays v respectively; 2) find eigenvalues of matrix A, A * and take out the real part of the four eigenvalues to exist in the array rRn (n = 1 ~ 4) respectively; 3) Find the indices of the four eigenvalues of matrix A, A * whose real parts are less than zero and store them in the array num; 4) Find the corresponding to-be-optimized parameters and speed value marks when the real parts of the four eigenvalues are less than zero, and store them in arrays p and q respectively: Each element p(i) in the array p is obtained by rounding up num(i) / l, and each element q(i) in the array q = num(i) - (p(i) - 1) * l, where i = 1 ~ j, j is the number of elements in the array num, is the number of elements in the array v. 5) Find the number of each to-be-optimized parameter mark in array p and store it in array aa: 6) Find the maximum value in the array aa and call it aa max ; 7) Find the maximum value aa in the array aa. max The index of the value is stored in the array Vrow, and the maximum value in the array Vrow is recorded as Vrow. max ; 8) sum of first Vrow elements in array aa is denoted by bb max -1 element sum is denoted by bb; 9) Find the marks corresponding to the maximum speed and the minimum speed in the maximum balance stable speed range of the unmanned bicycle, and mark them as q1 and q2 respectively: q1 is the (bb + aa)th element of the array q, q2 is the (bb + 1)th element of the array q max q1 is the (bb + aa)th element of the array q, q2 is the (bb + 1)th element 10) Take the first q1 element and the first q2 element in the speed v array as v1 and v2 respectively, and vf=v1-v2 is the maximum balance stable speed range of the unmanned bicycle.

5. The method of claim 1, wherein the method further comprises: In step 3, when taking the maximum balance stable speed range of the unmanned bicycle as the target, the specific steps of solving the optimal parameters under this target in the zero dynamics and the PD controller control are as follows: 1) Let the parameters to be optimized and the velocities vary in fixed steps in the ranges o min ~ o max and v min ~ v max respectively, in arrays o and arrays v respectively; 2) find eigenvalues of matrix A, A * and take the real part of the four eigenvalues and put them in the array rRn (n = 1 ~ 4) respectively; 3) Find the indices of the four eigenvalues of matrix A, A * whose real parts are less than zero and store them in the array num; 4) Find the corresponding to-be-optimized parameters and speed value marks when the real parts of the four eigenvalues are less than zero, and store them in arrays p and q respectively: Each element p(i) in the array p is obtained by rounding up num(i) / l, and each element q(i) in the array q = num(i) - (p(i) - 1) * l, where i = 1 ~ j, j is the number of elements in the array num, is the number of elements in the array v. 5) Find the number of each to-be-optimized in array p and store it in array aa: 6) Find the maximum value in the array aa and call it aa max ; 7) find the index of the maximum value aa in the array aa and put it in the array Vrow max ; 8) take the Vth element of the array of parameters to be optimized o and call it o * , o * is the optimal parameter.

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