Double-power combination sliding mode control method for lateral balance of unmanned bicycle

Abstract

The invention discloses a double-power combination sliding mode control method for lateral balance of an unmanned bicycle, and the method comprises the steps: introducing feed-forward compensation to process an LPV model of the unmanned bicycle, and carrying out the dimensionality reduction of the LPV model into an improved model which only comprises a lateral inclination angle of a bicycle body; estimating the lumped interference by designing a linear expansion state observer; then selecting a proper linear sliding mode surface function and designing a double-power combined sliding mode control law, and designing a controller by using a linear state observer and the double-power combined sliding mode control law to realize lateral balance control of the unmanned bicycle; and finally, numerical simulation and physical prototype experiments are carried out to prove the feasibility and reliability of the provided control method. According to the invention, the anti-interference capability of the unmanned bicycle system under multi-source interference is improved, the convergence speed of the unmanned bicycle is improved, and the stability of lateral balance of the unmanned bicycle is ensured. The double-power combination sliding mode control method for the unmanned bicycle is simple in structure, simple in calculation process, clear in physical meaning and convenient to apply in engineering, and has important engineering significance.

Description

Technical Field

[0001] The present invention relates to the technical field of balance bicycles, and particularly relates to a double-power combination sliding mode control method for the lateral balance of unmanned bicycles. Background Art

[0002] As a new type of intelligent transportation vehicle, balance control is the primary problem that needs to be solved for unmanned bicycles. During the balance motion control process, unmanned bicycles are affected by various interference factors such as external disturbances, internal parameter perturbations, and uncertainties of unmodeled dynamic systems, which will cause the lateral balance ability of the bicycle to decrease or even be lost. It can be seen that when facing disturbances, implementing feedback control on unmanned bicycles becomes one of the key technical links to achieve self-balancing.

[0003] The balance motion of unmanned bicycles is directly related to the design of the controller. The influencing factors of the controller mainly include two aspects. One is the geometric structure parameters of the bicycle. The commonly used mechanical model in the bicycle model is the linear variable parameter (LPV) mechanical model. Its advantage is that it can better describe the dynamic response relationship between geometric structure parameters and motion parameters when the vehicle speed changes little and the lateral inclination angle is limited within a small angle range. The other is the selection of the controller. Among the currently common control algorithms, partial feedback linearization method (PFLC), variable gain LQR method, LQR with inclination disturbance observer (ESO+LQR) method, composite control algorithm (PID+LQR), fuzzy sliding mode control method (FSMC), T-S fuzzy control method, Lyapunov fuzzy control method (LFC), linear active disturbance rejection control (LADRC) method, etc. have been applied to the balance motion control of bicycles. These methods have achieved good balance effects in the control of unmanned bicycles. Among them, the linear active disturbance rejection control method introduces a linear extended state observer (LESO), making the system show certain robustness. However, its state observer is based on the premise that the system disturbance is slowly changing (that is, assuming that the first derivative of the disturbance is 0). This assumption makes the estimation of complex high-order disturbance terms by the observer insufficient. Therefore, further measures need to be taken for this controller to improve its robustness and chattering performance.

[0004] The double-power combination sliding mode is a control method with strong robustness and weak chattering. It is composed of the double-power sliding mode and the fast-power sliding mode. The double-power combination sliding mode combines the advantages of the double-power sliding mode with small chattering when approaching the sliding surface and the fast-power sliding mode with fast convergence speed, that is, it can ensure the convergence speed and effectively reduce chattering, and has been widely applied in the fields of vehicle engineering and robotics. Summary of the Invention

[0005] Aiming at the deficiencies of the above-mentioned existing technologies, the present invention proposes a double-power combined sliding mode control method for the lateral balance of an unmanned bicycle, aiming to integrate the advantages of the fast power reaching rate and the double-power reaching rate, effectively reducing the chattering phenomenon of the unmanned bicycle and improving the robustness of the system.

[0006] The present invention is realized through the following technical solutions:

[0007] A double-power combined sliding mode control method for the lateral balance of an unmanned bicycle specifically includes the following steps:

[0008] Step 1: Referring to the LPV mechanical model of the unmanned bicycle, we transform it into a state-space equation, and regard the handlebar angle and the handlebar angular velocity as disturbance factors, thus realizing the dimensionality reduction of the system state variables. Next, we achieve the formal decoupling of the handlebar angle and the lateral inclination angle of the vehicle body, and also consider the perturbation of the internal parameters and structure of the system, as well as external disturbances, and equivalently regard them as a lumped disturbance term, thus obtaining an improved LPV model;

[0009] Step 2: Design a linear extended state observer. By selecting appropriate observation gains, the observation error gradually converges to a bounded range near 0. At the same time, observe the handlebar angle, the handlebar angular velocity and the lumped disturbance, and apply the disturbance observation quantity to the control input end through the feedforward compensation method;

[0010] Step 3: The observer model can be obtained from Step 2. Subsequently, according to the double-power combined sliding mode control principle, design a linear sliding mode surface function s, then obtain the fast power control term in the control law and design the double-power control term, and comprehensively combine the two to obtain the double-power combined sliding mode control law of the system;

[0011] Step 4: Combine the linear extended state observer described in Step 2 and the double-power sliding mode controller described in Step 3 to construct a robust controller, so that the lateral inclination state converges to the equilibrium point in a finite time; subsequently, apply the control torque τ generated by the controller to the LPV model, thus achieving the lateral balance control of the LPV model;

[0012] Step 5: Convert the control torque generated by the controller into a modulated pulse width signal (PWM), and send corresponding control commands by the STM32 single-chip microcomputer, thus achieving the purpose of balancing control of the unmanned bicycle.

[0013] Furthermore, the LPV mechanical model in Step 1 is specifically:

[0014]

[0015] In the formula are respectively the lateral inclination angle of the frame and the angle of the handlebar, and are the first and second derivatives of q(t) with respect to time respectively; M is the mass inertia matrix of the system, v(t)C 1 is the equivalent damping matrix of the system, (gK 0 +v 2 (t)K 2 ) is the equivalent stiffness matrix of the system, v(t) is the linear velocity of the vehicle body centroid, and g is the acceleration due to gravity; τ = (0, τ δ ) T is the control torque vector of the system, and τ δ is the control torque of the handlebar. In addition, the matrices M, C 1 , K 0 , K 2 can be determined by 25 physical parameters of the system.

[0016] Furthermore, taking the state variables the state space equation in Step 1 can be rewritten as:

[0017]

[0018] where A = (a ij ) 4×4 and B = (b ij ) 4×1 are the system state transition matrix and the system control input matrix respectively, and u(t) is the system control input vector.

[0019] Furthermore, in the said Step 1, considering two states of the vehicle body lateral inclination angle and the inclination angle velocity, regarding the handlebar rotation angle and the handlebar rotation angle velocity as interference terms for the vehicle body lateral inclination angle and adding the lumped interference term then the state space equation can be rewritten as the following dynamic response equation of the vehicle body lateral inclination angle of the system:

[0020]

[0021] In the above equation, and are matrices composed of the relevant elements of the first row and the third row of matrices A and B respectively, B ξ = (0, 1) T is the input matrix of the lumped interference, and the variables:

[0022]

[0023]

[0024]

[0025] then it can be rewritten as:

[0026]

[0027] Obviously, the equation only contains two states, namely the lateral tilt angle of the vehicle body and the steering handle angle. Formally, this equation eliminates the coupling effect of the steering handle angle (angular velocity) on the lateral tilt angle.

[0028] Furthermore, the linear extended state observer described in step 2 is as follows:

[0029]

[0030] In the formula, is 's estimated value,

[0031] C O =(1, 0, 0), the observation gain L O =(l 1 , l 2 , l 3 ), where l 1 , l 2 , l 3 are the observation gain coefficients.

[0032] Furthermore, the linear sliding mode surface function described in step 3 is as follows:

[0033]

[0034] In the formula, c Τ =(c 1 , c 2 ), c 1 >0, c 2 >0.

[0035] Assume is non-singular, the double power combination sliding mode control law in step 3 is as follows:

[0036]

[0037] In the formula, u s =-k 1 fal(s, a, λ)-k 2 |s| b sgn(s), is the estimated value of the lumped disturbance term , k 1 >0, k 2> 0, a = 1 + γ, b = 1 - γ, 0 < γ < 1, λ = 1, sgn(s) is the sign function, and the definition of the non - linear double - power combination function fal(s, a, λ) is as follows:

[0038]

[0039] Further, the control torque τ output by the controller in step 4 acts on the unmanned bicycle LPV model, so as to achieve the lateral balance effect.

[0040] Further, the relationship between the control torque in step 5 and PWM is as follows:

[0041] τ = k PWM ·V PWM

[0042] In the above formula, k PWM = k ω k τ (V S / 100 / R Ω ), R Ω is the internal resistance of the handlebar motor coil, k ω is the reduction ratio of the transmission, k τ is the current - torque coefficient of the drive motor, V S is the input voltage of the bridge,

[0043] V PWM is the duty cycle.

[0044] The beneficial effects of the present invention are as follows:

[0045] (1) The design structure of the present invention is clear, which can not only ensure the convergence speed but also effectively eliminate the chattering phenomenon. Moreover, the double - power combination sliding - mode control structure is relatively simple and easy to be applied in engineering.

[0046] (2) The present invention combines the linear extended state observer and the double - power combination sliding - mode control technology, which makes up for the deviation between the model and the actual dynamic response caused by the internal parameter perturbation of the bicycle to a certain extent, realizes the compensation of the lumped disturbance including the external disturbance, and improves the robustness and stability of the lateral balance control system of the unmanned bicycle.

[0047] (3) In the design of the double - power combination sliding - mode control law of the present invention, the hyperbolic tangent function is used to replace the traditional sign function, which ensures the continuity of the control quantity in the robust controller of the unmanned bicycle, reduces the influence of the controller chattering, and improves the overall performance and reliability of the unmanned bicycle under complex working conditions. Brief Description of the Drawings

[0048] Figure 1 It is a prototype of an unmanned bicycle and its structural sketch;

[0049] Figure 2 It is a simulation block diagram of a double-power combined sliding mode control method for the lateral balance of an unmanned bicycle;

[0050] Figure 3 It is a block diagram of the measurement and control system for the unmanned bicycle prototype;

[0051] Figure 4 It is the simulation response curves of state variables and torques caused by the influence of multi-source disturbances on the LPV model under the action of the double-power combined sliding mode controller;

[0052] Figure 5 It is the simulation response curves of state variables and torques caused by the influence of multi-source disturbances on the LPV model under the action of the non-singular terminal sliding mode controller;

[0053] Figure 6 It is the curves of state variables and torques caused when the unmanned bicycle is driving on a cement road surface;

[0054] Figure 7 It is the consecutive video capture images of the unmanned bicycle driving on a cement road surface. Specific implementation manners

[0055] To make the objectives, technical solutions, and advantages of the present invention clearer and easier to understand, we will further elaborate on the present invention in combination with specific embodiments. The described embodiments are only a part of the embodiments of the present invention, rather than all embodiments. According to the embodiments of the present invention, all other embodiments obtained by ordinary persons in the art without creative labor should be included within the protection scope of the present invention.

[0056] Embodiment 1 (simulation):

[0057] Aiming at the problems of insufficient robustness, slow convergence speed, and serious chattering of the current sliding mode control algorithm under the influence of multi-source disturbances, this embodiment proposes a double-power combined sliding mode control method for the lateral balance of an unmanned bicycle.

[0058] This invention mainly aims at the control problem of an unmanned bicycle, aiming to ensure that the vehicle body maintains lateral balance and can effectively cope with various uncertain disturbances, so as to maintain it in a stable position. Our control objective is to design a controller to ensure that the lateral inclination angle approaches zero within a finite time, and the specific steps are as follows:

[0059] Step 1: Analyze and improve the traditional linear parameter-varying (LPV) model of the unmanned bicycle according to the physical parameters of the whole vehicle and components of the unmanned bicycle shown in Table 1 and Table 2:

[0060]

[0061] In the formula, v is the vehicle speed. By extracting the relevant elements of the first and third rows of matrices A and B, we can obtain

[0062]

[0063]

[0064] a 32 = 0.648 - 1.985v 2 (t), a 34 = -0.844v(t), b 3 = -0.630

[0065] Furthermore, the structural schematic diagram of the research object is as shown in Figure 1 and the relevant physical parameter values of its LPV model are shown in Tables 1 and 2 as follows:

[0066] Table 1 Physical parameters of the unmanned bicycle

[0067] Parameter Symbol Value Total mass of the vehicle body <![CDATA[m t > 14.85 kg Wheelbase between the front and rear wheels ω 0.885m Height of the vehicle body's center of mass h 0.547m Horizontal distance from the vehicle body's center of mass to the origin of the coordinate system b 0.344m Rear offset of the front wheel contact point c 0.078m Fork rake angle α 75° Acceleration due to gravity g <![CDATA[9.81m / s 2 >

[0068] Table 2 Physical parameters of the components of the unmanned bicycle

[0069]

[0070] Step 2: Design a linear extended state observer to observe the handlebar angle, handlebar angular velocity, and lumped disturbance in the LPV model of the unmanned bicycle:

[0071]

[0072] In the above formula, take the observation gain L O = (1557, 538600, 41480000) T At this time, the three eigenvalues of A O - L O C O are -1102.6, -345.4, and -108.9 respectively, all of which contain negative real parts, satisfying the boundary conditions for the convergence of the linear extended state observer.

[0073] Step 3: Design a linear sliding mode surface function s:

[0074]

[0075] where c 1 = 3, c 2 = 1.

[0076] Design a double-power combination sliding mode reaching law:

[0077] u s = -k1 fal(s,a,λ)-k 2 |s| b tanh(s)

[0078] where k 1 = 1, k 2 = 0.1, a = 1.1, b = 0.9, λ = 1.

[0079] Design the double-power combination sliding mode control law u(t):

[0080]

[0081] Importantly, the present invention uses the hyperbolic tangent function tanh(s) to replace the sign function, aiming to reduce the adverse effect of high-frequency chattering.

[0082] Step 4, as Figure 2 shown, construct a robust controller by combining the linear extended state observer described in Step 2 and the double-power combination sliding mode controller described in Step 3 to ensure that the lateral tilt state reaches a stable state within a finite time; subsequently, apply the control torque τ generated by the controller to the LPV model, thereby achieving the lateral balance control of the LPV model.

[0083] The method of the present invention takes a second-order nonlinear unmanned bicycle LPV model with internal parameter perturbation and external disturbance as the research object, and constructs a robust controller composed of a linear extended state observer and a double-power combination sliding mode controller. This controller uses a linear sliding surface, can ensure the finite-time convergence of the sliding surface, uses a control law with a hyperbolic tangent function to reduce chattering, and also uses a linear extended state observer to estimate the lumped disturbance and compensate it in the controller, thereby improving the robustness of the system in the face of multi-source disturbances.

[0084] To verify the robust performance, anti-chattering effect and convergence speed and other performances of this embodiment, the existence of multi-source disturbances is fully considered, and the control effect of the lateral balance of the robust controller in the unmanned bicycle LPV model is verified based on the MATLAB simulation environment.

[0085] Simulation Group 1:

[0086] Set the simulation duration to 50 s and the step size to 0.005 s. Other settings are as follows:

[0087] (1) Set the initial state of the system: at the initial moment, the lateral tilt angle of the vehicle body is 10, the vehicle body tilt speed is 0, and the vehicle handlebar rotation angle and the vehicle handlebar rotation speed of the system are both set to 0;

[0088] (2) Simulation conditions: Set the vehicle speed V m = 2.1 m / s;

[0089] (3) Adding interference from internal sensors: Random interference is added to the frame inclination angle, handlebar rotation angle, frame inclination speed, and handlebar rotation speed respectively to simulate the effect of sensor noise.

[0090] (4) Adding interference from the external environment: By introducing lateral pulse torque interference on the frame, handlebar pulse torque interference, random handlebar torque interference, random lateral torque interference, and random interference of the vehicle body speed, various interferences brought about by environmental changes and terrain changes can be simulated.

[0091] From the data curve of Simulation Group 1 in the embodiment (Appendix Figure 4 ) it can be seen that:

[0092] (1) Generally, the amplitude of the lateral inclination angle of the unmanned bicycle is in the range of -0.170 to 0.110 rad, and the handlebar rotation angle also oscillates near the straight line of y = 0, indicating that the unmanned bicycle has achieved lateral balance.

[0093] (2) According to Figure 4 's schematic diagram, during this period, affected by multi-source interference, the lateral inclination angle of the frame quickly converges from 10 to about 0 within 0.8 s and fluctuates within the range of -0.01 to 0.01 rad; after being affected by the lateral pulse torque interference on the frame, it converges within 3.8 s, and the maximum inclination angle amplitude is within 0.07 rad; after being affected by the handlebar pulse torque interference, it converges within 1.6 s, and the maximum inclination angle amplitude is within 0.01 rad. The handlebar rotation angle is adjusted to about 0 within 1.1 s, and then swings within the range of -0.0 to 0.03 rad; after being affected by the lateral pulse torque interference on the frame, it converges within 3.6 s, and the maximum rotation angle amplitude is within 0.38 rad; after being affected by the handlebar pulse torque interference, it converges within 1.8 s, and the maximum rotation angle amplitude is within 0.2 rad.

[0094] Simulation Group 2:

[0095] Change the reaching law to a non-singular terminal sliding mode reaching law, and the remaining simulation settings are the same as those of Simulation Group 1.

[0096] From the data curve of Simulation Group 2 in the embodiment (Appendix Figure 5 ) it can be seen that:

[0097] (1) Generally, the amplitude of the lateral inclination angle of the unmanned bicycle is in the range of -0.210 to 0.240 rad, and the handlebar rotation angle also oscillates near the straight line of y = 0, indicating that the unmanned bicycle has achieved lateral balance.

[0098] (2) According to Figure 5As can be seen from the schematic diagram, during this period, affected by multi-source interference, the lateral tilt angle of the frame quickly converges from 10 to about 0 within 1.5 s and fluctuates within the range of -0.01 to 0.01 rad; after being affected by the lateral pulse torque of the frame, it converges within 2.2 s, and the maximum tilt angle amplitude is within 0.07 rad; after being affected by the pulse torque of the handlebar, it converges within 4.2 s, and the maximum tilt angle amplitude is within 0.21 rad. The handlebar angle is adjusted to about 0 within 1.8 s and then swings within the range of -0.15 to 0.15 rad; after being affected by the lateral pulse torque of the frame, it converges within 2 s, and the maximum rotation angle amplitude is within 0.24 rad; after being affected by the pulse torque of the handlebar, it converges within 4 s, and the maximum rotation angle amplitude is within 0.47 rad.

[0099] To sum up, by comparing the data curve graphs of Simulation Group 1 and Simulation Group 2, it can be seen that: the double-power combination sliding mode control method given by the present invention can greatly reduce the fluctuation range of the roll angle, greatly reduce the phenomenon of unmanned bicycle chatter, and the tilt angle and rotation angle of the closed-loop system can quickly converge to near 0 under the interference pulse. This shows that the closed-loop system has a strong anti-interference ability against multi-source interference within a certain range.

[0100] Embodiment 2 (physical prototype experiment):

[0101] The unmanned bicycle used in Embodiment 2 is as attached Figure 1 shown, and the measurement and control system is as attached Figure 3 shown.

[0102] The unmanned bicycle prototype is equipped with components such as a single-chip microcomputer system, an electronic control drive module, a Zigbee module, and an on-vehicle power supply system. Incremental encoders and absolute encoders are used to measure parameters such as the rotational speed of the rear wheel of the bicycle and the rotation angle of the handlebar; the MPU6050 gyroscope is used to measure the attitude of the vehicle; the main responsibility of the STM32 single-chip microcomputer is to receive the feedback of the vehicle body state from various sensors and implement servo control on the handlebar motor and the wheel motor, where the servo period is set to 5 ms; the main function of the Zigbee module is to transmit the state data and control instructions to the mobile device, and its communication period is set to 50 ms; the current sensor is responsible for collecting the drive current of the motor, and the bridge drives the motor according to the PWM signal sent by the single-chip microcomputer.

[0103] In this embodiment, the designs of the linear extended state observer, the linear sliding mode surface function, and the double-power combination sliding mode control law are the same as those in Embodiment 1, and this embodiment will directly use them.

[0104] Step 5: Control the output torque through the modulation pulse width signal of the STM32 single-chip microcomputer:

[0105] τ=k PWM ·V PWM

[0106] In the above formula, k PWM = k ω k τ (V S / 100 / R Ω ), where R Ω is the internal resistance of the handlebar motor coil, k ω is the reduction ratio of the transmission, k τ is the current torque coefficient of the drive motor, V S is the input voltage of the bridge, V PWM is the duty cycle. Taking R Ω as 3.4 Ω, V S as 24 V, k τ as 0.1109 N·m / A, and k ω as 71.

[0107] On a cement road surface, a physical prototype experiment of a driverless bicycle is carried out, and motion data is collected according to a cycle of 50 (ms / group).

[0108] From the data curve of Example 2 (Appendix Figure 6 ), it can be seen that:

[0109] Within 30 s of driving of the driverless bicycle, the fluctuations of the lateral inclination angle of the vehicle body and the handlebar rotation angle δ are both relatively small. The lateral inclination angle of the vehicle body fluctuates within the range of -0.016 to 0.022 rad, and the handlebar rotation angle oscillates within the range of -0.15 to 0.15 rad, indicating that the system jitter is small, the dynamic performance is good, and the driverless bicycle achieves good lateral balance.

[0110] In addition, as shown in Appendix Figure 7 , taking the roadblocks distributed in a straight line and marked with numbers as the reference objects during the driving process, it can be seen that the driverless bicycle achieves good balanced linear motion.

[0111] In summary, the double-power combination sliding mode control method given by the present invention can enable the driverless bicycle to reach a good balanced motion state, while ensuring the stability and fast convergence speed of the driving of the driverless bicycle, avoiding the chattering phenomenon, and thus ensuring the good dynamic performance of the driverless bicycle during driving.

[0112] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A dual-power combined sliding mode control method for lateral balance of an unmanned bicycle, comprising the following steps: Step 3. The observer model can be obtained from step 2. Then, the linear sliding surface function s is designed according to the double-power combined sliding mode control principle. Then, the fast power control term in the control law and the double-power control term are obtained. The double-power combined sliding mode control law of the system is obtained by combining the two.

2. The double-power combined sliding mode control method for lateral balance of an unmanned bicycle according to claim 1, characterized in that: The linear sliding surface function in step 3 is: In the formula, c Τ =(c1,c2), c1>0, c2>0. Assumptions Non-singular, the bi-power combined sliding mode control law in step 3 is: In the formula, u s =-k1fal(s,a,λ)-k2|s| b sgn(s), is the lumped interference term , k1>0, k2>0, a=1+γ, b=1-γ, 0<γ<1, λ=1, sgn(s) is the sign function, and the nonlinear double power combination function fal(s,a,λ) is defined as follows:

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