Self-adaptive control method based on balance car under-actuated model

Abstract

The invention provides a self-adaptive control method based on a balance car under-actuated model. According to the method, in order to facilitate design of a torque controller and transform an output matrix, the torque controller is divided into two new controllers to be designed respectively, and a new control quantity and an original control quantity have a mapping relation; according to the new control quantity, the balance car model is converted into a new balance car model, and the state change is designed into an integral chain form; and then designing a Lyapunov function, and designing an adaptive law through the Lee's stability theorem. The state quantity of the balance car is collected, and a new controller is adopted to obtain a new control quantity; and mapping back to the original control quantity to control the balance car to move. The pure self-adaptive control method is adopted, other control strategies do not need to be combined, parameter adjustment of the balance car under different control performance is met, continuous trial and error time is shortened, and robustness and stability of the control system can be guaranteed.

Description

Technical Field

[0001] The present invention relates to the technical field of balance vehicle control, and in particular to an adaptive control method based on an underactuated model of a balance vehicle. Background Art

[0002] As a typical underactuated nonlinear system, the self-balancing scooter is widely used in control theory and robotics research due to its compact structure and high control difficulty. An underactuated system is one in which the control input dimension is smaller than the system's degrees of freedom. This means that each degree of freedom cannot be independently controlled, resulting in significant challenges in motion control.

[0003] To address these issues, adaptive control methods have demonstrated significant advantages in controlling underactuated systems. Adaptive control can estimate unknown parameters online based on the system's operating state and dynamically adjust the control law, thereby enhancing the system's robustness to modeling errors and external disturbances. Compared to controllers with fixed parameters, adaptive controllers offer greater environmental adaptability and system robustness, making them particularly suitable for underactuated systems with complex structures and uncertain parameters.

[0004] However, because the under-actuated model has many unknown parameters, the current solution mostly uses a combination of adaptive control and other controls. Using only the adaptive control method is too difficult and the trial and error time is too long. Summary of the Invention

[0005] In view of this, the present invention provides an adaptive control method based on the under-actuated model of a balancing vehicle. It adopts a purely adaptive control method without the need to combine other control strategies. It not only meets the parameter adjustment requirements under different control performances of the balancing vehicle, but also reduces the time for continuous trial and error, and can ensure the robustness and stability of the control system.

[0006] In order to solve the above technical problems, the present invention is implemented as follows.

[0007] An adaptive control method based on an underactuated model of a balancing vehicle, comprising:

[0008] Step 1: Based on the characteristics of different state quantities in the self-balancing car model, the state quantities are divided into two categories, corresponding to two new control quantities u1 and u2 respectively. The new control quantities u1 and u2 have a mapping relationship with the original control quantities; the original control quantities are the output torques of the left and right wheel motors; based on the new control quantities u1 and u2, the self-balancing car model is converted into a new self-balancing car model;

[0009] Step 2: For the two new control variables u1 and u2, design an adaptive controller and its adaptive parameters to ensure that the new balancing car model meets the Lyapunov stability requirement.

[0010] Step 3: Collect the state quantity of the balance vehicle, update the adaptive law in combination with the adaptive parameters, and substitute it into the adaptive controller that conforms to Lyapunov stability to obtain the new control quantities u1 and u2; use the mapping relationship between the new control quantities u1 and u2 and the original control quantities to solve the original control quantities and control the movement of the balance vehicle.

[0011] Preferably, the step 1 is:

[0012] The mapping relationship between the new control quantities u1 and u2 and the original control quantities is: u1=T L +T R , u2=T L -T R ;T L is the output torque of the left wheel motor, T R Output torque for the right wheel motor;

[0013] According to the new control quantities u1 and u2, the balancing car model is converted into a new balancing car model:

[0014]

[0015] in:

[0016]

[0017] Where x is the displacement of the balancing vehicle, θ is the angle between the balancing vehicle and the vertical direction, and δ is the yaw angle of the balancing vehicle. and are the first and second derivatives of x, respectively. and are the first and second derivatives of θ, respectively. and are the first and second derivatives of δ respectively; m is the mass of the wheel, M is the mass of the vehicle body; l is the distance between the center of mass and the center of the chassis, g is the acceleration of gravity, I is the moment of inertia of the wheel, r is the radius of the wheel; d is the wheelbase, J δ is the moment of inertia of the vehicle body when it rotates in the vertical direction, J P is the moment of inertia of the vehicle body when it rotates around its center of mass.

[0018] Preferably, in step 2, based on Lyapunov stability, the new balancing car model is designed so that x, θ, The four stable states of the u1 controller are:

[0019]

[0020] in, is the estimated value of q1, Adaptive parameter k5>0; z1 and Adaptive laws need to be designed, and the adaptive laws are:

[0021]

[0022] in,

[0023]

[0024]

[0025] u1 controller and its z1 and There are 7 adaptive parameters that need to be adjusted in the adaptive law, namely: k1, k2, k5, σ1, γ1, these 7 adaptive parameters are all greater than 0, and need to meet the necessary conditions for system stability k2k3>k1k4; here k3, k4 are based on Substitute into formula (3) and (4) and reversely calculate;

[0026] In step 3, the adaptive parameters k1, k2, Substitute the values ​​of k5, σ1, and γ1 into formula (2) to update the adaptive law z1 and Then use formula (1) to obtain the u1 controller.

[0027] Preferably, in step 2, based on Lyapunov stability, the new balancing car model is designed so that δ, The two stable states of the u2 controller are:

[0028]

[0029] in, is the estimated value of q2, the adaptive parameter h3>0; z2 and Adaptive laws need to be designed, and the adaptive laws are:

[0030]

[0031] u2 controller and its z2 and There are five adaptive parameters that need to be adjusted in the adaptive law, namely: h1, h2, h3, σ2, γ2, and these five adaptive parameters are all greater than 0;

[0032] In step 3, determine the values ​​of adaptive parameters h1, h2, h3, σ2, γ2, and substitute them into formula (6) to update the adaptive law z2 and Then use formula (5) to obtain the u2 controller.

[0033] Preferably, in step 3, the original control amount is calculated by using the mapping relationship between the new control amounts u1 and u2 and the original control amount:

[0034]

[0035] The present invention also provides an adaptive controller based on the underactuated model of a balancing vehicle, comprising a system state quantity acquisition module, an adaptive parameter selection module, an adaptive law update module, a first controller u1, a second controller u2 and an original control quantity solution module;

[0036] According to the characteristics of different state quantities in the self-balancing vehicle model, the state quantities are divided into two categories, corresponding to two new control quantities u1 and u2 respectively. The new control quantities u1 and u2 have a mapping relationship with the original control quantities; the original control quantities are the output torques of the left and right wheel motors; according to the new control quantities u1 and u2, the self-balancing vehicle model is converted into a new self-balancing vehicle model; for the two new control quantities u1 and u2, adaptive controllers and their adaptive parameters are designed to make the new self-balancing vehicle model meet the Lyapunov stability requirement; the adaptive controllers that meet the Lyapunov stability requirement are the first controller u1 and the second controller u2 respectively;

[0037] The system state quantity acquisition module is used to collect the state quantity of the balance vehicle and provide it to the first controller u1, the second controller u2 and the adaptive law update module;

[0038] An adaptive parameter selection module is used to select adaptive parameters of the first controller u1 and the second controller u2 and provide them to the adaptive law update module;

[0039] An adaptive law updating module updates the adaptive laws of the first controller u1 and the second controller u2 using adaptive parameters and provides the adaptive laws to the first controller u1 and the second controller u2;

[0040] The first controller u1 and the second controller u2 output their respective control quantities u1 and u2, which are provided to the original control quantity solution module;

[0041] The original control quantity solution module solves the original control quantity according to the mapping relationship between u1 and u2 and the original control quantity, and controls the movement of the balance vehicle.

[0042] Preferably, the first controller u1 corresponds to x in the new balancing car model, θ, x is the displacement of the balancing car, θ is the angle between the balancing car and the vertical direction, is the first-order derivative of x, is the first-order derivative of θ;

[0043] Based on Lyapunov stability, we design the order x, θ, The first controller u1 of the four stable states is:

[0044]

[0045] in, is the estimated value of q1, Adaptive parameter k5>0; z1 and Adaptive laws need to be designed, and the adaptive laws are:

[0046]

[0047] in,

[0048]

[0049] The first controller u1 and its z1 and There are 7 adaptive parameters that need to be adjusted in the adaptive law, namely: k1, k2, k5, σ1, γ1, these 7 adaptive parameters are all greater than 0, and need to meet the necessary conditions for system stability k2k3>k1k4; here k3, k4 are based on Substitute into formula (3) and (4) and reversely calculate;

[0050] Where m is the mass of the wheel, M is the mass of the vehicle body; l is the distance between the center of mass and the center of the chassis, g is the acceleration of gravity, I is the moment of inertia of the wheel, r is the radius of the wheel; d is the wheelbase, J δ is the moment of inertia of the vehicle body when it rotates in the vertical direction, J P is the moment of inertia of the vehicle body when it rotates around its center of mass.

[0051] Preferably, the second controller u2 corresponds to δ in the new balancing car model, δ is the yaw angle of the balancing car, is the first derivative of δ;

[0052] Based on Lyapunov stability, the design of δ, The second controller u2 with two stable states is:

[0053]

[0054] in, is the estimated value of q2, the adaptive parameter h3>0; z2 in the second controller u2 and Adaptive laws need to be designed, and the adaptive laws are:

[0055]

[0056] The second controller u2 and its z2 and There are five adaptive parameters that need to be adjusted in the adaptive law, namely: h1, h2, h3, σ2, and γ2. These five adaptive parameters are all greater than 0.

[0057] Preferably, the new control quantities u1 and u2 have a mapping relationship with the original control quantities as follows:

[0058] u1=T L +T R ; u2=T L -T R ;

[0059] Among them, T L is the output torque of the left wheel motor, T R Output torque for the right wheel motor;

[0060] Then the original control quantity solution module solves the original control quantity according to the mapping relationship as follows:

[0061]

[0062] Beneficial effects:

[0063] The present invention establishes a model through kinematics. To facilitate the design of a torque controller, the output matrix is ​​transformed, the torque controller is divided into two controllers for separate design, and the state change of the modified model is designed in the form of an integral chain. At the same time, a Lyapunov function is designed, and an adaptive law is designed through the Lipschitz stability theorem to directly determine the adaptive parameters of the Lipschitz stability.

[0064] Compared with other traditional control applications on under-actuated systems, this invention designs a novel adaptive controller and proposes an adaptive parameter adjustment method for the adaptive controller, which makes up for the defect that the system performance is affected by the inability to change the system's own parameters.

[0065] Moreover, the present invention adopts a purely adaptive control method without the need to combine other control strategies. It not only satisfies the adjustment of parameters under different control performances of the balancing vehicle, but also reduces the time for continuous trial and error, and can ensure the robustness and stability of the control system. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a schematic diagram of the adaptive control method based on the under-actuated model of the balancing vehicle of the present invention.

[0067] Figure 2 This is the displacement tracking effect diagram under the original system parameters.

[0068] Figure 3 This is the tilt angle tracking effect diagram under the original system parameters.

[0069] Figure 4This is the steering angle tracking effect diagram under the original system parameters.

[0070] Figure 5 This is the displacement tracking effect diagram when the system changes its own parameters.

[0071] Figure 6 This is a diagram of the tilt angle tracking effect when the system changes its own parameters.

[0072] Figure 7 This is a diagram of the steering angle tracking effect when the system changes its own parameters.

[0073] Figure 8 This is a diagram of the displacement tracking effect when the system changes its own parameters and adaptive parameters.

[0074] Figure 9 This is a diagram of the tilt angle tracking effect when the system changes its own parameters and adaptive parameters.

[0075] Figure 10 This is a diagram of the steering angle tracking effect when the system changes its own parameters and adaptive parameters. DETAILED DESCRIPTION

[0076] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0077] The present invention provides an adaptive control method based on an underactuated model of a balancing vehicle. First, a model is established through kinematics. To facilitate the design of a torque controller, the output matrix is ​​transformed and the torque controller is divided into two controllers for separate design. The two controllers subsequently have almost the same design ideas, that is, the state change of the modified model is designed in the form of an integral chain. Then, a Lyapunov function is designed, and an adaptive law is designed through the Lipschitz stability theorem to directly determine the adaptive parameters of the Lipschitz stability.

[0078] The present invention adopts a purely adaptive control method without the need to combine other control strategies. It not only satisfies the adjustment of parameters under different control performances of the balancing vehicle, but also reduces the time for continuous trial and error, and can ensure the robustness and stability of the control system.

[0079] The specific steps of the present invention are as follows:

[0080] Step 1: First build a balance car model.

[0081] The parameters of the balance car are shown in the following table:

[0082]

[0083]

[0084] Table 1 Balance vehicle parameters

[0085] The balance car model is as follows:

[0086]

[0087] Where, and denote the first and second derivatives of ·, respectively; A 23 、A 43 is the one-dimensional parameter of the system matrix, B 21 、B 41 、B 62 is the one-dimensional parameter of the input matrix.

[0088] From the above model, it can be seen that the two torque controllers T L ,T R Control six variables x, θ, δ, Due to the form of the input matrix, the current model cannot be directly converted to an integrating chain form. However, the integrating chain form is a relatively common structure that can significantly simplify the subsequent control design process. Therefore, the present invention simplifies the model to an integrating chain form to achieve more efficient controller development in subsequent designs.

[0089] Therefore, the present invention transforms the input matrix into a special form to generate two new controllers u1 and u2. The new controllers u1 and u2 are consistent with the original control quantity T L ,T R Have a mapping relationship; the former controller controls the first four variables x, θ, The latter controller controls the last two variables δ, The specific form is as follows:

[0090] u1=T L +T R

[0091] u2=T L -T R

[0092] Based on the new controllers u1 and u2, the balance car model is converted to a new balance car model as follows:

[0093]

[0094] in:

[0095]

[0096] Step 2: Design the u1 controller.

[0097] For the control variable u1, an adaptive controller and its adaptive parameters are designed to make the balancing car model of formula (1) meet the Lyapunov stability.

[0098] The design process of this step is as follows: first, the model of formula (1) is transformed into an integral chain form, an equivalent model is designed based on the integral chain form, and the stability is judged by Routh criterion. Subsequently, the adaptive law and u1 controller are designed based on Li's stability.

[0099] The specific steps are as follows:

[0100] Step 2.1: Perform state transition:

[0101] In order to design the model state matrix into a standard form, the following state transformation is first performed:

[0102]

[0103] Among them, y1, y2, y3, y4 are new state quantities;

[0104] Let z1 = k1y1 + k2y2 + k3y3 + k4y4, where k1, k2, k3, k4 > 0, and y0 = [y1 y2 y3] T Combined with formula (3), we get the new system expression:

[0105]

[0106] From formula (4), we can see that the necessary condition for system stability is k2k3>k1k4.

[0107] Step 2.2: Design u1 controller and adaptive law:

[0108] During the controller design process, in order to ensure the stability of the system and simplify the derivation process of the Lyapunov function, after multiple analyses and attempts, the controller was finally designed as follows:

[0109]

[0110] in and is the estimated value of q1, And k5>0. From equation (5), z1 in the controller and Adaptive laws need to be designed, and their adaptive laws are:

[0111]

[0112] The parameters in formula (6) are defined as follows:

[0113]

[0114] σ1>0,γ1>0

[0115] Step 2.3: Perform stability analysis

[0116] By designing the Lyapunov function V1 as follows:

[0117]

[0118] in, And α1, α2> 0, P is an arbitrary positive definite matrix, and further derivation of the controller in formula (5) yields:

[0119]

[0120] When a>0 and β0>0 exists, Combining formula (7), we can conclude that there must be a set of adaptive parameters k1, k2, k5, σ1, γ1 make the system (4) stable, and the system (4) is a variation of the balancing car model (1), so when the controller is designed as (5), except for δ and The other four states are stable.

[0121] And when k5 and σ1 are large enough If γ1 is increased further, V1(∞) will be small enough, and y1 will be small enough, so the error can be arbitrarily small. Therefore, it can be concluded that k5 needs to be large enough. For the relationship between σ1 and γ1, the former is large enough, and the latter is appropriately large to meet the control accuracy when the former is determined.

[0122] Step 3: Design the u2 controller.

[0123] Similar to the design of controller u1, for the control quantity u1, an adaptive controller and its adaptive parameters are designed to make the balancing car model of formula (2) meet the Lyapunov stability.

[0124] Step 3.1: Perform state transition

[0125] Let w1=δ, Then the system transforms into the following form:

[0126]

[0127] in,

[0128] Step 3.2: Design controller u2 and adaptive law

[0129]

[0130] in and is the estimated value of q2 h3>0. From the controller in equation (9), it can be seen that z2 is related to Adaptive laws need to be designed, and their adaptive laws are:

[0131]

[0132] Among them, h 1,2 >0,σ2>0,γ2>0.

[0133] Step 3.3: Perform stability analysis

[0134] By designing the Lyapunov function V2 as follows:

[0135]

[0136] in, w0=[w1w2] T α3, α4>0, P is an arbitrary positive definite matrix. Similar to step 2.3, there must exist a set of adaptive parameters h1, h2, h3, σ2, γ2 that make system (8) stable. When h3 is large enough, the control performance will be improved. However, σ2 and γ2 cannot be blindly increased because they will affect the control performance in an inversely proportional manner during the adjustment process.

[0137] After the design of steps 2 and 3, the adaptive parameters are summarized as follows:

[0138] For the controller u1, there are seven adaptive parameters that need to be adjusted to control the displacement and pitch angle of the balancing car, namely k1, k2, k5, σ1, γ1. For controller u2, to control the steering angle of the self-balancing vehicle, there are five adaptive parameters that need to be adjusted: h1, h2, h3, σ2, and γ2. These 12 adaptive parameters must be greater than 0 and satisfy k2k3>k1k4. All parameters should be greater than zero.

[0139] Step 3: Control the movement of the balance car.

[0140] The state quantity of the balancing vehicle is collected, and the adaptive law is updated in combination with the adaptive parameters. The new control quantities u1 and u2 are obtained by substituting them into an adaptive controller that conforms to Lyapunov stability. The original control quantities are solved by using the mapping relationship between the new control quantities u1 and u2 and the original control quantities to control the movement of the balancing vehicle.

[0141] The original control quantity solving module solves the original control quantity according to the mapping relationship as follows:

[0142]

[0143] This concludes the process.

[0144] The present invention significantly improves the tracking performance of displacement, tilt angle and steering angle by adjusting the system parameters and applying adaptive parameters. Under the original system parameters, displacement tracking ( Figure 2 ) shows good tracking,accuracy and stability, and can accurately follow the target trajectory.,At the same time, the tilt angle tracking ( Figure 3 ) and steering angle tracking ( Figure 4 ) also demonstrated ideal performance. The system was able to respond quickly and stabilize at the target angle, accurately adjusting the steering angle to meet control requirements.

[0145] When the system changes its own parameters, the displacement tracking ( Figure 5 ), tilt angle tracking ( Figure 6 ) and steering angle tracking ( Figure 7 ) still maintains good results. Although parameter changes increase system complexity, tracking performance is not significantly affected, demonstrating the system's adaptability to dynamic changes. This shows that even with parameter changes, the system can still maintain high tracking accuracy and stability, meeting the dynamic requirements of practical applications.

[0146] Furthermore, when the system introduces adaptive parameters while changing its own parameters, displacement tracking ( Figure 8 ), tilt angle tracking ( Figure 9 ) and steering angle tracking ( Figure 10 ) performance has been significantly improved. The application of adaptive parameters enables the system to more efficiently respond to parameter changes, further optimizing tracking accuracy and adaptability. This improvement not only enhances the system's robustness but also enables it to maintain high-performance tracking capabilities under more complex operating conditions, providing a more reliable solution for practical applications.

[0147] Based on the above method, the present invention also provides an adaptive controller based on the underactuated model of the balancing vehicle, such as Figure 1 As shown, it includes a system state quantity acquisition module, an adaptive parameter selection module, an adaptive law update module, a first controller u1, a second controller u2 and an original control quantity solution module.

[0148] According to the characteristics of different state quantities in the balance car model, the state quantities are divided into two categories, corresponding to two new control quantities u1 and u2 respectively. The new control quantities u1 and u2 have a mapping relationship with the original control quantities; the original control quantities are the output torques of the left and right wheel motors; according to the new control quantities u1 and u2, the balance car model is converted into a new balance car model; for the two new control quantities u1 and u2, the adaptive controllers and their adaptive parameters that make the new balance car model meet the Lyapunov stability are designed; the adaptive controllers that meet the Lyapunov stability are u1 controller and u2 controller respectively.

[0149] The system state quantity acquisition module is used to collect the state quantity of the balance vehicle and provide it to the u1 controller, u2 controller and adaptive law update module.

[0150] The adaptive parameter selection module is used to select the adaptive parameters of the u1 controller and the u2 controller and provide them to the adaptive law update module.

[0151] The adaptive law update module uses the adaptive parameters to update the adaptive laws of the u1 controller and the u2 controller, and provides them to the u1 controller and the u2 controller.

[0152] The u1 controller and u2 controller output their respective control quantities u1 and u2, which are provided to the original control quantity solution module.

[0153] The original control quantity solution module solves the original control quantity according to the mapping relationship between u1 and u2 and the original control quantity, and controls the movement of the balance vehicle.

[0154] Among them, the first controller u1 corresponds to x in the new balancing car model, θ, x is the displacement of the balancing car, θ is the angle between the balancing car and the vertical direction, is the first-order derivative of x, is the first-order derivative of θ;

[0155] Based on Lyapunov stability, we design the order x, θ, The first controller u1 of the four stable states is:

[0156]

[0157] in, is the estimated value of q1, Adaptive parameter k5>0; z1 and Adaptive laws need to be designed, and the adaptive laws are:

[0158]

[0159] in,

[0160]

[0161] The first controller u1 and its z1 and There are 7 adaptive parameters that need to be adjusted in the adaptive law, namely: k1, k2, k5, σ1, γ1, these 7 adaptive parameters are all greater than 0, and need to meet the necessary conditions for system stability k2k3>k1k4; here k3, k4 are based on Substitute into formula (3) and (4) and reversely calculate to obtain:

[0162] Among them, the second controller u2 corresponds to δ in the new balancing car model, δ is the yaw angle of the balancing car, is the first derivative of δ;

[0163] Based on Lyapunov stability, the design of δ, The second controller u2 with two stable states is:

[0164]

[0165] in, is the estimated value of q2, the adaptive parameter h3>0; z2 in the second controller u2 and Adaptive laws need to be designed, and the adaptive laws are:

[0166]

[0167] The second controller u2 and its z2 and There are five adaptive parameters that need to be adjusted in the adaptive law, namely: h1, h2, h3, σ2, and γ2. These five adaptive parameters are all greater than 0.

[0168] The above specific embodiments merely illustrate the design principles of the present invention. The shapes and names of the components described herein may vary and are not limiting. Therefore, those skilled in the art may modify or substitute equivalents for the technical solutions described in the above embodiments. Such modifications and substitutions, without departing from the inventive spirit and technical solutions of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. An adaptive control method based on an underactuated model of a balancing vehicle, characterized in that: include: Step 1: Based on the characteristics of different state quantities in the self-balancing car model, the state quantities are divided into two categories, corresponding to two new control quantities u1 and u2 respectively. The new control quantities u1 and u2 have a mapping relationship with the original control quantities; the original control quantities are the output torques of the left and right wheel motors; based on the new control quantities u1 and u2, the self-balancing car model is converted into a new self-balancing car model; Step 2: For the two new control variables u1 and u2, design an adaptive controller and its adaptive parameters to ensure that the new balancing car model meets the Lyapunov stability requirement. Step 3: Collect the state quantity of the balance vehicle, update the adaptive law in combination with the adaptive parameters, and substitute it into the adaptive controller that conforms to Lyapunov stability to obtain the new control quantities u1 and u2; use the mapping relationship between the new control quantities u1 and u2 and the original control quantities to solve the original control quantities and control the movement of the balance vehicle.

2. The method according to claim 1, wherein The step 1 is: The mapping relationship between the new control quantities u1 and u2 and the original control quantities is: u1=T L +T R , u2=T L -T R ;T L is the output torque of the left wheel motor, T R Output torque for the right wheel motor; According to the new control quantities u1 and u2, the balancing car model is converted into a new balancing car model: in: Where x is the displacement of the balancing vehicle, θ is the angle between the balancing vehicle and the vertical direction, and δ is the yaw angle of the balancing vehicle. and are the first and second derivatives of x, respectively. and are the first and second derivatives of θ, respectively. and are the first and second derivatives of δ respectively; m is the mass of the wheel, M is the mass of the vehicle body; l is the distance between the center of mass and the center of the chassis, g is the acceleration of gravity, I is the moment of inertia of the wheel, r is the radius of the wheel; d is the wheelbase, J δ is the moment of inertia of the vehicle body when it rotates in the vertical direction, J P is the moment of inertia of the vehicle body when it rotates around its center of mass.

3. The method according to claim 2, wherein In step 2, based on Lyapunov stability, the new balancing car model is designed so that x, θ, The four stable states of the u1 controller are: in, is the estimated value of q1, Adaptive parameter k5>0; z1 and Adaptive laws need to be designed, and the adaptive laws are: in, u1 controller and its z1 and There are 7 adaptive parameters that need to be adjusted in the adaptive law, namely: k1, k2, k5, σ1, γ1, these 7 adaptive parameters are all greater than 0, and need to meet the necessary conditions for system stability k2k3>k1k4; here k3, k4 are based on Substitute into formula (3) and (4) and reversely calculate; In step 3, the adaptive parameters k1, k2, Substitute the values ​​of k5, σ1, and γ1 into formula (2) to update the adaptive law z1 and Then use formula (1) to obtain the u1 controller.

4. The method according to claim 2, wherein In step 2, based on Lyapunov stability, the new balancing car model is designed so that δ, The two stable states of the u2 controller are: in, is the estimated value of q2, the adaptive parameter h3>0; z2 and Adaptive laws need to be designed, and the adaptive laws are: u2 controller and its z2 and There are five adaptive parameters that need to be adjusted in the adaptive law, namely: h1, h2, h3, σ2, γ2, and these five adaptive parameters are all greater than 0; In step 3, determine the values ​​of adaptive parameters h1, h2, h3, σ2, γ2, and substitute them into formula (6) to update the adaptive law z2 and Then use formula (5) to obtain the u2 controller.

5. The method according to claim 2, wherein In step 3, the mapping relationship between the new control quantities u1 and u2 and the original control quantities is used to calculate the original control quantities as follows:

6. An adaptive controller based on the underactuated model of a balancing vehicle, characterized in that: It includes a system state quantity acquisition module, an adaptive parameter selection module, an adaptive law update module, a first controller u1, a second controller u2 and an original control quantity solution module; According to the characteristics of different state quantities in the self-balancing vehicle model, the state quantities are divided into two categories, corresponding to two new control quantities u1 and u2 respectively. The new control quantities u1 and u2 have a mapping relationship with the original control quantities; the original control quantities are the output torques of the left and right wheel motors; according to the new control quantities u1 and u2, the self-balancing vehicle model is converted into a new self-balancing vehicle model; for the two new control quantities u1 and u2, adaptive controllers and their adaptive parameters are designed to make the new self-balancing vehicle model meet the Lyapunov stability requirement; the adaptive controllers that meet the Lyapunov stability requirement are the first controller u1 and the second controller u2 respectively; The system state quantity acquisition module is used to collect the state quantity of the balance vehicle and provide it to the first controller u1, the second controller u2 and the adaptive law update module; An adaptive parameter selection module is used to select adaptive parameters of the first controller u1 and the second controller u2 and provide them to the adaptive law update module; An adaptive law updating module updates the adaptive laws of the first controller u1 and the second controller u2 using adaptive parameters and provides the adaptive laws to the first controller u1 and the second controller u2; The first controller u1 and the second controller u2 output their respective control quantities u1 and u2, which are provided to the original control quantity solution module; The original control quantity solution module solves the original control quantity according to the mapping relationship between u1 and u2 and the original control quantity, and controls the movement of the balance vehicle.

7. The device according to claim 6, characterized in that The first controller u1 corresponds to x in the new balancing car model, θ, x is the displacement of the balancing car, θ is the angle between the balancing car and the vertical direction, is the first-order derivative of x, is the first-order derivative of θ; Based on Lyapunov stability, we design the order x, θ, The first controller u1 of the four stable states is: in, is the estimated value of q1, Adaptive parameter k5>0; z1 and Adaptive laws need to be designed, and the adaptive laws are: in, The first controller u1 and its z1 and There are 7 adaptive parameters that need to be adjusted in the adaptive law, namely: k1, k2, k5, σ1, γ1, these 7 adaptive parameters are all greater than 0, and need to meet the necessary conditions for system stability k2k3>k1k4; here k3, k4 are based on Substitute into formula (3) and (4) and reversely calculate; Where m is the mass of the wheel, M is the mass of the vehicle body; l is the distance between the center of mass and the center of the chassis, g is the acceleration of gravity, I is the moment of inertia of the wheel, r is the radius of the wheel; d is the wheelbase, J δ is the moment of inertia of the vehicle body when it rotates in the vertical direction, J P is the moment of inertia of the vehicle body when it rotates around its center of mass.

8. The device according to claim 6, wherein The second controller u2 corresponds to the new balancing car model δ, δ is the yaw angle of the balancing car, is the first derivative of δ; Based on Lyapunov stability, the design of δ, The second controller u2 with two stable states is: in, is the estimated value of q2, the adaptive parameter h3>0; z2 in the second controller u2 and Adaptive laws need to be designed, and the adaptive laws are: The second controller u2 and its z2 and There are five adaptive parameters that need to be adjusted in the adaptive law, namely: h1, h2, h3, σ2, and γ2. These five adaptive parameters are all greater than 0.

9. The device according to claim 6, wherein The mapping relationship between the new control quantities u1 and u2 and the original control quantities is: u1=T L +T R ;u2=T L -T R ; Among them, T L is the output torque of the left wheel motor, T R Output torque for the right wheel motor; Then the original control quantity solution module solves the original control quantity according to the mapping relationship as follows:

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