Method for controlling traveling of two-wheeled traveling system, and two-wheeled traveling system

Abstract

Provided are a method for controlling travel of a two-wheel travel system, a two-wheel travel system, and a computer-readable storage medium. The two-wheel travel system includes a front handle steering assembly and a rear wheel driving assembly. The method includes: determining a dynamic characteristic quantity and a kinematic characteristic quantity of the two-wheel travel system based on a travel state parameter of the two-wheel travel system; determining a tracking constraint condition for the two-wheel travel system to continue traveling along a desired trajectory based on the kinematic characteristic quantity of the two-wheel travel system and the desired trajectory; determining a balance constraint condition for the two-wheel travel system to maintain dynamic balance during travel based on the dynamic characteristic quantity and the kinematic characteristic quantity of the two-wheel travel system; and determining a travel driving force provided by the rear wheel driving assembly and a steering angle acceleration provided by the front handle steering assembly based on the above. The method ensures that the two-wheel travel system travels along a desired trajectory accurately while maintaining dynamic balance.

Description

Technical Field

[0001] Embodiments of this disclosure relate to a method for controlling the movement of a two-wheeled driving system, the two-wheeled driving system, and a computer-readable storage medium. Background Technology

[0002] With the widespread application of artificial intelligence and robotics in civilian and commercial fields, robots based on artificial intelligence and robotics are playing an increasingly important role in fields such as intelligent transportation and smart homes, and are also facing higher requirements.

[0003] A mobile robot is a mechanical device capable of automatically performing tasks. It can be controlled by humans in real time, run pre-programmed routines, or act according to principles established using artificial intelligence. Its purpose is to assist or replace humans in certain tasks, such as in manufacturing, construction, or hazardous work. Based on their mode of movement, mobile robots are classified as: wheeled mobile robots, legged mobile robots, snake-like mobile robots, tracked mobile robots, crawling robots, etc.

[0004] Autonomous bicycles are a typical example of mobile robots, being environmentally friendly, inexpensive, and easy to manufacture. Currently, autonomous bicycles are already capable of carrying children and disabled people, delivering packages, and avoiding traffic accidents in confined environments.

[0005] However, compared to four-wheel drive cars, autonomous bicycles have only two contact points with the road during operation, making it difficult to maintain balance and prone to tipping over. Furthermore, autonomous bicycles need to follow a desired trajectory to avoid obstacles and reach a predetermined location. However, ensuring the autonomous bicycle maintains its balance while precisely following the desired trajectory remains a pressing problem to be solved. Summary of the Invention

[0006] At least one embodiment of this disclosure provides a method for controlling the driving of a two-wheeled driving system, wherein the two-wheeled driving system includes a front handlebar steering assembly and a rear wheel drive assembly. The method includes: acquiring driving state parameters of the two-wheeled driving system, and determining dynamic and kinematic characteristic quantities of the two-wheeled driving system; based on the dynamic and kinematic characteristic quantities and a desired trajectory of the two-wheeled driving system, determining a driving force provided by the rear wheel drive assembly and a steering angular acceleration provided by the front handlebar steering assembly; wherein the driving force provided by the rear wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly cause the two-wheeled driving system to continue driving along the desired trajectory and maintain dynamic balance during driving.

[0007] At least one embodiment of this disclosure provides a two-wheel driving system, the two-wheel driving system including a front handlebar steering assembly and a rear wheel drive assembly, wherein the driving force provided by the rear wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly are determined according to the aforementioned method.

[0008] At least one embodiment of this disclosure provides a computer-readable storage medium having computer-readable instructions stored thereon, which, when executed by a computer, perform the above-described method.

[0009] According to another aspect of this disclosure, a computer program product or computer program is provided, comprising computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable medium and executes the computer instructions, causing the computer device to perform the methods provided in the foregoing aspects or various alternative implementations of the foregoing aspects.

[0010] The method for controlling a two-wheeled driving system disclosed herein determines the propulsion force and steering angular velocity of the two-wheeled driving system by means of dynamic characteristic quantities, kinematic characteristic quantities and desired trajectory, thereby ensuring the dynamic balance of the two-wheeled driving system while ensuring that the two-wheeled driving system travels accurately along the desired trajectory. Attached Figure Description

[0011] To more clearly illustrate the technical solutions of the embodiments of this disclosure, the accompanying drawings of the embodiments will be briefly described below. Obviously, the drawings described below only relate to some embodiments of this disclosure and are not intended to limit this disclosure.

[0012] Figure 1 This is an example schematic diagram of a two-wheeled driving system 10 according to an embodiment of the present disclosure.

[0013] Figure 2A This is a flowchart of a method for a two-wheeled driving system according to at least one embodiment of the present disclosure.

[0014] Figure 2B This is a schematic diagram illustrating the parameter annotations of the driving state parameters of a two-wheel driving system according to at least one embodiment of the present disclosure.

[0015] Figure 3 This is yet another exemplary flowchart of a method for controlling the movement of a two-wheeled driving system according to embodiments of the present disclosure.

[0016] Figure 4A Here are examples of parameters for a two-wheeled driving system according to at least one embodiment of the present disclosure.

[0017] Figure 4B According to Figure 4A A curve comparing the predetermined trajectory and the actual trajectory of a two-wheeled driving system traveling around a predetermined "circle-line" trajectory, determined by the parameters.

[0018] Figure 4C According to Figure 4A The diagram shows four different moments when the two-wheeled driving system, with parameters determined, is traveling along a predetermined "circle-line" trajectory.

[0019] Figure 4D According to Figure 4A The graph shows the comparison between the predetermined trajectory and the actual trajectory of the two-wheeled driving system that travels around a predetermined "8" shape, determined by the parameters.

[0020] Figure 4E According to Figure 4A The diagram shows four different moments when the two-wheeled driving system, with parameters determined, is traveling along a predetermined "8"-shaped trajectory.

[0021] Figure 5 A schematic diagram of an electronic device according to an embodiment of the present disclosure is shown.

[0022] Figure 6 A schematic diagram of the architecture of an exemplary computing device according to an embodiment of the present disclosure is shown.

[0023] Figure 7 A schematic diagram of a storage medium according to an embodiment of the present disclosure is shown. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of this disclosure clearer, the technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this disclosure. All other embodiments obtained by those skilled in the art based on the described embodiments of this disclosure without creative effort are within the scope of protection of this disclosure.

[0025] Unless otherwise defined, the technical or scientific terms used in this disclosure shall have the ordinary meaning understood by one of ordinary skill in the art to which this disclosure pertains. The terms “first,” “second,” and similar terms used in this disclosure do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as “comprising” or “including” mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as “connected” or “linked” are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as “upper,” “lower,” “left,” and “right” are used only to indicate relative positional relationships, and these relative positional relationships may change accordingly when the absolute position of the described objects changes.

[0026] To make the objectives, technical solutions, and advantages of this disclosure clearer, the embodiments of this disclosure will be described in further detail below with reference to the accompanying drawings.

[0027] Artificial intelligence (AI) is the theory, methods, technology, and application systems that use mathematical or digital computers to control machines to simulate, extend, and expand human intelligence, perceive the environment, acquire knowledge, and use that knowledge to achieve optimal results. In other words, AI is a comprehensive technology within computer science that attempts to understand the essence of intelligence and produce new intelligent machines that can react in a way similar to human intelligence. AI studies the design principles and implementation methods of various intelligent machines, enabling them to possess perception, reasoning, and decision-making capabilities.

[0028] Artificial intelligence (AI) is a comprehensive discipline encompassing a wide range of fields, including both hardware and software technologies. Fundamental AI technologies generally include sensors, dedicated AI chips, cloud computing, distributed storage, big data processing, operating / interactive systems, and mechatronics.

[0029] A robot is a machine device that automatically performs tasks and is controlled by computer programs or electronic circuits. A robot generally consists of actuators, drive mechanisms, detection devices, control systems, and complex mechanical components.

[0030] Based on the different spaces in which the control variables reside, robot control can be divided into joint space control and Cartesian space control. For serial multi-joint robots, joint space control controls the variables of each joint, while Cartesian space control controls the variables of the robot's end effector. According to the different control variables, robot control can be categorized into: position control, velocity control, acceleration control, force control, and force-position hybrid control. These controls can be either joint space control or end-effector Cartesian space control.

[0031] For example, robot control methods can be categorized into PID (Proportional-Integral-Differential) control, variable structure control, adaptive control, fuzzy control, and neural network control. PID control calculates the control quantity based on the control system's error using proportional, integral, and derivative functions. Variable structure control involves multiple controllers in the control system, employing different controllers under different conditions according to certain rules. Adaptive control allows the designed system to adaptively adjust system parameters or control strategies to meet design requirements even when the input or disturbance changes significantly. Fuzzy control involves fuzzifying the input quantity into fuzzy variables, using fuzzy rules to derive a fuzzy output, and then defuzzifying to obtain a clear output for control. Neural network control is a new branch of intelligent control, a product of the combination of neural network theory and control theory, and is an evolving discipline. It integrates theories, technologies, methods, and research results from disciplines including mathematics, biology, neurophysiology, brain science, genetics, artificial intelligence, computer science, and automatic control.

[0032] Figure 1 This is an example schematic diagram of a two-wheeled driving system 10 according to an embodiment of the present disclosure.

[0033] The two-wheel driving system 10 may include: a main frame 110, a front handlebar steering assembly 120, and a rear-wheel drive assembly 130. Optionally, the two-wheel driving system 10 may also include a static balancing assembly 140.

[0034] In this embodiment of the disclosure, the two-wheeled driving system 10 refers to a powered tool that can maintain its own balance and has two wheels. Exemplarily, the two-wheeled driving system 10 can be any of the following: a self-balancing two-wheeled driving system, a self-balancing robot, a self-balancing motorcycle, a self-balancing electric vehicle, a self-balancing two-wheeled car, or other tools with two wheels. This embodiment of the disclosure does not limit the product form of the two-wheeled driving system 10. In one possible implementation, the two-wheeled driving system 10 can be applied in a manned scenario; in another possible implementation, the two-wheeled driving system 10 can be applied in a non-manned scenario, such as an autonomous driving scenario, a delivery scenario (delivering express packages, food delivery, goods delivery, etc.), or other scenarios. It should be noted that... Figure 1 The two-wheel driving system 10 is described in the form of a two-wheel driving system only, and is merely an example and should not be construed as limiting the two-wheel driving system 10.

[0035] The front handlebar steering assembly 120 and the rear-wheel drive assembly 130 are two independent components. The front handlebar steering assembly 120 controls the direction of travel of the two-wheeled driving system 10, and the rear-wheel drive assembly 130 enables the movement of the two-wheeled driving system 10. The main frame 110 supports and connects the front handlebar steering assembly 120 and the rear-wheel drive assembly 130, ensuring that they maintain a relatively suitable position. Exemplarily, the main frame 110 can be a one-piece main frame, a trapezoidal main frame, a beam-type main frame, or other types of main frames. In possible implementations, when the two-wheeled driving system 10 is a two-wheeled driving system, the main frame 110 can be a vehicle frame. In an illustrative embodiment, the power required for the two-wheeled driving system 10 can be provided by the front handlebar steering assembly 120, the rear-wheel drive assembly 130, or both the front handlebar steering assembly 120 and the rear-wheel drive assembly 130 together.

[0036] The front handlebar steering assembly 120 and the rear wheel drive assembly 130 are respectively connected to the main frame 110.

[0037] The front handlebar steering assembly 120 includes a front wheel 121, a front handlebar 122, and a steering motor 123. The front wheel 121 is fitted onto the front handlebar 122, and the steering motor 123 is provided at the connection between the front handlebar 122 and the frame 110. The steering motor 123 drives the rotation of the front handlebar 122 to achieve steering control of the front wheel 121, thereby achieving dynamic balance.

[0038] The rear-wheel drive assembly 130 includes a rear wheel 131 and a drive motor 132, which drives the rear wheel 131 to rotate to provide driving force for the balanced two-wheel drive system to move forward.

[0039] Optionally, the frame 110 is also equipped with an inertial measurement unit (IMU) to acquire tilt angle data and acceleration data of the frame 110 in order to understand the current state of the frame. Furthermore, the frame 110 is also equipped with an auxiliary wheel to support the frame 110 when it tilts, preventing damage to the hardware caused by the fall of the balanced two-wheel driving system.

[0040] Optionally, the static balancing assembly 140 can also be mounted on the main frame 110. The static balancing assembly 140 may include a momentum wheel 141 (also known as a flywheel) and a momentum wheel motor 142. The shaft of the momentum wheel 141 is arranged along the front-rear direction of the self-balancing two-wheeled vehicle, that is, the direction of the shaft of the momentum wheel 141 is perpendicular to the direction of the front and rear wheel axles. The momentum wheel 141 is sleeved on the output shaft 143 of the momentum wheel motor 142. The momentum wheel motor 142 drives the rotation of the momentum wheel 141 through the output shaft 143 to provide the torque to achieve static balance.

[0041] Based on the above-mentioned balanced two-wheel driving system structure, the dynamic balancing process can be achieved by controlling the rotation of the front handlebar 122 of the two-wheel driving system through the steering motor 123; the static balancing process can be achieved by the momentum wheel 141 additionally set on the two-wheel driving system, through the torque generated during the rotation of the momentum wheel 141; the two can be combined to achieve the balance of the two-wheel driving system under dynamic and static conditions respectively.

[0042] Embodiments of this disclosure provide a method for controlling the driving of a two-wheeled driving system, wherein the two-wheeled driving system includes a front handlebar steering assembly and a rear wheel drive assembly. The method includes: acquiring driving state parameters of the two-wheeled driving system, and determining dynamic characteristic quantities and kinematic characteristic quantities of the two-wheeled driving system; based on the dynamic characteristic quantities, kinematic characteristic quantities, and desired trajectory of the two-wheeled driving system, determining the driving force provided by the rear wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly; wherein the driving force provided by the rear wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly enable the two-wheeled driving system to continue driving along the desired trajectory and maintain dynamic balance during driving.

[0043] Embodiments of this disclosure also provide a method for controlling a two-wheeled driving system, wherein the two-wheeled driving system includes a front handlebar steering assembly and a rear wheel drive assembly. The method includes: determining dynamic and kinematic characteristic quantities of the two-wheeled driving system based on driving state parameters of the two-wheeled driving system; determining tracking constraints for the two-wheeled driving system to continue driving along the desired trajectory based on the kinematic characteristic quantities of the two-wheeled driving system and the desired trajectory; determining balance constraints for the two-wheeled driving system to maintain dynamic balance during driving based on the dynamic and kinematic characteristic quantities of the two-wheeled driving system; and determining the driving force provided by the rear wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly based on the balance constraints and the tracking constraints.

[0044] The method for controlling a two-wheeled driving system disclosed herein determines the propulsion force and steering angular velocity of the two-wheeled driving system through interrelated balance constraints and tracking constraints, thereby ensuring the dynamic balance of the two-wheeled driving system while ensuring that the two-wheeled driving system travels accurately along the required trajectory.

[0045] Figure 2A This is a flowchart of a method 20 for a two-wheeled driving system 10 according to at least one embodiment of the present disclosure. Figure 2B This is a schematic diagram illustrating the driving state parameters of a two-wheel driving system 10 according to at least one embodiment of the present disclosure.

[0046] See Figure 2A The method 20 according to at least one embodiment of the present disclosure may include steps S201 to S202.

[0047] In step S201, the driving state parameters of the two-wheel driving system are obtained, and the dynamic characteristic quantities and kinematic characteristic quantities of the two-wheel driving system are determined.

[0048] In step S202, based on the dynamic characteristics, kinematic characteristics, and desired trajectory of the two-wheeled driving system, the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the handlebar steering assembly are determined. The driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the handlebar steering assembly enable the two-wheeled driving system to continue traveling along the desired trajectory and maintain dynamic balance during driving.

[0049] For example, the dynamic characteristic quantities of the two-wheeled driving system 10 are intended to characterize the dynamic characteristics possessed by the two-wheeled driving system 10, such as its kinetic energy, potential energy, momentum, etc. The motion characteristics of the two-wheeled driving system 10 are intended to characterize the features possessed by the two-wheeled driving system 10 during motion, such as its motion mode, motion speed, current motion acceleration, etc. The embodiments of this disclosure are not limited to the specific composition of the dynamic characteristic quantities and kinematic characteristic quantities of the two-wheeled driving system 10.

[0050] For example, driving state parameters, dynamic characteristics, and kinematic characteristics may all be related to the structure of the two-wheel driving system 10. See below for reference. Figure 2B The driving state parameters, dynamic characteristics and kinematic characteristics involved in the two-wheel driving system 10 according to an embodiment of the present disclosure are described.

[0051] As one embodiment, the two-wheel drive system 10 may include a frame crossbeam. The front steering assembly of the two-wheel drive system 10 includes a front wheel, a front handlebar, and a steering motor. The rear-wheel drive assembly includes a rear wheel and a drive motor.

[0052] Optionally, in the presence of the above structure, the driving state parameters may include one or more of the following: the roll angle of the two-wheeled driving system, the actual steering angle of the handlebars, the angle between the bottom bracket of the handlebars and the frame crossbeam, the contact point position of the rear wheel with the ground, the contact point position of the front wheel with the ground, the center of gravity position of the two-wheeled driving system, the distance between the contact point position of the rear wheel with the ground and the contact point position of the front wheel with the ground, the intersection of the bottom bracket of the handlebars with the ground, the yaw angle of the two-wheeled driving system, the forward speed of the two-wheeled driving system, the total mass of the two-wheeled driving system, the moment of inertia of the two-wheeled driving system, and the height of the center of gravity of the two-wheeled driving system.

[0053] Figure 2B The driving state parameters related to the dynamic and kinematic characteristics of the two-wheel driving system 10 are shown. These driving state parameters can all be detected by sensors on the two-wheel driving system 10 at time t. Those skilled in the art will understand that the driving state parameters related to the dynamic and kinematic characteristics of the two-wheel driving system 10 can include not only... Figure 2B The driving state parameters shown may include all or some of the driving state parameters, and may also include more or fewer driving state parameters. This disclosure does not impose any limitations on this.

[0054] For example, in Figure 2BThe basic three-dimensional coordinate system O-XYZ is marked, and a three-dimensional coordinate system P1-xyz for the two-wheeled driving system 10 is constructed based on the contact point P1 between the two-wheeled driving system 10 and the ground. The straight line P1z extends in the vertical direction, the straight line P1x extends in the vehicle direction of the two-wheeled driving system 10, and the straight line P1y extends perpendicular to both the straight line P1x and the straight line P1z. The reference plane R1 is defined by the straight lines P1z and P1x.

[0055] For example, in some embodiments, Figure 2B Further annotations are provided: the roll angle θ of the two-wheel driving system 10 (the angle between the two-wheel driving system 10 and the reference plane R1), which defines a roll plane R2 including the straight line P1x and having an angle θ with the plane R1; and the actual steering angle δ of the handlebars of the two-wheel driving system 10 (the angle between the handlebars and the roll plane R2), which defines a steering plane R3 having an angle δ with the roll plane R2.

[0056] For example, in some embodiments, Figure 2B Further annotations are provided: the angle α between the bottom axle of the handlebars of the two-wheeled driving system 10 and the crossbeam of the frame of the two-wheeled driving system 10; the horizontal distance b between the contact point P1 of the rear wheel of the two-wheeled driving system 10 and the projection point of the center of mass of the two-wheeled driving system 10 in the P1x direction; the distance L between the contact points of the front wheel and the ground and the contact points of the rear wheel of the two-wheeled driving system 10 and the ground along the P1x direction; and the distance Δ between the intersection of the bottom axle of the handlebars of the two-wheeled driving system 10 and the ground and the contact point of the front wheel of the two-wheeled driving system 10 and the ground.

[0057] For example, based on the actual steering angle δ and roll angle θ of the handlebars of the two-wheel driving system 10, the effective steering angle δ of the two-wheel driving system 10 can be calculated. f (The angle between the handlebars of the two-wheel driving system 10 and the reference plane R1).

[0058] For example, the effective steering angle δ of the front handlebars can be obtained based on the following formula (1). f When δ is not equal to zero, the two-wheel driving system 10 will move along a circle.

[0059] tan(δ f cos(θ)=tan(δ)sin(α) (1)

[0060] When δ is not equal to zero, the two-wheel driving system 10 follows... Figure 2B The diagram shows the circular motion of a circle with center C and curvature σ. Based on... Figure 2B σ can be calculated using formula (2).

[0061] σ=tan(δ f ) / L (2)

[0062] Combining formulas (1) and (2), we can obtain formula (3a).

[0063]

[0064] Therefore, based on the above formulas (1), (2), and (3a), the formula used to calculate u can be determined. σ Formula (3b), u σ That is, the turning acceleration of a bicycle when it is moving in a circle.

[0065]

[0066] The total mass of the two-wheeled driving system 10 is m. The moment of inertia of the two-wheeled driving system 10 is I, the height of the center of mass of the two-wheeled driving system 10 is h, and the gravitational acceleration is g, which can be taken as 9.8 N / kg for example.

[0067] In the following text, x and y will be used to represent the position of P1 in the R1 plane, and ψ (not shown) will represent the yaw angle formed by OX and P1x. In some embodiments, the forward speed v of the rear wheel of the two-wheeled driving system 10 when it has a contact point P1 with the road is detected by sensors on the two-wheeled driving system 10. Based on the transformation relationship between the R1 plane and the R2 plane, the center point of the two-wheeled driving system 10 in the R2 plane (e.g., ...) can be determined based on the forward speed v. Figure 2B (As shown by the small black dot in the image) the velocity v along the directions P1x, P1y, and P1z x v y and v z For example, the velocity v can be determined according to formula (4). x v y and v z .

[0068]

[0069] In the following text, u will be used δ This refers to the steering angular acceleration provided by the front steering assembly; specifically, the steering angular acceleration u. δ Let F be the derivative of the actual steering angle δ. F will be used to represent the total thrust exerted by the rear-wheel drive assembly and the front steering assembly on the two-wheel drive system 10.

[0070] The following is based on Figure 2BThe driving state parameters shown are provided as an example of determining the dynamic and kinematic characteristics of the two-wheel driving system based on the driving state parameters of the two-wheel driving system. Those skilled in the art should understand that the methods for determining the dynamic and kinematic characteristics of the two-wheel driving system based on the driving state parameters of the two-wheel driving system are not limited to this.

[0071] For example, since the two-wheeled driving system 10 can be modeled as a single pendulum model or an inverted pendulum model, the kinetic energy T and potential energy U of the two-wheeled driving system 10 can be determined according to formula (5).

[0072]

[0073] The two-wheel driving system 10 is a typical steel structure, therefore, the following Euler-Lagrange equation (i.e., formula (6)) can be calculated.

[0074]

[0075] in, For the Lagrange operator; q i Let τ be the i-th dimension vector in the multidimensional angle vector q. The multidimensional angle vector q is, for example, a two-dimensional angle vector and includes two sub-elements: the roll angle θ of the two-wheel drive system 10 and the rotation angle of the rear wheel. In this case, τ is the external force and is a two-dimensional vector. i The torque vector τ represents the torque corresponding to the i-th sub-element of the two-dimensional angle vector, where i is a positive integer greater than or equal to 1 and less than or equal to 2. The multidimensional angle vector q can also include angle vectors of more dimensions. For example, when the static balance component 140 also performs work on the two-wheel driving system 10, the sub-elements of the multidimensional angle vector q can also include the rotation angle of the momentum wheel 141. This disclosure does not limit the dimension of the multidimensional angle vector q.

[0076] Therefore, based on formula (6), the relationship between the dynamic characteristic quantities of the two-wheel driving system 10 can be obtained. The relationship between the dynamic characteristic quantities of the two-wheel driving system 10 is shown below using formulas (7a) and (7b).

[0077]

[0078]

[0079] Where τ Δ (θ,δ f The error is caused by the caster effect of the two-wheel driving system 10. The other parameters are as described above and will not be repeated here.

[0080] Based on ω=-vσ and the kinematic principles of the two-wheel driving system 10, the total propulsion force F can be designed as follows: Therefore, ignoring τ Δ (θ,δ f Under the influence of the above dynamic characteristic quantities, the relationship between the kinematic characteristic quantities of the two-wheel driving system 10 can be obtained at least in part based on the relationship between the above dynamic characteristic quantities. The relationship between the kinematic characteristic quantities of the two-wheel driving system 10 is shown below by formulas (8a) to (8f).

[0081]

[0082]

[0083]

[0084]

[0085]

[0086]

[0087] in,

[0088] Here, all the above parameters correspond to the actual values ​​measured by the two-wheeled driving system 10 at time t. For example, v represents the actual forward speed detected at time t when the two-wheeled driving system is traveling along the desired trajectory (i.e., the forward speed of the two-wheeled driving system). x represents the projection of the actual position of the two-wheeled driving system detected at time t along the desired trajectory onto the x-axis in the R1 plane (i.e., the horizontal component of the contact point position of the two-wheeled driving system). y represents the projection of the actual position of the two-wheeled driving system detected at time t along the desired trajectory onto the y-axis in the R1 plane (i.e., the vertical component of the contact point position of the two-wheeled driving system). ω represents the steering angular velocity of the two-wheeled driving system with respect to the yaw angle detected at time t when the two-wheeled driving system is traveling along the desired trajectory (i.e., the steering angular velocity of the two-wheeled driving system). ψ represents the actual yaw angle detected at time t when the two-wheeled driving system is traveling along the desired trajectory (i.e., the yaw angle of the two-wheeled driving system). u ω The value represents the actual steering angular acceleration (i.e., the steering angular acceleration of the two-wheeled driving system) detected at time t for the yaw angle as the two-wheeled driving system travels along the desired trajectory. vLet ω, v, u represent the actual forward acceleration detected at time t when the two-wheeled driving system travels along the desired trajectory (i.e., the forward acceleration of the two-wheeled driving system). Let θ represent the roll angle detected at time t when the two-wheeled driving system travels along the desired trajectory (i.e., the roll angle of the two-wheeled driving system), θ∈(-π / 2,π / 2). ω and u v All are bounded, and for all t>0, v>0.

[0089] Optionally, the desired trajectory indicates the ideal driving parameters that the two-wheeled driving system is expected to have as it travels from its current position to a target position. In some embodiments, the desired trajectory is represented by the forward speed, position, and steering angular velocity that the ideal two-wheeled driving system should achieve at the current moment when traveling along the desired trajectory. In other embodiments, the desired trajectory is represented by the steering angular acceleration, forward acceleration, and so on that the ideal two-wheeled driving system should have at the current moment when traveling along the desired trajectory. Those skilled in the art will understand that this disclosure is not limited thereto.

[0090] As an example, assume that the desired trajectory is represented by formulas (9a) to (9f).

[0091]

[0092]

[0093]

[0094]

[0095]

[0096]

[0097] In this context, the driving state parameters of an ideal two-wheeled driving system traveling along a desired trajectory are denoted by the subscript d. For example, v d x represents the forward speed that an ideal two-wheeled driving system should reach at time t when traveling along the desired trajectory (i.e., the forward speed set by the desired trajectory). d y represents the projection of the position that the ideal two-wheeled driving system should reach at time t when traveling along the desired trajectory onto the x-axis of the R1 plane (i.e., the horizontal component of the contact point position set by the desired trajectory). d ω represents the projection of the position that the ideal two-wheeled driving system should reach at time t along the desired trajectory onto the y-axis of the R1 plane (i.e., the vertical component of the contact point position set by the desired trajectory). dψ represents the steering angular velocity (i.e., the steering angular velocity set for the desired trajectory) that an ideal two-wheeled driving system should achieve at time t with respect to the yaw angle when traveling along the desired trajectory. d This represents the yaw angle that an ideal two-wheeled driving system should reach at time t when traveling along the desired trajectory (i.e., the yaw angle set by the desired trajectory). ω , d This represents the steering angular acceleration (i.e., the steering angular acceleration set for the desired trajectory) that an ideal two-wheeled driving system should achieve at time t with respect to the yaw angle when traveling along the desired trajectory. v,d θ represents the forward acceleration that an ideal two-wheeled driving system should achieve at time t when traveling along a desired trajectory (i.e., the forward acceleration set by the desired trajectory). d Let θ represent the roll angle that an ideal two-wheeled driving system should reach at time t when traveling along the desired trajectory (i.e., the roll angle set by the desired trajectory). d ∈(-π / 2,π / 2). ω d ,v d ,u ω,d and u v,d All are bounded, and for all t>0, v d >0.

[0098] Therefore, in order to ensure that the driving trajectory of the two-wheel driving system 10 can follow the desired trajectory as accurately as possible, x should be guaranteed. d The difference between x and y d The difference between y and v d The difference between v and ψ d The difference between ψ and ω d The difference between ω and ω should be as small as possible.

[0099] Optionally, step S202 further includes: determining the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly, such that the two-wheel drive system satisfies tracking constraints and balance constraints. The tracking constraints are determined based on the kinematic characteristics of the two-wheel drive system and the desired trajectory, while the balance constraints are determined based on the dynamic and kinematic characteristics of the two-wheel drive system.

[0100] Optionally, any constraint that enables the two-wheeled driving system 10 to travel along the desired trajectory as accurately as possible can be called a tracking constraint. For example, a tracking constraint can be one or more of the following: x d The maximum difference between x and y d The maximum difference between v and y d The maximum difference between ψ and vd The maximum difference between ψ and ω d The maximum difference between x and ω, etc. Tracking constraints can also be one or more of the following: x d The difference between x and y converges / stabilizes, or y d The difference between v and y converges / stabilizes, or v d The difference between ψ and v converges / stable, ψ d The difference between ψ and ω converges / stabilizes, and ω d The difference between ω and ω converges / stabilizes, etc. This disclosure does not impose further restrictions on the tracking constraints, as long as they contribute to a sufficiently small difference between the actual driving trajectory and the desired trajectory of the two-wheel driving system 10.

[0101] Optionally, to maintain balance in a two-wheeled driving system, the roll angle θ should be as small as possible, ideally less than 90° (if the roll angle is equal to 90°, the two-wheeled driving system will tip over). Simultaneously, the rotational speed at the roll angle θ should not be too large and needs to converge to 0 before contact with the ground; that is, the downward rotational kinetic energy should ideally converge as quickly as possible. Therefore, balance constraints for maintaining dynamic equilibrium of the two-wheeled driving system during operation can be designed based on the dynamic characteristics of the system.

[0102] In some embodiments, any constraint condition that benefits the two-wheeled driving system 10 in maintaining dynamic balance during driving is referred to as a balance constraint condition. Since the dynamic balance constraint condition is related to the roll angle θ, the balance constraint condition can be obtained based on formulas (8f) and (9f). For example, the balance constraint condition can be any one or more of the following: roll angle θ d The maximum difference between the roll angle θ and the rotational speed at the roll angle θ The maximum value of the rotational acceleration at the roll angle θ Convergence / stability, etc. This disclosure does not impose further restrictions on the balance constraints, as long as they contribute to maintaining the dynamic balance of the two-wheeled driving system 10 during operation.

[0103] Optionally, the balance constraint and the tracking constraint can be expressed mathematically. For example, the mathematical expression is: In some embodiments, the mathematical expression is: In some embodiments, the mathematical expression is: The mathematical expressions above are not intended to limit this disclosure, but are only for further explanation below.

[0104] The driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly will act on the two-wheel driving system 10. Therefore, at time t, the driving state parameters x, y, ψ, ω, v, θ, etc., are all related to the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly. Based on both balance constraints and tracking constraints, the driving force that the rear-wheel drive assembly of the two-wheel driving system 10 should provide at time t, and the steering angular acceleration that the front handlebar steering assembly should provide at time t, can be determined.

[0105] Those skilled in the art will understand that the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly can be determined based on even more constraints. For example, regarding Figure 1 Regarding the two-wheel driving system 10 shown, the constraint conditions for the steering angular acceleration provided by the front handlebar steering assembly can also be determined based on the model of the steering motor 123, the maximum torque that the steering motor 123 can provide, the mechanical structure of the front handlebar 122, the torque of the front handlebar 122, etc. Similarly, the constraint conditions for the driving force provided by the rear wheel drive assembly can be determined based on the model of the drive motor 132, the maximum torque that the drive motor 132 can provide, the mechanical structure of the rear wheel 131, the torque of the rear wheel 131, etc. This disclosure is not limited to these limitations.

[0106] Therefore, the method for controlling a two-wheeled driving system provided in this disclosure determines the propulsion force and steering angular velocity of the two-wheeled driving system by means of dynamic characteristic quantities, kinematic characteristic quantities and desired trajectory, thereby ensuring the dynamic balance of the two-wheeled driving system while ensuring that the two-wheeled driving system travels accurately along the desired trajectory.

[0107] The following is for reference Figure 3 The method for determining the balance constraints and the tracking constraints is further described.

[0108] Optionally, the tracking constraint condition is tracking error convergence, and the tracking error includes: the error between the forward speed of the two-wheel driving system and the forward speed set by the desired trajectory, and the error between the forward acceleration of the two-wheel driving system and the forward acceleration set by the desired trajectory.

[0109] Optionally, refer to Figure 3 The step of determining the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly, so that the two-wheel driving system satisfies the tracking constraint condition and the balance constraint condition, further includes: calculating the tracking error using a tracking error sub-model; and determining the driving force provided by the rear-wheel drive assembly so that the tracking error converges.

[0110] Optionally, such as Figure 3 As shown, the tracking error sub-model is determined by the tracking constraints and the balance constraints.

[0111] For example, refer to Figure 3 Various tracking errors associated with the tracking constraints can be defined as follows. Tracking errors may include x as defined in formula (10). e ,y e ,ψ e ,ω e ,v e One or more of them.

[0112]

[0113] Where x is the component of the rear wheel's contact point with the ground in the forward direction. t is the component of the rear wheel's contact point with the ground perpendicular to the forward direction. ψ is the yaw angle of the two-wheel drive system. v is the forward velocity of the two-wheel drive system. ω is the steering angular velocity of the two-wheel drive system.

[0114] Where, x d The component of the rear wheel contact point with the ground in the forward direction, set for the desired trajectory. y d ψ is the component of the rear wheel contact point position with the ground, set for the desired trajectory, perpendicular to the direction of travel. d The yaw angle set for the desired trajectory. d The forward velocity set for the desired trajectory. ω d The steering angular velocity set for the desired trajectory.

[0115] Where, x e The component of the error in the forward direction between the contact point position of the rear wheel and the ground and the contact point position set for the desired trajectory. e ψ is the component of the error between the contact point position of the rear wheel and the ground and the contact point position set for the desired trajectory, perpendicular to the direction of travel. e The error between the yaw angle of the two-wheeled driving system and the yaw angle set for the desired trajectory. e The error between the forward speed of the two-wheeled driving system and the forward speed set for the desired trajectory. ω e The error between the steering angular velocity of the two-wheel driving system and the steering angular velocity set for the desired trajectory.

[0116] As described above, in some embodiments, the tracking constraint is satisfied if any one of the tracking errors converges. In some embodiments, the tracking constraint is satisfied if multiple tracking errors converge. In some embodiments, the tracking constraint is satisfied if any one of the tracking errors is less than a predetermined value. In some embodiments, the tracking constraint is satisfied if all multiple tracking errors are less than their corresponding predetermined values. This disclosure is not limited thereto.

[0117] Optionally, the balance constraint condition ensures that the balance error sub-model remains stable. Determining the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly, such that the two-wheel drive system satisfies the tracking constraint condition and the balance constraint condition, further includes: using the balance error sub-model to determine the steering angular acceleration provided by the front handlebar steering assembly, so that the balance error sub-model remains stable when the steering angular acceleration is used as input; wherein, the balance error sub-model is jointly determined by the tracking constraint condition and the balance constraint condition, and while the balance error sub-model remains stable, the two-wheel drive system maintains dynamic balance during driving.

[0118] For example, various parameters associated with the balance constraints can be defined as follows. The various parameters associated with the balance constraints may include η1 and η2 involved in formula (11), and the parameters associated with η1 and η2. η 1,e η 2,e .

[0119] Where η1=θ and Using approximations, sin(θ) = θ and cos(θ) = 1, equations (8f) and (9f) can be obtained using equation (11).

[0120]

[0121] in, m is the total mass of the two-wheeled driving system, h is the height of the center of gravity of the two-wheeled driving system, I is the moment of inertia of the two-wheeled driving system, g is the acceleration due to gravity, and b is the horizontal distance between the contact point between the rear wheel and the ground and the center of gravity of the two-wheeled driving system.

[0122] Furthermore, η 1,e =η 1,d -η1 and η 2,e =η 2,d -η2. That is, η 1,e This represents the roll angle θ of the two-wheel driving system compared to the roll angle θ set for the desired trajectory.d The error between them. η 2,e The parameter η2, which is associated with the roll angle θ of the two-wheel drive system, is related to the roll angle θ set for the desired trajectory. d The associated parameter η 2,d The error between them. η 1,d The derivative is η 2,d The derivative is The derivative of η1 is The derivative of η2 is

[0123] As described above, in some embodiments, the balance constraint condition is satisfied if any one of the aforementioned balance errors converges. In some embodiments, the balance constraint condition is satisfied if multiple of the aforementioned balance errors converge. In some embodiments, the balance constraint condition is satisfied if any one of the aforementioned balance errors is less than a predetermined value. In some embodiments, the balance constraint condition is satisfied if all of the aforementioned balance errors are less than their corresponding predetermined values. This disclosure is not limited thereto.

[0124] Therefore, based on formula 8-11, and using the approximate value ω e v e =0, and the following driving error model can be obtained.

[0125]

[0126]

[0127] ∑ t This represents the tracking error submodel because it contains x e and y e . ∑ b This represents the equilibrium error sub-model because it contains η 1,e , and η 2,e Both the tracking error sub-model and the balancing error sub-model involve the same or related parameters, for example, v. e .

[0128] Where ω is the steering angular velocity of the two-wheel driving system. e The component of the error in the forward direction between the contact point position of the rear wheel and the ground and the contact point position set for the desired trajectory. e The component of the error between the contact point position of the rear wheel and the ground and the contact point position set for the desired trajectory, in the direction perpendicular to the forward direction. e The error between the forward speed of the two-wheeled driving system and the forward speed set for the desired trajectory. d The forward velocity set for the desired trajectory. ψe The error between the yaw angle of the two-wheeled driving system and the yaw angle set for the desired trajectory. v,d The forward acceleration, u, is set for the desired trajectory. v The forward acceleration of the two-wheel driving system. For x e The derivative of . For y e The derivative of . For v e The derivative of .

[0129] Among them, u ω,d The steering angle acceleration, u, is set for the desired trajectory. ω ω is the steering angular acceleration provided by the front steering assembly. d The steering angular velocity, v, is set for the desired trajectory. e The error between the forward speed of the two-wheeled driving system and the forward speed set for the desired trajectory.

[0130]

[0131] η 1,e =η 1,d -η1, η 2,e =η 2,d -η2, η 1,d The derivative is η 2,d The derivative is The derivative of η1 is The derivative of η2 is

[0132] η1=θ,

[0133] v d The forward speed is set for the desired trajectory, θ is the roll angle of the two-wheeled driving system, m is the total mass of the two-wheeled driving system, h is the height of the center of gravity of the two-wheeled driving system, I is the moment of inertia of the two-wheeled driving system, g is the acceleration due to gravity, and b is the horizontal distance between the contact point between the rear wheel and the ground and the center of gravity of the two-wheeled driving system.

[0134] The above formula (12a) is only for the tracking error sub-model ∑ t An example. Of course, the tracking error submodel ∑ t It can also include more or less tracking error, and formula (12a) is not a tracking error sub-model ∑ t The unique expression for . Those skilled in the art should understand that the tracking error sub-model ∑ tThe number of parameters and equations / inequalities can be introduced depending on the rigidity of the two-wheeled driving system.

[0135] The above formula (12b) is only for the equilibrium error sub-model ∑ b An example. However, the balanced error submodel ∑ b It can also include more or fewer parameters, and formula (12b) is not a balanced error sub-model ∑ b The unique expression for ∑. Those skilled in the art should understand that the equilibrium error sub-model ∑ b The number of parameters and equations / inequalities can be introduced depending on the rigidity of the two-wheeled driving system.

[0136] The following further describes how to determine the driving force provided by the rear-wheel drive assembly that controls the convergence of the tracking error of the tracking error sub-model. Those skilled in the art will understand that the driving force provided by the rear-wheel drive assembly that controls the convergence of the tracking error of the tracking error sub-model can be determined in various ways. The following uses backstepping as an example to explain one way of obtaining the driving force provided by the rear-wheel drive assembly; however, those skilled in the art should understand that this disclosure is not limited thereto.

[0137] For example, see Figure 3 Based on the tracking error sub-model, the driving force provided by the rear-wheel drive assembly, which controls the convergence of the tracking error of the tracking error sub-model, is determined using the backstepping method. According to formula (12a), when ψ e =0, x e =c1ωy e When c1 is a positive value and a constant, y e It can be stable at zero. Therefore, by backstepping, the following variables are defined.

[0138]

[0139] According to formulas (12a) and (13), and The representation is:

[0140]

[0141] Formula (14) reduces the order of the tracking error sub-model.

[0142] According to formula (14), u can be designed v The driving force provided by the rear-wheel drive assembly is related to u v Proportional.

[0143] For ease of description, we define formula (15).

[0144]

[0145] Where c2 is a positive constant. Therefore, The expression is (see formula (16)).

[0146]

[0147] definition Then u v It is determined to be (see formula (17)):

[0148]

[0149] Where c1, c2, and c3 are all positive numbers. u ω For a two-wheeled driving system, the steering angular acceleration with respect to the yaw angle. for The derivative of . At this point, the driving force provided by the rear-wheel drive assembly is determined to be positively correlated with the steering angular acceleration of the two-wheel drive system with respect to the yaw angle.

[0150] To facilitate analysis, the u determined by formula (17) is used. v To determine whether the stability of the driving error model / tracking error sub-model will be affected, a candidate Lyapunov function V for the tracking error sub-model is defined here. t .

[0151]

[0152] Combining formulas (12a), (14)-(18), we can obtain V. t The derivative with respect to t is (see formula (19)):

[0153]

[0154] if If u is less than zero, then the tracking error corresponding to the tracking error sub-model must be convergent. Therefore, u v The optimal value should make Less than zero. Therefore, in some embodiments, the candidate Lyapunov function of the error submodel is... A value less than zero can also be used as a tracking constraint or a balance constraint.

[0155] The following further describes how the steering angular acceleration provided by the front handlebar steering assembly is determined. Those skilled in the art will understand that for each fixed v... d The corresponding steering angular acceleration u provided by the front steering assembly can be determined in various ways.ω See also Figure 3 The following uses the optimal control method as an example to explain an example of how to obtain the steering angular acceleration provided by the front handlebar steering assembly. Those skilled in the art should understand that this disclosure is not limited thereto.

[0156] Optionally, based on the above derivation, it can be determined that the mismatch interference of the tracking error sub-model with respect to the balance error sub-model is at least partially based on the steering angular velocity of the desired trajectory and the error between the forward speed of the two-wheel driving system and the forward speed set for the desired trajectory. For example, according to formula (12b), for ∑ b ω d v e It can be considered to originate from ∑ t The mismatch interference (i.e., the mismatch interference between the tracking error sub-model and the balance error sub-model). Therefore, the optimal control method is used to design u. ω The purpose is to make ω d v e The impact on the stability of χ can be minimized.

[0157] Based on the above derivation, using the optimal control method, u can be expressed by the following formula (20). ω .

[0158]

[0159] in,

[0160] μ and φ are any values ​​greater than zero, y e The component of the error between the contact point position of the rear wheel and the ground and the contact point position set for the desired trajectory, perpendicular to the forward direction, is considered. At this time, the steering angular acceleration provided by the front handlebar steering assembly is determined to be positively correlated with the component of the error between the contact point position of the rear wheel and the ground and the contact point position set for the desired trajectory, perpendicular to the forward direction.

[0161] Therefore, formula (12b) can be rewritten as formula (21).

[0162]

[0163] in, According to the optimal control method It can be designed as (see formula (22)):

[0164]

[0165] The matrix K can be obtained by solving the following Riccati formula (see formula (23)):

[0166]

[0167] in, Matrix R is the Riccati equation constructed based on matrices A, B, and D. The parameter is P, which is a solution to the Riccati equation. A T Let B be the transpose of matrix A. T This is the transpose of matrix B. Where I4 and O4 are the four-dimensional identity matrix and the zero matrix, respectively. γ is a real number. As an example, γ is 1.5. Of course, γ can also be other values, and this disclosure is not limited to them.

[0168] To facilitate analysis, the u determined by formula (20) is used. ω To determine whether the stability of the driving error model / balance error sub-model will be affected, a candidate Lyapunov function V for the balance error sub-model is defined here. b That is, formula (24).

[0169]

[0170] According to optimal control theory, if formula (25) holds, then the equilibrium error sub-model is stable.

[0171]

[0172] In order to make the candidate Lyapunov function V of the balanced error submodel b Candidate Lyapunov function V for tracking error submodel t All of these methods can stabilize the aforementioned balance error sub-model, tracking error sub-model, and driving error model, requiring adjustments to the parameters that may be involved in these models.

[0173] The following describes two methods for adjusting the parameters in the driving error model. Those skilled in the art should understand that there may be various ways to adjust the parameters in the driving error model, and this disclosure does not limit them.

[0174] For bounded ω and u ω (That is, the mathematical expression is: |ω|≤M(ω) and |u ω |≤M(u ω ), where M(ω) is also the boundary of ω, M(u ω That is, u ωRegarding the boundary conditions, the following describes two methods for adjusting the parameters in the driving error model in two cases: ω≠0 and ω=0. Method one applies to ω≠0, and method two applies to ω=0.

[0175] See Figure 3 The tracking error sub-model and the balance error sub-model constitute a driving error model. The tracking error sub-model has a first gain relative to the balance error sub-model, and the balance error sub-model has a second gain relative to the tracking error sub-model. The first gain and the second gain constitute the total gain of the driving force and the steering angle acceleration relative to the driving error model. The parameters in the tracking error sub-model and the balance error sub-model are adjusted based on the total gain so that the two-wheel driving system satisfies the tracking constraint condition and the balance constraint condition.

[0176] Therefore, Method 1 further includes: determining a first gain of the tracking error sub-model to the balance error sub-model and a second gain of the balance error sub-model to the tracking error sub-model based on the tracking error sub-model and the balance error sub-model; determining the total gain of the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly to the driving error model based on the first gain and the second gain; adjusting the parameters in the tracking error sub-model and the balance error sub-model based on the total gain; and determining the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly based on the adjusted tracking error sub-model and the balance error sub-model.

[0177] In the case of ω≠0, ω≠0 implies that there exists ρ>0 such that |ω|>ρ. According to Young's inequality theorem and formula (19), the following inequality (26) can be obtained:

[0178]

[0179] because, and According to formula (26), the following inequality (27) can be obtained:

[0180]

[0181] in, and The following formula (28) can guarantee that and

[0182]

[0183] Next, according to formula (15), the following inequality (29) can be obtained:

[0184]

[0185] also, and As a result, using formula (25), we can obtain the following inequality (30):

[0186]

[0187] According to formula (27), from ∑ b To ∑ t The gain can be calculated using formula (31), which is the second gain mentioned above:

[0188]

[0189] According to formula (30), from ∑ t To ∑ b The gain can be calculated using formula (32), which is the first gain mentioned above:

[0190]

[0191] Where, ω d ,v d And φ satisfy the following conditions (i.e., formula (33)):

[0192]

[0193] Therefore, if formula (28) is satisfied, then the total gain g bt g tb <1. According to the small gain theory, the driving error system is asymptotically stable at this point.

[0194] That is, by adjusting parameters c1 and c2, so that and Where, |ω|≤M(ω), |u ω |≤M(u ω The formula |ω|>ρ>0 ensures that the above-mentioned balance error sub-model, tracking error sub-model, and driving error model are asymptotically stable when ω≠0.

[0195] Of course, those skilled in the art should understand that the total gain g bt g tbThe expression can change accordingly with variations in the rigidity of the two-wheeled driving system. This disclosure does not specifically limit the method of adjusting the parameters in the tracking error sub-model and the balancing error sub-model, as long as the total gain g is satisfied. bt g tb <1 is sufficient.

[0196] See also Figure 3 The tracking error sub-model and the balance error sub-model constitute a driving error model. The driving error model is equivalent to a combination of a cascaded first stability analysis sub-model and a second stability analysis sub-model. The parameters in the tracking error sub-model and the balance error sub-model are configured such that the first stability analysis sub-model is input-to-state stable and the second stability analysis sub-model is locally exponentially low stable. When the first stability analysis sub-model is input-to-state stable and the second stability analysis sub-model is locally exponentially low stable, the two-wheel driving system satisfies the tracking constraint condition and the balance constraint condition.

[0197] Therefore, further, Method 2 includes: determining a first stability analysis sub-model and a second stability analysis sub-model based on the driving error model, wherein the first stability analysis sub-model and the second stability analysis sub-model are cascaded; adjusting the parameters in the driving error model so that the first stability analysis sub-model is input-to-state stable and the second stability analysis sub-model is exponentially stable; determining the tracking error sub-model and the balance error sub-model based on the driving error model after parameter adjustment; and determining the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly based on the determined tracking error sub-model and the balance error sub-model.

[0198] When ω = 0, according to the stability theorem (Lemma) for nonlinear feedforward systems (the driving error model is a typical nonlinear feedforward system): if the influencing variables in the nonlinear feedforward system are bounded (i.e., |ω| ≤ M(ω) and |u| ≤ M(ω)), then... ω |≤M(u ω If a nonlinear feedforward system can be decomposed into two cascaded subsystems, and the lower cascaded subsystem is input-state stable while the upper cascaded subsystem is locally exponentially unstable, then the nonlinear feedforward system is globally asymptotically stable.

[0199] The stability theorem for nonlinear feedforward systems can be defined mathematically as follows.

[0200] If a nonlinear feedforward system defined by expression (34) has f(0) = 0 and l(0) = 0, and is defined as follows: And given G = g(0), then μ exists when the following two conditions are met. * >0 and φ * >0, such that for any μ∈(0,μ * ) and φ∈(0,φ * This nonlinear feedforward system is globally asymptotically stable at the origin.

[0201]

[0202] The two conditions mentioned above are as follows:

[0203] Condition ①: It is an input-to-state (ISS) system and It is locally exponentially stable (LES).

[0204] Condition ②: HW -1 G < 0. Locally exponentially stable (LES) can also be called locally asymptotically stable.

[0205] That is, there exists μ * >0 and φ * >0, such that for any μ∈(0,μ * ) and φ∈(0,φ * The closed-loop system defined by the following formula (35) is globally asymptotically stable at the origin.

[0206]

[0207] When ω=0, At that time, based on the u obtained in the above steps v and u ω The driving error model in formulas (12a) and (12b) can be written in the following form, namely formula (36):

[0208]

[0209] Where, ∑ ξ This is the first stability analysis sub-model. In formula (36), Bu is removed. c The part following the component is the second stability analysis sub-model.

[0210] Define ∑ ξ The candidate Lyapunov function is given by formula (37).

[0211]

[0212] Where a > 0 and is a constant scalar. Consider u. c =0, according to formula (36), It can be expressed as formula (38).

[0213]

[0214] If formula (33) is to be satisfied, it means that:

[0215]

[0216] Therefore, there exists Make:

[0217]

[0218] Formula (40) can be used to derive the following inequality (41).

[0219]

[0220] Therefore, there exist a,λ>0 such that Therefore, when u c When = 0, ∑ ξ It is the input that reaches a stable state. At this point, ∑ ξ It is ISS (that is, the first stability analysis sub-model is input-to-state stable), while the second stability analysis sub-model is locally exponentially low stable. Therefore, condition ① holds for formula (36).

[0221] At this point, we can directly verify whether the current parameters meet condition ②. Once condition ② is met, the driving error model is asymptotically stable.

[0222] That is, by adjusting parameters c1, c2, and c3, so that Where a is a inequality and Any real number of ω can make the above-mentioned balance error sub-model, tracking error sub-model and driving error model asymptotically stable when ω=0.

[0223] Of course, those skilled in the art should understand that the expressions for the first and second stability analysis sub-models can change accordingly with variations in the rigidity of the two-wheeled driving system. This disclosure does not specifically limit the method of adjusting the parameters in the tracking error sub-model and the balance error sub-model, as long as the first stability analysis sub-model is input-to-state stable and the second stability analysis sub-model is locally exponentially low stable. Once the parameters in the driving error model are adjusted to make the first stability analysis sub-model input-to-state stable and the second stability analysis sub-model locally exponentially low stable, the driving error model stabilizes / converges when ω = 0. At this point, the determined propulsion force and steering angular velocity of the two-wheeled driving system can ensure both the dynamic balance of the two-wheeled driving system and its precise movement along the desired trajectory.

[0224] Figure 4A Here are examples of parameters for a two-wheeled driving system according to at least one embodiment of the present disclosure. Figure 4B According to Figure 4A A curve comparing the predetermined trajectory and the actual trajectory of a two-wheeled driving system traveling around a predetermined "circle-line" trajectory, determined by the parameters. Figure 4C According to Figure 4A The diagram shows four different moments when the two-wheeled driving system, with parameters determined, is traveling along a predetermined "circle-line" trajectory. Figure 4D According to Figure 4A The graph shows the comparison between the predetermined trajectory and the actual trajectory of the two-wheeled driving system that travels around a predetermined "8" shape, determined by the parameters. Figure 4E According to Figure 4A The diagram shows four different moments when the two-wheeled driving system, with parameters determined, is traveling along a predetermined "8"-shaped trajectory.

[0225] See Figure 4A Assuming Figure 1 and Figure 2B The two-wheeled driving system 10 shown has the parameters shown in the parameter table of the two-wheeled driving system. The content shown in [] is the unit of the parameter.

[0226] The following parameters were used to verify that the driving force provided by the rear-wheel drive assembly and the steering angle acceleration provided by the front handlebar steering assembly, as determined by method 20, can ensure the dynamic balance of the two-wheel drive system while ensuring that the two-wheel drive system travels accurately along the desired trajectory.

[0227] Specifically, the parameters in the experiment were set as follows: c1 = 2, c2 = 3, c3 = 200, μ = 4, φ = 4, γ = 0.3, R = 1, Q = diag[1,1,1,1] and ε = 0.1.

[0228] Figure 4B A predetermined trajectory of a "circle-line" shape was defined (which is in... Figure 4B (The curve is represented by a dashed line in graph (a)). The radius of the circle in the predetermined trajectory is 10m. The two-wheeled driving system 10 moves forward at a speed v. d =4m / s, trace the circle three times counterclockwise, and then move forward along the straight line shown by the dotted line. Figure 4B The horizontal axis of the curve (a) is the projection of the contact point between the rear wheel of the two-wheel driving system 10 and the ground in the X-axis direction of the basic three-dimensional coordinate system O-XYZ. Figure 4B The vertical axis of the curve (a) is the projection of the contact point between the rear wheel of the two-wheel driving system 10 and the ground in the Y-axis direction of the basic three-dimensional coordinate system O-XYZ.

[0229] The initial state of the two-wheel driving system 10 is x0 = 12, y0 = -1, ψ0 = π / 2, v0 = 0, ω0 = 0, θ0 = 0. And δ0 = 0. In the initial 0.2 seconds, as the two-wheel drive system 10 accelerates from a standstill, the static balancing component 140 is used to balance the two-wheel drive system 10. See also... Figure 4B The curve (a) shows the actual trajectory of the two-wheeled driving system 10 under the aforementioned parameters, represented by a solid line. It can be seen that the difference between the actual trajectory and the predetermined trajectory of the two-wheeled driving system 10 is very small. That is, under these parameters, the two-wheeled driving system can accurately travel along the desired trajectory.

[0230] Figure 4B The graph (b) further illustrates the changes in the horizontal components of the actual trajectory and the planned trajectory over time. Specifically, Figure 4B The vertical axis of the curve (b) is the projection of the contact point between the rear wheel of the two-wheel driving system 10 and the ground in the X-axis direction of the basic three-dimensional coordinate system O-XYZ, and the unit is meters (m). Figure 4B The horizontal axis of the graph (b) represents time, with the unit being seconds (s).

[0231] The dashed line represents the predetermined trajectory, and the solid line represents the actual trajectory. It can be seen that the actual trajectory x asymptotically converges to x0. d .

[0232] Figure 4B The graph (c) further illustrates the changes in the horizontal components of the actual trajectory and the planned trajectory over time. Specifically, Figure 4B The vertical axis of the curve (b) is the projection of the contact point between the rear wheel of the two-wheel driving system 10 and the ground in the Y-axis direction of the basic three-dimensional coordinate system O-XYZ, and the unit is meters (m). Figure 4B The horizontal axis of the graph (b) represents time, with the unit being seconds (s).

[0233] The dashed line represents the predetermined trajectory, and the solid line represents the actual trajectory. It can be seen that the actual trajectory y asymptotically converges to y0. d .

[0234] Figure 4B The graph (d) further illustrates the changes in the roll angle θ in the actual trajectory and the roll angle θ in the predetermined trajectory over time. Specifically, Figure 4B The vertical axis of the curve (d) represents the roll angle θ of the two-wheel driving system 10, in rad. Figure 4B The horizontal axis of the curve (d) represents time, with the unit being seconds (s). Figure 4B In graph (d), when the two-wheeled driving system 10 travels counterclockwise, it must balance its roll angle θ, which is negative, at which point gravity can be counteracted by centrifugal force. When the two-wheeled driving system 10 travels in a straight line, the required roll angle θ is zero. The dashed line represents the predetermined trajectory, and the solid line represents the actual trajectory. It can be seen that the roll angle θ of the actual trajectory asymptotically converges to the roll angle of the predetermined trajectory.

[0235] Figure 4B The graph (e) further illustrates the forward velocity v in the actual trajectory and the forward velocity v in the predetermined trajectory. d Changes over time. Specifically, Figure 4B The vertical axis of the curve (e) represents the forward speed of the two-wheel driving system 10, in m / s. Figure 4B The horizontal axis of the graph (e) represents time, with the unit being seconds (s). Figure 4B In the curve graph (e), the dashed line represents the predetermined trajectory, and the solid line represents the actual trajectory. It can be seen that the forward velocity v of the actual trajectory gradually converges to the forward velocity v of the predetermined trajectory. d .

[0236] Figure 4B The graph (f) further illustrates the change of the steering angle over time in the actual trajectory. Specifically, Figure 4B The vertical axis of the curve (f) represents the steering angle of the two-wheel driving system 10, in rad. Figure 4B The horizontal axis of the graph (f) represents time, with the unit being seconds (s).

[0237] Figure 4C Schematic diagram (a) shows the two-wheeled driving system 10 traveling along a predetermined "circle-line" trajectory at time t = 4.415. At this time, the contact point between the rear wheel of the two-wheeled driving system 10 and the ground is located at x = -1.738, y = 8.311 in the basic three-dimensional coordinate system O-XYZ.

[0238] Figure 4CSchematic diagram (b) shows the two-wheeled driving system 10 traveling along a predetermined "circle-line" trajectory at time t = 8.415. At this time, the contact point between the rear wheel of the two-wheeled driving system 10 and the ground is located at x = -8.014, y = -3.424 in the basic three-dimensional coordinate system O-XYZ.

[0239] Figure 4C Schematic diagram (c) shows the two-wheeled driving system 10 traveling along a predetermined "circle-line" trajectory at time t = 31.144. At this time, the contact point between the rear wheel of the two-wheeled driving system 10 and the ground is located at x = 9.932, y = -1.085 in the basic three-dimensional coordinate system O-XYZ.

[0240] Figure 4C Schematic diagram (d) shows the two-wheeled driving system 10 traveling along a predetermined "circle-line" trajectory at time t = 57.586. At this time, the contact point between the rear wheel of the two-wheeled driving system 10 and the ground is located at x = 10.390, y = 41.840 in the basic three-dimensional coordinate system O-XYZ.

[0241] Figure 4D A predetermined trajectory in the shape of an "8" was set (which is based on...) Figure 4D (The curve is represented by a dashed line in graph (a)). The radius of the circle in the predetermined trajectory is 10m. The two-wheeled driving system 10 moves forward at a speed v. d =4m / s, traveling counterclockwise around the right circle for one revolution. Then, the two-wheel driving system 10 will travel clockwise around the left circle for one revolution at the same speed. Figure 4D The horizontal axis of the curve (a) is the projection of the contact point between the rear wheel of the two-wheel driving system 10 and the ground in the X-axis direction of the basic three-dimensional coordinate system O-XYZ. Figure 4D The vertical axis of the curve (a) is the projection of the contact point between the rear wheel of the two-wheel driving system 10 and the ground in the Y-axis direction of the basic three-dimensional coordinate system O-XYZ.

[0242] The initial state of the two-wheel driving system 10 is x0=0, y0=0, ψ0=-π / 2, v0=0, ω0=0, θ0=0. And δ0 = 0. In the initial 0.2 seconds, as the two-wheel drive system 10 accelerates from a standstill, the static balancing component 140 is used to balance the two-wheel drive system 10. See also... Figure 4D The curve (a) shows the actual trajectory of the two-wheeled driving system 10 under the aforementioned parameters, represented by a solid line. It can be seen that the difference between the actual trajectory and the predetermined trajectory of the two-wheeled driving system 10 is very small. That is, under these parameters, the two-wheeled driving system can accurately travel along the desired trajectory.

[0243] When switching from the left circle to the right circle, or from the right circle to the left circle, the two-wheel driving system 10 must balance to the opposite roll angle θ, so its position will deviate from the predetermined trajectory. After the two-wheel driving system 10 has traveled half a circle, or when time t reaches infinity, the actual trajectory will converge back to the predetermined trajectory.

[0244] Figure 4D The graph (b) further illustrates the changes in the horizontal components of the actual trajectory and the planned trajectory over time. Specifically, Figure 4D The vertical axis of the curve (b) is the projection of the contact point between the rear wheel of the two-wheel driving system 10 and the ground in the X-axis direction of the basic three-dimensional coordinate system O-XYZ, and the unit is meters (m). Figure 4D The horizontal axis of graph (b) represents time, in seconds (s). Dashed lines represent the predetermined trajectory, and solid lines represent the actual trajectory. It can be seen that the actual trajectory x asymptotically converges to x0. d .

[0245] Figure 4D The graph (c) further illustrates the changes in the horizontal components of the actual trajectory and the planned trajectory over time. Specifically, Figure 4D The vertical axis of the curve (b) is the projection of the contact point between the rear wheel of the two-wheel driving system 10 and the ground in the Y-axis direction of the basic three-dimensional coordinate system O-XYZ, and the unit is meters (m). Figure 4D The horizontal axis of the curve (b) represents time, in seconds (s). The dashed line represents the predetermined trajectory, and the solid line represents the actual trajectory. It can be seen that the actual trajectory y asymptotically converges to y0. d .

[0246] Figure 4D The graph (d) further illustrates the changes in the roll angle θ in the actual trajectory and the roll angle θ in the predetermined trajectory over time. Specifically, Figure 4D The vertical axis of the curve (d) represents the roll angle θ of the two-wheel driving system 10, in rad. Figure 4D The horizontal axis of the curve (d) represents time, with the unit being seconds (s). Figure 4D In graph (d), when the two-wheeled driving system 10 travels counterclockwise, it must balance its roll angle θ, which is negative, at which point gravity can be counteracted by centrifugal force. When the two-wheeled driving system 10 travels in a straight line, the required roll angle θ is zero. The dashed line represents the predetermined trajectory, and the solid line represents the actual trajectory. It can be seen that the roll angle θ of the actual trajectory asymptotically converges to the roll angle of the predetermined trajectory.

[0247] Figure 4D The graph (e) further illustrates the forward velocity v in the actual trajectory and the forward velocity v in the predetermined trajectory. d Changes over time. Specifically, Figure 4DThe vertical axis of the curve (e) represents the forward speed of the two-wheel driving system 10, in m / s. Figure 4D The horizontal axis of the graph (e) represents time, with the unit being seconds (s). Figure 4D In the curve graph (e), the dashed line represents the predetermined trajectory, and the solid line represents the actual trajectory. It can be seen that the forward velocity v of the actual trajectory gradually converges to the forward velocity v of the predetermined trajectory. d .

[0248] Figure 4D The graph (f) further illustrates the change of the steering angle over time in the actual trajectory. Specifically, Figure 4D The vertical axis of the curve (f) represents the steering angle of the two-wheel driving system 10, in rad. Figure 4D The horizontal axis of the graph (f) represents time, with the unit being seconds (s).

[0249] Figure 4E Schematic diagram (a) shows the two-wheeled driving system 10 traveling along a predetermined "8"-shaped trajectory at time t = 4.367. At this time, the contact point between the rear wheel of the two-wheeled driving system 10 and the ground is located at x = 10.571, y = -10.429 in the basic three-dimensional coordinate system O-XYZ.

[0250] Figure 4E Schematic diagram (b) shows the two-wheeled driving system 10 traveling along a predetermined figure-eight trajectory at time t = 12.317. At this time, the contact point between the rear wheel of the two-wheeled driving system 10 and the ground is located at x = 8.6661, y = 9.908 in the basic three-dimensional coordinate system O-XYZ.

[0251] Figure 4E Schematic diagram (c) shows the two-wheeled driving system 10 traveling along a predetermined "8"-shaped trajectory at time t = 31.144. At this time, the contact point between the rear wheel of the two-wheeled driving system 10 and the ground is located at x = -7.100, y = -10.230 in the basic three-dimensional coordinate system O-XYZ.

[0252] Figure 4E Schematic diagram (d) shows the two-wheeled driving system 10 traveling along a predetermined "8"-shaped trajectory at time t = 19.295. At this time, the contact point between the rear wheel of the two-wheeled driving system 10 and the ground is located at x = -10.360, y = 10.024 in the basic three-dimensional coordinate system O-XYZ.

[0253] It is evident that the method for controlling a two-wheeled driving system provided in this disclosure can ensure the dynamic balance of the two-wheeled driving system while also ensuring that the two-wheeled driving system travels accurately along the required trajectory.

[0254] Therefore, this disclosure also provides a two-wheel driving system, the two-wheel driving system including a front handlebar steering assembly and a rear wheel drive assembly, wherein the driving force provided by the rear wheel drive assembly and the steering angle acceleration provided by the front handlebar steering assembly are determined according to the above-described method 20 for controlling the driving of the two-wheel driving system.

[0255] like Figure 5 As shown, the computing terminal of the above-described method 20 can be an electronic device 2000 (also referred to as: device 2000). The electronic device 2000 may include one or more processors 2010 and one or more memories 2020. The memory 2020 stores computer-readable code, which, when run by the one or more processors 2010, can execute the various methods described above.

[0256] The processor in this embodiment can be an integrated circuit chip with signal processing capabilities. The processor can be a general-purpose processor, a digital signal processor (DSP), an application-specific integrated circuit (ASIC), an off-the-shelf programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components. It can implement or execute the methods, steps, and logic block diagrams disclosed in the embodiments of this application. The general-purpose processor can be a microprocessor or any conventional processor, and can be based on an x86 architecture or an ARM architecture.

[0257] In general, the various exemplary embodiments of this disclosure can be implemented in hardware or dedicated circuitry, software, firmware, logic, or any combination thereof. Some aspects can be implemented in hardware, while others can be implemented in firmware or software that can be executed by a controller, microprocessor, or other computing device. When aspects of embodiments of this disclosure are illustrated or described as block diagrams, flowcharts, or using some other graphical representation, it will be understood that the blocks, apparatuses, systems, techniques, or methods described herein can be implemented as non-limiting examples in hardware, software, firmware, dedicated circuitry or logic, general-purpose hardware or controllers or other computing devices, or some combination thereof.

[0258] For example, the method or apparatus according to embodiments of this disclosure can also be used by means of Figure 6 The architecture of the computing device 3000 shown is used for implementation. For example... Figure 6As shown, the computing device 3000 may include a bus 3010, one or more CPUs 3020, a read-only memory (ROM) 3030, a random access memory (RAM) 3040, a communication port 3050 connected to a network, an input / output component 3060, a hard disk 3070, etc. The storage devices in the computing device 3000, such as the ROM 3030 or the hard disk 3070, may store various data or files used in the processing and / or communication of the method for determining the driving risk of a vehicle provided in this disclosure, as well as program instructions executed by the CPU. The computing device 3000 may also include a user interface 3080. Of course, Figure 6 The architecture shown is merely exemplary and can be omitted as needed when implementing different devices. Figure 6 One or more components in the computing device shown.

[0259] According to another aspect of this disclosure, a computer-readable storage medium is also provided. Figure 7 A schematic diagram of a storage medium 4000 according to the present disclosure is shown.

[0260] like Figure 7 As shown, the computer storage medium 4020 stores computer-readable instructions 4010. When the computer-readable instructions 4010 are executed by a processor, various methods according to embodiments of the present disclosure described with reference to the above figures can be performed. The computer-readable storage medium in the embodiments of the present disclosure may be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. Non-volatile memory may be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory may be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of RAM are available, such as static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDRSDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct memory bus random access memory (DR RAM). It should be noted that the memory used in the methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0261] Embodiments of this disclosure also provide a computer program product or computer program including computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform various methods according to embodiments of this disclosure.

[0262] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0263] In general, the various exemplary embodiments of this disclosure can be implemented in hardware or dedicated circuitry, software, firmware, logic, or any combination thereof. Some aspects can be implemented in hardware, while others can be implemented in firmware or software that can be executed by a controller, microprocessor, or other computing device. When aspects of embodiments of this disclosure are illustrated or described as block diagrams, flowcharts, or using some other graphical representation, it will be understood that the blocks, apparatuses, systems, techniques, or methods described herein can be implemented as non-limiting examples in hardware, software, firmware, dedicated circuitry or logic, general-purpose hardware or controllers or other computing devices, or some combination thereof.

[0264] The exemplary embodiments of this disclosure described in detail above are merely illustrative and not restrictive. Those skilled in the art will understand that various modifications and combinations can be made to these embodiments or their features without departing from the principles and spirit of this disclosure, and such modifications should fall within the scope of this disclosure.

Claims

1. A method for controlling the movement of a two-wheeled driving system, wherein, The two-wheel driving system includes a front steering assembly and a rear-wheel drive assembly, and the method includes: Obtain the driving state parameters of the two-wheel driving system, and determine the dynamic and kinematic characteristic quantities of the two-wheel driving system; Based on the dynamic characteristics, kinematic characteristics, and desired trajectory of the dual-wheel driving system, the driving force provided by the rear wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly are determined using the tracking error sub-model and the balance error sub-model. The driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly enable the two-wheel driving system to continue traveling along the desired trajectory and maintain dynamic balance during driving. The tracking error sub-model and the balance error sub-model together constitute the driving error model. The tracking error sub-model has a first gain relative to the balance error sub-model, and the balance error sub-model has a second gain relative to the tracking error model. The first gain and the second gain constitute the total gain of the driving force and the steering angle acceleration relative to the driving error model. The parameters in the tracking error sub-model and the balance error sub-model are adjusted based on the total gain so that the two-wheel driving system satisfies the tracking constraint and the balance constraint.

2. The method as described in claim 1, wherein, The tracking constraints are determined based on the kinematic characteristics of the two-wheeled driving system and the desired trajectory, while the balance constraints are determined based on the dynamic and kinematic characteristics of the two-wheeled driving system. The tracking constraint condition is that the tracking error converges, and the balance constraint condition is that the balance error sub-model maintains a stable state.

3. The method as described in claim 2, wherein, The tracking error includes: the error between the forward speed of the two-wheeled driving system and the forward speed set for the desired trajectory, and the error between the forward acceleration of the two-wheeled driving system and the forward acceleration set for the desired trajectory. The determination of the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front steering assembly further includes: The tracking error is calculated using a tracking error sub-model; and Determine the driving force provided by the rear-wheel drive assembly so that the tracking error converges; The tracking error sub-model is determined by the tracking constraints and the balance constraints.

4. The method of claim 2, wherein, The determination of the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly further includes: Using the balance error sub-model, the steering angle acceleration provided by the front handlebar steering assembly is determined so that the balance error sub-model remains stable when the steering angle acceleration is taken as input; The balance error sub-model is determined by the tracking constraint and the balance constraint, and the two-wheel driving system maintains dynamic balance during driving while the balance error sub-model remains stable.

5. The method of claim 4, wherein, The mismatch interference of the tracking error sub-model to the balance error sub-model is at least in part based on the steering angular velocity of the desired trajectory and the error between the forward speed of the two-wheel driving system and the forward speed set for the desired trajectory.

6. The method of claim 3, wherein, Determining the driving force provided by the rear-wheel drive assembly so that the tracking error converges further includes: Using the backstepping method, the driving force provided by the rear-wheel drive assembly is determined based on the tracking error sub-model so that the tracking error converges. The driving force provided by the rear-wheel drive assembly is determined to be positively correlated with the steering angular acceleration of the two-wheel drive system with respect to the yaw angle.

7. The method of claim 4, wherein, The method of determining the steering angular acceleration provided by the front handlebar steering assembly using the balance error sub-model further includes: Using the optimal control method, the steering angle acceleration provided by the front steering assembly is determined based on the balance error sub-model, so that the balance error sub-model remains stable when the steering angle acceleration is used as input. The steering angular acceleration provided by the front handlebar steering assembly is determined to be positively correlated with the component of the error between the contact point position of the rear wheel and the ground and the contact point position set by the desired trajectory in the direction perpendicular to the forward direction.

8. The method of claim 7, wherein, The determination of the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the handlebar steering assembly further includes: Based on the tracking error sub-model and the balancing error sub-model, determine the first gain of the tracking error sub-model to the balancing error sub-model and the second gain of the balancing error sub-model to the tracking error model; Based on the first gain and the second gain, the total gain of the driving force provided by the rear-wheel drive assembly and the steering angle acceleration provided by the front handlebar steering assembly with respect to the driving error model is determined. Based on the total gain, the parameters in the tracking error sub-model and the balance error sub-model are adjusted so that the two-wheel driving system satisfies the tracking constraint and the balance constraint.

9. The method of claim 7, wherein, The determination of the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the handlebar steering assembly further includes: Based on the tracking error sub-model and the equilibrium error sub-model, a first stability analysis sub-model and a second stability analysis sub-model are determined, and the first stability analysis sub-model and the second stability analysis sub-model are cascaded. The parameters in the tracking error sub-model and the equilibrium error sub-model are adjusted so that the first stability analysis sub-model is input-to-state stable and the second stability analysis sub-model is locally exponentially low stable. Specifically, when the first stability analysis sub-model is input to a stable state and the second stability analysis sub-model is locally exponentially low stable, the two-wheel driving system satisfies the tracking constraint and the balance constraint.

10. The method of claim 7, wherein, The driving error model is equivalent to a combination of a cascaded first stability analysis sub-model and a second stability analysis sub-model. The parameters in the tracking error sub-model and the balance error sub-model are configured such that the first stability analysis sub-model is input-to-state stable and the second stability analysis sub-model is locally exponentially low stable. Specifically, when the first stability analysis sub-model is input to a stable state and the second stability analysis sub-model is locally exponentially low stable, the two-wheel driving system satisfies the tracking constraint and the balance constraint.

11. The method of claim 1, wherein, The front handlebar steering assembly includes: a front wheel, a front handlebar, and a steering motor; The rear-wheel drive assembly includes: rear wheels and a drive motor; The two-wheel driving system also includes: a frame crossbeam; The driving state parameters include one or more of the following: the roll angle of the two-wheel driving system, the actual steering angle of the handlebars, the angle between the bottom bracket of the handlebars and the frame crossbeam, the contact point position of the rear wheel with the ground, the contact point position of the front wheel with the ground, the center of gravity position of the two-wheel driving system, the distance between the contact point position of the rear wheel with the ground and the contact point position of the front wheel with the ground, the intersection of the bottom bracket of the handlebars with the ground, the yaw angle of the two-wheel driving system, the forward speed of the two-wheel driving system, the total mass of the two-wheel driving system, the moment of inertia of the two-wheel driving system, and the height of the center of gravity of the two-wheel driving system.

12. A two-wheel driving system, the two-wheel driving system comprising a front handlebar steering assembly and a rear wheel drive assembly, wherein, The method for controlling the driving of a two-wheel driving system according to any one of claims 1-11 is determined by the driving force provided by the rear-wheel drive assembly and the steering angle acceleration provided by the front handlebar steering assembly.

13. A computer-readable storage medium having stored thereon computer-readable instructions that, when executed by a computer, perform the method of any one of claims 1-11.

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