Method for determining the driving trajectory of a two-wheel driving system and two-wheel driving system

Abstract

Provided are a method for determining a driving trajectory of a two-wheel driving system, a two-wheel driving system, and a computer-readable storage medium. The two-wheel driving system includes a front handlebar steering assembly and a rear wheel drive assembly, and the method includes: determining a candidate trajectory set of the two-wheel driving system based on a starting position and a target position of the two-wheel driving system; for each candidate trajectory in the candidate trajectory set, determining a tracking constraint condition for the two-wheel driving system to drive along the candidate trajectory and a balance constraint condition for the two-wheel driving system to maintain dynamic balance during driving along the candidate trajectory based on the candidate trajectory; and determining whether the two-wheel driving system can smoothly drive from the starting position to the target position along the candidate trajectory based on the balance constraint condition and the tracking constraint condition.

Description

Technical Field

[0001] Embodiments of the present disclosure relate to a method for determining a driving trajectory of a two-wheel driving system, a two-wheel driving system, and a computer-readable storage medium. Background Art

[0002] With the widespread application of artificial intelligence and robotics technology in civil and commercial fields, robots based on artificial intelligence and robotics technology are playing an increasingly important role in smart transportation, smart home and other fields, and are also facing higher requirements.

[0003] A mobile robot is a mechanical device that can automatically perform work tasks. It can accept human commands in real time, run pre-programmed programs, or act according to principles formulated with artificial intelligence technology. Its task is to assist or replace part of human work, such as in manufacturing, construction, or some dangerous work. According to different ways of movement, mobile robots are divided into: wheeled mobile robots, legged mobile robots, snake-like mobile robots, tracked mobile robots, crawling robots, etc.

[0004] Self-driving bicycles are a typical mobile robot that is not only environmentally friendly, cheap, but also easy to manufacture. Currently, self-driving bicycles can already carry children and disabled people, deliver express parcels, and avoid traffic accidents in restricted environments.

[0005] However, compared to four-wheel drive cars, there are only two contact points between self-driving bicycles and the road during driving, and it is difficult for them to maintain balance during driving and they are prone to tipping over. For this reason, compared to four-wheel drive cars, the trajectory planning of self-driving bicycles has more restrictions. For example, bicycles can only travel forward and backward, and it is difficult to turn more than 90 degrees to the left or right, and it is impossible to move directly to the left or right in a direction perpendicular to the forward and backward driving direction. However, how to plan the driving trajectory of self-driving bicycles while ensuring the balance of self-driving bicycles is still a difficult problem that needs to be solved urgently. Summary of the invention

[0006] At least one embodiment of the present disclosure provides a method for determining a driving trajectory of a two-wheel driving system, wherein the two-wheel driving system includes a front handlebar steering assembly and a rear-wheel drive assembly, and the method includes: determining a set of candidate trajectories of the two-wheel driving system based on a starting position and a target position of the two-wheel driving system; for each candidate trajectory in the candidate trajectory set, determining, based on the candidate trajectory, a tracking constraint condition for the two-wheel driving system to drive along the candidate trajectory, and a balance constraint condition for the two-wheel driving system to maintain dynamic balance while driving along the candidate trajectory; and determining, based on the balance constraint condition and the tracking constraint condition, whether the two-wheel driving system can smoothly drive from the starting position to the target position along the candidate trajectory; wherein the tracking constraint condition is determined based on a kinematic feature quantity of the two-wheel driving system and the candidate trajectory, and the balance constraint condition is determined based on a dynamic feature quantity and a kinematic feature quantity of the two-wheel driving system.

[0007] At least one embodiment of the present disclosure provides a two-wheel driving system, which includes a front handlebar steering assembly and a rear wheel drive assembly, and a driving trajectory of the two-wheel driving system is determined according to the aforementioned method.

[0008] At least one embodiment of the present disclosure provides a computer-readable storage medium having computer-readable instructions stored thereon. When the instructions are executed by a computer, the above method is executed.

[0009] According to another aspect of the present disclosure, a computer program product or a computer program is provided, the computer program product or the computer program including computer instructions, the computer instructions being stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable medium, and the processor executes the computer instructions, so that the computer device executes the methods provided in the above-mentioned various aspects or various optional implementations of the above-mentioned various aspects.

[0010] The method for determining the driving trajectory of a two-wheel driving system provided by the present disclosure plans the driving path of the two-wheel driving system based on balance constraints, a starting position and a target position, thereby ensuring that the two-wheel driving system can smoothly drive to the target position according to the planned path. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings of the embodiments will be briefly introduced below. Obviously, the drawings in the following description only relate to some embodiments of the present disclosure, but are not intended to limit the present disclosure.

[0012] Figure 1 FIG. 1 is a schematic diagram of an example of a two-wheel travel system 10 according to an embodiment of the present disclosure.

[0013] Figure 2A The present invention is a flowchart of a method for determining a driving trajectory of a two-wheel driving system according to at least one embodiment of the present disclosure.

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

[0015] Figure 2C Schematic diagram of candidate trajectories for a two-wheel travel system according to at least one embodiment of the present disclosure.

[0016] Figure 2D is another exemplary flow chart of a method for determining a driving trajectory of a two-wheel driving system according to an embodiment of the present disclosure.

[0017] Figure 3 is another exemplary flow chart of a method for determining a driving trajectory of a two-wheel driving system according to an embodiment of the present disclosure.

[0018] Figure 4A 2 is an example of parameters of a two-wheel travel system according to at least one embodiment of the present disclosure.

[0019] Figure 4B Based on Figure 4A A comparison curve diagram of the candidate trajectory of the two-wheel driving system determined by the parameters around the "circle-line" candidate trajectory and the simulated trajectory.

[0020] Figure 4C Based on Figure 4A Schematic diagram of four different moments when the two-wheel driving system determined by the parameters of is driving around the "circle-line" candidate trajectory.

[0021] Figure 4D Based on Figure 4A A comparison curve diagram of the candidate trajectory of the two-wheel driving system determined by the parameters traveling around the "8"-shaped candidate trajectory and the simulated trajectory.

[0022] Figure 4E Based on Figure 4A Schematic diagram of four different moments when the two-wheel driving system determined by the parameters is driving around the "8"-shaped candidate trajectory.

[0023] Figure 5 A schematic diagram of an electronic device according to an embodiment of the present disclosure is shown.

[0024] Figure 6 A schematic diagram showing the architecture of an exemplary computing device according to an embodiment of the present disclosure.

[0025] Figure 7 A schematic diagram of a storage medium according to an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical solution and advantages of the embodiments of the present disclosure clearer, the technical solution of the embodiments of the present disclosure will be clearly and completely described below in conjunction with the drawings of the embodiments of the present disclosure. Obviously, the described embodiments are part of the embodiments of the present disclosure, not all of the embodiments. Based on the described embodiments of the present disclosure, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present disclosure.

[0027] Unless otherwise defined, the technical terms or scientific terms used in the present disclosure should be understood by people with ordinary skills in the field to which the present disclosure belongs. The "first", "second" and similar words used in the present disclosure do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0028] In order to make the objectives, technical solutions and advantages of the present disclosure more clear, the embodiments of the present disclosure will be further described in detail below with reference to the accompanying drawings.

[0029] Artificial Intelligence (AI) is the theory, method, technology and application system that uses a machine controlled by a mathematical computer or a digital computer to simulate, extend and expand human intelligence, perceive the environment, acquire knowledge and use knowledge to obtain the best results. In other words, artificial intelligence is a comprehensive technology in computer science that attempts to understand the essence of intelligence and produce a new intelligent machine that can respond in a similar way to human intelligence. Artificial intelligence is to study the design principles and implementation methods of various intelligent machines so that machines have the functions of perception, reasoning and decision-making.

[0030] Artificial intelligence is a comprehensive discipline that covers a wide range of fields, including both hardware-level and software-level technologies. The basic technologies of artificial intelligence generally include sensors, dedicated artificial intelligence chips, cloud computing, distributed storage, big data processing technology, operating / interactive systems, mechatronics, and other technologies.

[0031] A robot is a machine device that automatically performs tasks and is controlled by a computer program or electronic circuit. A robot is generally composed of an actuator, a drive device, a detection device, a control system, and complex machinery.

[0032] According to the different spaces where the control quantity is located, robot control can be divided into joint space control and Cartesian space control. For serial multi-joint robots, joint space control is the control of the variables of each joint of the robot, and Cartesian space control is the control of the variables at the end of the robot. According to the different control quantities, robot control can be divided into: position control, speed control, acceleration control, force control, force-position mixed control, etc. These controls can be joint space control or end Cartesian space control.

[0033] Exemplarily, the control methods of robots can be divided into PID (Proportional-Integral-Differential) control, variable structure control, adaptive control, fuzzy control, neural network control and other methods. PID control is to calculate the control quantity according to the error of the control system by using proportion, integration and differentiation. Variable structure control means that there are multiple controllers in the control system, and different controllers are used in different situations according to certain rules. Adaptive control means that when the input or interference of the control system changes over a large range, the designed system can adaptively adjust the system parameters or control strategies so that the output can still meet the design requirements. Fuzzy control means that the input quantity is called fuzzy variable after fuzzy quantization, and the fuzzy variable obtains fuzzy output after reasoning with fuzzy rules, and the clear output quantity is obtained for control after defuzzification. Neural network control is a new branch of intelligent control, which is the product of the combination of neural network theory and control theory, and is a developing discipline. It brings together theories, technologies, methods and research results of disciplines including mathematics, biology, neurophysiology, brain science, genetics, artificial intelligence, computer science, automatic control, etc.

[0034] Figure 1 FIG. 1 is a schematic diagram of an example of a two-wheel travel system 10 according to an embodiment of the present disclosure.

[0035] The two-wheel travel 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 travel system 10 may also include a static balancing assembly 140. The front handlebar steering assembly 120 and the rear wheel drive assembly 130 each form a contact point with the ground.

[0036] In the disclosed embodiment, the two-wheel travel system 10 refers to a power tool that can maintain its own balance and has two wheels. Exemplarily, the two-wheel travel system 10 is any one of the following: a self-balancing two-wheel travel 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. The disclosed embodiment does not limit the product form of the two-wheel travel system 10. In one possible implementation, the two-wheel travel system 10 can be applied to manned scenarios; in another possible implementation, the two-wheel travel system 10 can be applied to unmanned scenarios, such as unmanned driving scenarios, delivery scenarios (delivery of express, delivery of takeout, delivery of goods, etc.) or other scenarios. It should be noted that Figure 1 The two-wheel travel system 10 is introduced in the form of a two-wheel travel system, which is only exemplary and should not limit the two-wheel travel system 10 .

[0037] The front handlebar steering assembly 120 and the rear wheel drive assembly 130 are two independent components. The front handlebar steering assembly 120 is used to control the driving direction of the two-wheel driving system 10, and the rear wheel drive assembly 130 is used to realize the movement of the two-wheel driving system 10. The main frame 110 is used to support and connect the front handlebar steering assembly 120 and the rear wheel drive assembly 130, so that the front handlebar steering assembly 120 and the rear wheel drive assembly 130 maintain a relatively appropriate position. Exemplarily, the main frame 110 can be an integrated main frame, a trapezoidal main frame, a beam-type main frame or other types of main frames. In a possible implementation, when the product form of the two-wheel driving system 10 is a two-wheel driving system, the main frame 110 can be a frame. In an illustrative embodiment, the power required for the two-wheel driving system 10 to travel can be provided by the front handlebar steering assembly 120, the power required for the two-wheel driving system 10 to travel can be provided by the rear wheel drive assembly 130, and the power required for the two-wheel driving system 10 can also be provided by the front handlebar steering assembly 120 and the rear wheel drive assembly 130 together.

[0038] The front handlebar steering assembly 120 and the rear wheel driving assembly 130 are respectively connected to the main frame 110 .

[0039] The front handlebar steering assembly 120 includes a front wheel 121, a front handlebar 122 and a steering motor 123, wherein the front wheel 121 is sleeved on the front handlebar 122, and the steering motor 123 is provided at the connection between the front handlebar 122 and the frame 110, and the steering motor 123 drives the rotation of the front handlebar 122 to realize the steering control of the front wheel 121, thereby achieving dynamic balance.

[0040] The rear wheel drive assembly 130 includes a rear wheel 131 and a drive motor 132. The drive motor 132 is used to drive the rear wheel 131 to rotate to provide a driving force for the balanced two-wheel driving system to move forward.

[0041] In some embodiments, the static balancing assembly 140 is also mounted on the main frame 110, and the static balancing assembly 140 includes: a momentum wheel 141 (the momentum wheel is also called a flywheel) and a momentum wheel motor 142. The momentum wheel 141 axis is arranged along the front-to-back direction of the body of the self-balancing two-wheeled vehicle, that is, the direction of the momentum wheel 141 axis is perpendicular to the direction of the front wheel axis and the rear wheel axis. The momentum wheel 141 is sleeved on the output shaft 143 of the momentum wheel motor 142, and the momentum wheel motor 142 drives the rotation of the momentum wheel 141 through the output shaft 143 to provide a torque for achieving static balance.

[0042] Optionally, the frame 110 is also provided with a gyroscope (Inertial measurement unit, IMU), which is used to obtain the inclination data and acceleration data of the frame 110 to understand the current state of the frame. Furthermore, the frame 110 is also provided with auxiliary wheels, which are used to support the frame 110 when the frame 110 topples over, so as to prevent the balanced two-wheel driving system from falling over and causing damage to the hardware.

[0043] Based on the above-mentioned balanced two-wheel travel system structure, the dynamic balancing process can be achieved by controlling the rotation of the front handle 122 of the two-wheel travel system through the steering motor 123; the static balancing process can be achieved by the momentum wheel 141 additionally provided on the two-wheel travel system through the torque generated during the rotation of the momentum wheel 141; the combination of the two can respectively achieve the balance of the two-wheel travel system in dynamic and static conditions.

[0044] An embodiment of the present disclosure provides a method for determining a driving trajectory of a two-wheel driving system, wherein the two-wheel driving system includes a front handlebar steering assembly and a rear-wheel drive assembly, and the method includes: determining a set of candidate trajectories of the two-wheel driving system based on a starting position and a target position of the two-wheel driving system; for each candidate trajectory in the candidate trajectory set, determining, based on the candidate trajectory, a tracking constraint condition for the two-wheel driving system to drive along the candidate trajectory, and a balance constraint condition for the two-wheel driving system to maintain dynamic balance while driving along the candidate trajectory; and determining, based on the balance constraint condition and the tracking constraint condition, whether the two-wheel driving system can smoothly drive from the starting position to the target position along the candidate trajectory; wherein the tracking constraint condition is determined based on a kinematic feature quantity of the two-wheel driving system and the candidate trajectory, and the balance constraint condition is determined based on a dynamic feature quantity and a kinematic feature quantity of the two-wheel driving system.

[0045] The method for determining the driving trajectory of a two-wheel driving system provided by the present disclosure plans the driving path of the two-wheel driving system based on balance constraints, a starting position and a target position, thereby ensuring that the two-wheel driving system can smoothly drive to the target position according to the planned path.

[0046] Figure 2A 4 is a flowchart of a method 20 for determining a driving trajectory of a two-wheel driving system 10 according to at least one embodiment of the present disclosure. Figure 2B Schematic diagram of parameter annotation of simulated driving state parameters of the two-wheel driving system 10 according to at least one embodiment of the present disclosure. Figure 2C Schematic diagram of candidate trajectories of the two-wheel travel system 10 according to at least one embodiment of the present disclosure. Figure 2D is another exemplary flow chart of the method 20 for determining the driving trajectory of the two-wheel driving system 10 according to an embodiment of the present disclosure.

[0047] See also Figure 2A According to at least one embodiment of the present disclosure, method 20 may include steps S201 to S204.

[0048] In step S201, a candidate trajectory set of the two-wheel travel system is determined based on the starting position and the target position of the two-wheel travel system.

[0049] Step S202 includes step S2021 and step S2022.

[0050] In step S2021, based on the candidate trajectory, tracking constraints for the two-wheel driving system to travel along the candidate trajectory and balance constraints for the two-wheel driving system to maintain dynamic balance while traveling along the candidate trajectory are determined.

[0051] In step S2022, based on the balance constraint and the tracking constraint, it is determined whether the two-wheel driving system can smoothly drive from the starting position to the target position along the candidate trajectory.

[0052] Among them, the tracking constraint condition is determined based on the kinematic characteristic quantity of the two-wheel travel system and the candidate trajectory, and the balance constraint condition is determined based on the dynamic characteristic quantity and kinematic characteristic quantity of the two-wheel travel system.

[0053] For example, the dynamic characteristic quantity of the two-wheel travel system 10 is intended to characterize the dynamic characteristics of the two-wheel travel system 10, such as its kinetic energy, potential energy, momentum, etc. The motion characteristics of the two-wheel travel system 10 are intended to characterize the characteristics of the two-wheel travel system 10 during the movement, such as its movement mode, movement speed, current movement acceleration, etc. The disclosed embodiments are not limited by the specific composition of the dynamic characteristic quantity and kinematic characteristic quantity of the two-wheel travel system 10. The dynamic characteristic quantity or the kinematic characteristic quantity can be associated with the simulated driving state parameter.

[0054] For example, both the dynamic characteristic quantity and the kinematic characteristic quantity may also be associated with the structure of the two-wheel travel system 10. As an embodiment, for example, the two-wheel travel system 10 according to at least one embodiment of the present disclosure further includes a frame crossbeam. The front handlebar steering assembly of the two-wheel travel 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.

[0055] For another example, the kinematic characteristic quantity and the dynamic characteristic quantity of the two-wheel driving system are associated with the performance parameters of the front handlebar steering assembly and the rear wheel drive assembly, the performance parameters of the front handlebar steering assembly at least include the range of the steering angular acceleration provided by the front handlebar steering assembly, and the performance parameters of the rear wheel drive assembly at least include the range of the driving force provided by the rear wheel drive assembly. Optionally, the range of the steering angular acceleration provided by the front handlebar steering assembly can be determined by the performance parameters such as the power or torque of the above-mentioned steering motor. Optionally, the range of the driving force provided by the rear wheel drive assembly can be determined by the performance parameters such as the power or torque of the above-mentioned drive motor.

[0056] The following reference Figure 2B The simulated driving state parameters, dynamic characteristic quantities, and kinematic characteristic quantities involved in the two-wheel driving system 10 according to the embodiment of the present disclosure are described.

[0057] Optionally, in the presence of the above-mentioned structure, the simulated driving state parameters include one or more of the following: the roll angle of the two-wheel driving system, the simulated steering angle of the front handlebar, the angle between the center axis of the front handlebar 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 mass 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 center axis of the front handlebar and 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 center of mass height of the two-wheel driving system.

[0058] Figure 2B The simulated driving state parameters related to the dynamic characteristic quantity and kinematic characteristic quantity of the two-wheel driving system 10 are shown. These simulated driving state parameters can be obtained by simulating the process of the two-wheel driving system 10 driving along the candidate trajectory, and the sensor may detect the value obtained at time t. Those skilled in the art should understand that the simulated driving state parameters related to the dynamic characteristic quantity and kinematic characteristic quantity of the two-wheel driving system 10 can include not only Figure 2B All or part of the simulated driving state parameters shown in , may also include more or fewer simulated driving state parameters. The present disclosure is not limited to this.

[0059] For example, in Figure 2B The basic three-dimensional coordinate system O-XYZ is marked in the figure, and the three-dimensional coordinate system P1-xyz of the two-wheel travel system 10 based on the two-wheel travel system 10 is constructed based on the contact point P1 of the two-wheel travel system 10 with the ground, wherein the straight line P1z extends in the vertical direction, the straight line P1x extends in the body direction of the two-wheel travel system 10, the straight line P1y extends perpendicular to the straight line P1x and perpendicular to the straight line P1z, and the reference plane R1 is defined by the straight lines P1z and P1x.

[0060] For example, in some embodiments, Figure 2B Further marked are: the roll angle θ of the two-wheel travel system 10 (the angle between the two-wheel travel 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; the simulated steering angle δ of the front handlebar of the two-wheel travel system 10 (the angle that the front handlebar has with respect to the roll plane R2), which defines a steering plane R3 having an angle δ with the roll plane R2 via the simulated steering angle of the front handlebar.

[0061] For example, in some embodiments, Figure 2B Further marked are: the angle α between the center axis of the front handlebar of the two-wheel travel system 10 and the frame crossbeam of the two-wheel travel system 10, the horizontal distance b between the contact point P1 of the rear wheel of the two-wheel travel system 10 with the ground and the projection point of the center of mass of the two-wheel travel system 10 in the P1x direction, the distance L between the contact point of the front wheel of the two-wheel travel system 10 with the ground and the contact point of the rear wheel of the two-wheel travel system 10 with the ground along the P1x direction, and the distance Δ between the intersection of the center axis of the front handlebar of the two-wheel travel system 10 with the ground and the contact point of the front wheel of the two-wheel travel system 10 with the ground.

[0062] For example, based on the simulated steering angle δ and the roll angle θ of the front handlebar of the two-wheel travel system 10, the effective steering angle δ of the two-wheel travel system 10 can be calculated. f (The angle between the front handlebar of the two-wheel travel system 10 and the reference plane R1).

[0063] For example, the effective steering angle δ of the front handlebar can be obtained based on the following formula (1): f , when δ is not equal to zero, the two-wheel travel system 10 will move in a circle.

[0064] tan(δ f )cos(θ)=tan(δ)sin(α) (1)

[0065] When δ is not equal to zero, the two-wheel travel system 10 moves along Figure 2B The circular motion of a circle with C as the center and σ as the curvature is shown. Figure 2B,σ can be calculated by formula (2).

[0066] σ=tan(δ f ) / L (2)

[0067] Combining formula (1) and formula (2), we can get formula (3a).

[0068]

[0069] Therefore, based on the above formula (1), formula (2), and formula (3a), it can be determined that the formula used to calculate u σ Formula (3b), u σ That is, the steering acceleration when the two-wheel drive system 10 performs a circular motion.

[0070]

[0071] The total mass of the two-wheeled travel system 10 is m. The moment of inertia of the two-wheeled travel system 10 is I, the height of the center of mass of the two-wheeled travel system 10 is h, and the acceleration due to gravity g can be, for example, 9.8 N / kg.

[0072] Hereinafter, 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, by simulating the driving process of the two-wheel driving system along the candidate trajectory, the forward speed v of the rear wheel of the two-wheel driving system 10 when it has a contact point P1 with the road can be simulated. Based on the conversion relationship between the R1 plane and the R2 plane, the center point of the two-wheel driving system 10 in the R2 plane (such as Figure 2B The speed v along the directions of P1x, P1y, and P1z is shown as the small black dots in the figure. x 、v y and v z For example, the speed v can be determined according to formula (4): x 、v y and v z .

[0073]

[0074] In the following, we will use u δ represents the steering angular acceleration provided by the front handlebar steering assembly, specifically, the steering angular acceleration u δ is the derivative of the simulated steering angle δ. F is used to represent the total propulsion force of the two-wheel travel system 10 by the rear wheel drive assembly and the front handlebar steering assembly.

[0075] The following is based on Figure 2BThe simulated driving state parameters shown in the figure are exemplarily an example of associating the simulated driving state parameters of the two-wheel driving system with the dynamic characteristic quantities / kinematic characteristic quantities. Those skilled in the art should understand that the manner of associating the simulated driving state parameters of the two-wheel driving system with the dynamic characteristic quantities / kinematic characteristic quantities of the two-wheel driving system is not limited to this.

[0076] For example, since the two-wheel travel system 10 can be modeled as a simple pendulum model, an inverted pendulum model or the like, the kinetic energy T and potential energy U of the two-wheel travel system 10 can be determined according to formula (5).

[0077]

[0078] The two-wheel travel system 10 is a typical steel structure, and therefore the following Euler-Lagrange equation (ie, formula (6)) can be calculated.

[0079]

[0080] in, is the Lagrange operator; q i is 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 travel system 10 and the turning angle of the rear wheel. In this case, τ is the external force and is a two-dimensional vector, τ i The torque corresponding to the i-th sub-element of the two-dimensional angle vector in the torque vector τ is characterized, and i is a positive integer greater than or equal to 1 and less than or equal to 2. The multi-dimensional angle vector q may also include angle vectors of more dimensions. For example, when the static balancing component 140 also performs work on the two-wheel driving system 10, the sub-element of the multi-dimensional angle vector q may also include the rotation angle of the momentum wheel 141. The present disclosure does not limit the dimension of the multi-dimensional angle vector q.

[0081] Thus, based on formula (6), it is possible to obtain the relationship between the dynamic characteristic quantities of the two-wheel travel system 10. The relationship between the dynamic characteristic quantities of the two-wheel travel system 10 is shown below in formula (7a) and formula (7b).

[0082]

[0083]

[0084] where τ Δ (θ,δ f ) is the error amount caused by the caster effect of the two-wheel travel system 10, and the remaining parameters are as described above and will not be repeated here.

[0085] According to ω=-vσ and the kinematic principle of the two-wheel travel system 10, the total propulsion force F can be designed as Therefore, ignoring τ Δ (θ,δ f ), at least partially based on the relationship between the above dynamic characteristic quantities, the relationship between the kinematic characteristic quantities of the two-wheel travel system 10 can be obtained. The relationship between the kinematic characteristic quantities of the two-wheel travel system 10 is shown below with formulas (8a) to (8f).

[0086]

[0087]

[0088]

[0089]

[0090]

[0091]

[0092] in,

[0093] Among them, the above parameters all correspond to the simulated detection values ​​measured by the simulated two-wheel driving system 10 at time t. For example, v represents the simulated forward speed detected at time t when the two-wheel driving system is driving along the candidate trajectory (that is, the forward speed of the two-wheel driving system). x represents the projection of the simulated position detected at time t when the two-wheel driving system is driving along the candidate trajectory on the x-axis in the R1 plane (that is, the horizontal component of the contact point position of the two-wheel driving system). y represents the projection of the simulated position detected at time t when the two-wheel driving system is driving along the candidate trajectory on the y-axis in the R1 plane (that is, the vertical component of the contact point position of the two-wheel driving system). ω represents the steering angular velocity for the yaw angle detected at time t when the two-wheel driving system is driving along the candidate trajectory (that is, the steering angular velocity of the two-wheel driving system). ψ represents the simulated yaw angle detected at time t when the two-wheel driving system is driving along the candidate trajectory (that is, the yaw angle of the two-wheel driving system). u ω The simulated steering angular acceleration for the yaw angle (ie, the steering angular acceleration of the two-wheel travel system) detected at time t when the two-wheel travel system is traveling along the candidate trajectory is represented by u. vθ represents the simulated forward acceleration detected at time t when the two-wheel driving system travels along the candidate trajectory (i.e., the forward acceleration of the two-wheel driving system). θ represents the roll angle detected at time t when the two-wheel driving system travels along the candidate trajectory (i.e., the roll angle of the two-wheel driving system), θ∈(-π / 2, π / 2). ω,v,u ω and u v are all bounded, and v>0 for all t>0.

[0094] Optionally, the starting position of the two-wheel travel system may be equal to any one of the contact point position of the rear wheel and the ground, the contact point position of the front wheel and the ground, the center of mass position of the two-wheel travel system, and the intersection point of the middle axis of the front handlebar and the ground. The following description is made by taking the starting position of the two-wheel travel system as equal to the contact point position of the rear wheel and the ground as an example. Those skilled in the art should understand that the starting position of the two-wheel travel system is not limited to this.

[0095] Figure 2C The square filled with oblique lines indicates the starting position of the two-wheel travel system 10. The two-wheel travel system 10 maintains balance at the starting position.

[0096] The target position can be determined according to the driving purpose of the two-wheel driving system 10. For example, if the two-wheel driving system 10 is suitable for transporting goods from point A to point B, point B can be used as the target position. Similarly, the target position of the two-wheel driving system can be equivalent to any one of the contact point position where the rear wheel should contact the ground after a period of time, the contact point position where the front wheel should contact the ground, the center of mass position that the two-wheel driving system should reach, and the position that the intersection of the center axis of the front handlebar and the ground should reach. The following is an example in which the target position of the two-wheel driving system is equivalent to the contact point position where the rear wheel should contact the ground after a period of time. Those skilled in the art should understand that the target position of the two-wheel driving system is not limited to this.

[0097] Figure 2C The black filled square indicates the target position of two-wheel drive system 10 .

[0098] Figure 2CFour candidate trajectories in the candidate trajectory set are schematically shown with dotted lines and solid lines. The candidate trajectory can be generated based on prior knowledge. Prior knowledge can be based on the calculation of the dynamic model, or it can be an abstraction of some physical constraints based on debugging experience. For example: the two-wheel driving system 10 can only drive forward and backward, and it is difficult to turn more than 90 degrees directly to the left and right, and it is impossible to move directly in the left and right directions perpendicular to the front and rear driving directions. When the two-wheel driving system 10 goes on the single-plank bridge, the driving direction of the front of the two-wheel driving system 10 should be consistent with the direction of the single-plank bridge within a short distance before going on the bridge, otherwise it is difficult to adjust the direction of the form during the balancing process. Similarly, the trajectory on which the two-wheel driving system 10 can stably travel can be regarded as a series of straight lines and circular arcs with large turning radius. These straight lines and circular arcs with large turning radius should be continuous at the junction, and should be differentiable or even high-order differentiable to ensure the smoothness of the trajectory. Those skilled in the art should understand that the above method is only an example, and the scope of prior knowledge includes but is not limited to the above examples.

[0099] Figure 2C The gray filled squares indicate the sampling points of the two-wheel driving system 10 on a candidate trajectory. The sampling points can be obtained by sampling at a certain sampling space interval. d ,y d ) is used to identify a sampling point on a candidate trajectory, which indicates the position in the R1 plane that the two-wheel travel system 10 should reach at time t if traveling along the candidate trajectory.

[0100] Take the candidate trajectory marked by the solid line as an example. Assume that the sampling point (x d ,y d ) The driving state parameters set are expressed by formulas (9a) to (9f).

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] If the two-wheel driving system 10 travels along the candidate trajectory, at the sampling point (x d ,y d) are all indicated by the subscript d. For example, v d x represents the forward speed that the two-wheel driving system 10 should reach at time t when driving along the candidate trajectory (that is, the forward speed set by the candidate trajectory). d y represents the projection of the position that the two-wheel driving system 10 should reach at time t when driving along the candidate trajectory on the x-axis in the R1 plane (that is, the horizontal component of the contact point position set by the candidate trajectory). d ω represents the projection of the position that the two-wheel driving system 10 should reach at time t when driving along the candidate trajectory on the y-axis in the R1 plane (that is, the vertical component of the contact point position set by the candidate trajectory). d ψ represents the steering angular velocity for the yaw angle that the two-wheel drive system 10 should achieve at time t when driving along the candidate trajectory (that is, the steering angular velocity set by the candidate trajectory). d u represents the yaw angle that the two-wheel driving system 10 should reach at time t when driving along the candidate trajectory (that is, the yaw angle set by the candidate trajectory). ω , d u represents the steering angle acceleration for the yaw angle that the two-wheel drive system 10 should achieve at time t when driving along the candidate trajectory (that is, the steering angle acceleration set by the candidate trajectory). v,d θ represents the forward acceleration that the two-wheel driving system 10 should achieve at time t when driving along the candidate trajectory (that is, the forward acceleration set by the candidate trajectory). d represents the roll angle that the two-wheel driving system 10 should reach at time t when driving along the candidate trajectory (that is, the roll angle set by the candidate trajectory), θ d ∈(-π / 2,π / 2). ω d ,v d ,u ω,d and u v,d are bounded, and for all t>0, v d >0.

[0108] Therefore, in order to make the driving trajectory of the two-wheel driving system 10 travel along the candidate trajectory as accurately as possible, it should be ensured that x 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 is as small as possible.

[0109] Optionally, any constraint condition that is conducive to the two-wheel driving system 10 to travel along the candidate trajectory as accurately as possible can be called a tracking constraint condition. For example, the tracking constraint condition can be one or more of the following: dThe maximum difference between x and y d The maximum difference between y and v d The maximum difference between v and ψ d The maximum difference between ψ and ω d The maximum difference between x and ω, etc. The tracking constraint can also be one or more of the following: d The difference between x converges / stabilizes, or y d The difference between y converges / stable, or v d The difference between v converges / stable, ψ d The difference between ψ converges / stabilizes, and ω d The difference between and ω converges / stabilizes, etc. The present disclosure does not impose any further restrictions on the tracking constraint conditions, as long as they help the difference between the simulated driving state parameters of the two-wheel driving system 10 and the driving state parameters set by the candidate trajectory to be small enough.

[0110] In some embodiments, in order to keep the two-wheel driving system balanced, the roll angle θ should be as small as possible and cannot be equal to 90°. At the same time, the rotation speed of the roll angle θ cannot be too large and needs to converge to 0 before touching the ground, that is, the kinetic energy of the downward rotation needs to converge as quickly as possible. To this end, the balance constraint conditions for the two-wheel driving system to maintain dynamic balance during driving can be designed according to the dynamic characteristic quantity of the two-wheel driving system.

[0111] Optionally, any constraint condition that is conducive to the two-wheel driving system 10 maintaining dynamic balance during driving can be 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 formula (8f) and formula (9f). For example, the balance constraint condition can be any one or more of the following: roll angle θ d The maximum difference from the roll angle θ, the rotation speed of the roll angle θ The maximum value of the roll angle θ Convergence / stability, etc. The present disclosure does not impose any further limitations on the balance constraint conditions, as long as they help the two-wheel driving system 10 maintain dynamic balance during driving.

[0112] Optionally, the above-mentioned balance constraint and tracking constraint can be expressed as a mathematical expression. For example, the mathematical expression is lim t→∞ |[xx d ,yy d ,ψ-ψ d ,ω-ω d ,vv d ,θ-θ d ] T|=0. In some embodiments, the mathematical expression is lim t→∞ |[xx d ,yy d ,ψ-ψ d ,vv d ,θ-θ d ] T |=0. In some embodiments, the mathematical expression is lim t→∞ |[yy d ,ψ-ψ d ,vv d ,θ-θ d ] T |=0. The above mathematical expressions are not intended to limit the present disclosure, but are only for further explanation below.

[0113] If the above expression x d ,y d , d ,ω d 、v d , and θ d One or more of the candidate trajectories defined in can satisfy the balance constraints and tracking constraints (for example, can make lim t→∞ |[xx d ,yy d ,ψ-ψ d ,ω-ω d ,vv d ,θ-θ d ] T |=0), it is determined that the two-wheel driving system can smoothly drive from the starting position to the target position along the candidate trajectory. Otherwise, it is determined that the two-wheel driving system cannot smoothly drive from the starting position to the target position along the candidate trajectory.

[0114] If the two-wheel driving system 10 can smoothly travel from the starting position to the target position along the candidate trajectory, the candidate trajectory can be used as the planned trajectory of the two-wheel driving system 10. If the two-wheel driving system 10 cannot smoothly travel from the starting position to the target position along the candidate trajectory, the candidate trajectory cannot be used as the planned trajectory of the two-wheel driving system 10.

[0115] In addition, 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, so that at time t, the simulated driving state parameters x, y, ψ, ω, v, θ, etc. are all associated with the driving force provided by the rear wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly. Therefore, the maximum / minimum driving force that can be provided by the rear wheel drive assembly (hereinafter referred to as the range of the driving force provided by the rear wheel drive assembly) and the maximum / minimum steering angular acceleration provided by the front handlebar steering assembly (hereinafter referred to as the range of the steering angular acceleration provided by the front handlebar steering assembly) may be used to further define whether the two-wheel driving system can smoothly travel from the starting position to the target position along the candidate trajectory.

[0116] Those skilled in the art will appreciate that it is also possible to determine whether the two-wheel driving system can smoothly drive from the starting position to the target position along the candidate trajectory based on more constraints. Figure 1 For the two-wheel driving system 10 shown, it is also possible to determine whether the two-wheel driving system can smoothly travel from the starting position to the target position along the candidate trajectory 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 handle 122, the torque of the front handle 122, etc. For another example, it is possible to determine whether the two-wheel driving system can smoothly travel from the starting position to the target position along the candidate trajectory 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. The present disclosure is not limited thereto.

[0117] For example, refer to Figure 2D , a driving error model can be determined based on the balance constraint and the tracking constraint, and then based on the driving error model, it is determined whether the position of the two-wheel driving system deviates too far from the sampling point at each sampling point. If the position of the two-wheel driving system does not deviate too far from the sampling point for each sampling point, the candidate trajectory is qualified. Otherwise, the candidate trajectory is unqualified. Finally, based on the qualified candidate trajectory, the two-wheel driving system is controlled to travel along the candidate trajectory to the target position.

[0118] Based on the above judgment, the embodiment of the present disclosure can select a suitable candidate trajectory from the candidate trajectory set to plan the driving path of the two-wheel driving system, thereby ensuring that the two-wheel driving system can smoothly drive to the target position according to the planned path.

[0119] Therefore, the method for determining the driving trajectory of a two-wheel driving system provided by the present invention plans the driving path of the two-wheel driving system based on the balance constraint conditions, the starting position and the target position, thereby ensuring that the two-wheel driving system can smoothly drive to the target position according to the planned path.

[0120] Figure 3 is another exemplary flow chart of a method for determining a driving trajectory of a two-wheel driving system according to an embodiment of the present disclosure. Figure 3 How to determine the balancing constraint and the tracking constraint is further described.

[0121] Optionally, the above-mentioned step S2022 may also include: determining a driving error model based on the balance constraint and the tracking constraint; determining a tracking error sub-model and a balance error sub-model based on the driving error model; using the tracking error sub-model and the balance error sub-model to determine whether the two-wheel driving system satisfies the balance constraint and the tracking constraint; if the two-wheel driving system satisfies the balance constraint and the tracking constraint, determining that the two-wheel driving system can smoothly travel from the starting position to the target position along the candidate trajectory; if the two-wheel driving system does not satisfy the balance constraint and the tracking constraint, determining that the two-wheel driving system cannot smoothly travel from the starting position to the target position along the candidate trajectory.

[0122] For example, refer to Figure 3 , various tracking errors associated with the tracking constraint condition may be defined in the following manner. 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. The tracking error may include x defined in formula (10): e ,y e ,ψ e ,ω e ,v e One or more of .

[0123]

[0124] It is assumed that the two-wheel driving system should travel to the sampling point (x d ,y d). x is the component of the simulated contact point position between the rear wheel and the ground at time t in the forward direction. y is the component of the simulated contact point position between the rear wheel and the ground at time t in the perpendicular direction to the forward direction. ψ is the simulated yaw angle of the two-wheel travel system at time t. v is the forward speed of the two-wheel travel system at time t. ω is the steering angular velocity of the two-wheel travel system at time t.

[0125] Among them, x d The component of the position of the contact point between the rear wheel and the ground at time t in the forward direction set for the candidate trajectory. d The component of the position of the rear wheel contacting the ground at time y perpendicular to the forward direction set for the candidate trajectory. d The yaw angle set for the candidate trajectory at time y. d The forward speed set for the candidate trajectory. ω d The steering angular velocity at time y set for the candidate trajectory.

[0126] Among them, x e is the component of the error in the forward direction between the simulated contact point position of the rear wheel and the ground at time t and the contact point position set by the candidate trajectory. e is the component of the error between the simulated contact point position of the rear wheel and the ground at time t and the contact point position set by the candidate trajectory in the perpendicular direction to the forward direction. e is the error between the simulated yaw angle of the two-wheel drive system at time t and the yaw angle set for the candidate trajectory at time t. e is the error between the simulated forward speed of the two-wheel driving system at time t and the forward speed set by the candidate trajectory. e is the error between the simulated steering angle velocity of the two-wheel drive system at time t and the steering angle velocity at time t set for the candidate trajectory.

[0127] As described above, if any one or more of the above tracking errors converge or are less than a predetermined value, the tracking constraint condition is satisfied.

[0128] For example, various parameters associated with the balance constraint condition may be defined in the following manner. Various parameters associated with the balance constraint condition may include η1, η2 involved in formula (11), and η 1,e , η 2,e .

[0129] Where η1 = θ and Using the approximation, sin(θ) = θ and cos(θ) = 1, equations (8f) and (9f). It can be obtained as equation (11)

[0130]

[0131] in, m is the total mass of the two-wheel travel system, h is the height of the center of mass of the two-wheel travel system, I is the moment of inertia of the two-wheel travel system, g is the acceleration of gravity, and b is the horizontal distance between the contact point of the rear wheel with the ground and the center of mass of the two-wheel travel system.

[0132] Furthermore, η 1,e =η 1,d -η1 and η 2,e =η 2,d -η2. That is, η 1,e represents the roll angle θ of the two-wheel driving system at time t and the roll angle θ of the candidate trajectory setting d The error between 2,e The parameter η2 associated with the roll angle θ of the two-wheel drive system at time t and the roll angle θ of the candidate trajectory setting are represented by d The associated parameter η 2,d The error between 1,d The derivative of η 2,d The derivative of The derivative of η1 is The derivative of η2 is

[0133] As described above, if any one or more of the above parameters converge or are less than a predetermined value, the equilibrium constraint condition is satisfied.

[0134] Therefore, based on formula 8-11, and using the approximate value ω e v e =0, the following driving error model can be obtained. That is, based on the above-mentioned balance constraint condition and the tracking constraint condition, the driving error model can be determined as follows:

[0135]

[0136]

[0137] ∑ t represents the tracking error submodel because it contains x e and e ∑ b represents the balanced error submodel because it contains η 1,e , and η 2,e The tracking error submodel and the balancing error submodel both involve the same or interrelated parameters, for example, v eThus, based on the driving error model, a tracking error sub-model and a balancing error sub-model can be determined.

[0138] Wherein, ω is the simulated steering angular velocity of the two-wheel driving system at time t. e y is the component of the error in the forward direction between the contact point position of the rear wheel and the ground at time t and the contact point position set by the candidate trajectory. e v is the component of the error between the contact point position of the rear wheel and the ground at time t and the contact point position set by the candidate trajectory in the perpendicular direction to the forward direction. e is the error between the forward speed of the two-wheel driving system at time t and the forward speed set by the candidate trajectory. d is the forward speed set for the candidate trajectory at time t. e is the error between the yaw angle of the two-wheel drive system at time t and the yaw angle set by the candidate trajectory. v,d The forward acceleration at time t set for the candidate trajectory, u v The forward acceleration of the two-wheel drive system at time t. For x e The derivative of . for y e The derivative of . v e The derivative of .

[0139] Among them, u ω,d The steering angular acceleration at time t set for the candidate trajectory, u ω is the simulated steering angular acceleration provided by the front handlebar steering assembly at time t, ω d The steering angular velocity at time t set for the candidate trajectory, v e is the error between the simulated forward speed of the two-wheel travel system at time t and the forward speed set by the candidate trajectory.

[0140]

[0141] η 1,e =η 1,d -η1,η 2,e =η 2,d -η2,η 1,d The derivative of η 2,d The derivative of The derivative of η1 is The derivative of η2 is

[0142] η1=θ,

[0143] v d is the forward speed set for the candidate trajectory at time t, θ is the simulated roll angle of the two-wheel travel system at time t, m is the total mass of the two-wheel travel system, h is the height of the center of mass of the two-wheel travel system, I is the moment of inertia of the two-wheel travel system, g is the acceleration of gravity, and b is the horizontal distance between the contact point of the rear wheel with the ground and the center of mass of the two-wheel travel system.

[0144] For example, the above formula (12a) is only the tracking error submodel ∑ t An example of a tracking error submodel ∑ t It can also include more or less tracking errors, and formula (12a) is not a tracking error submodel ∑ t A person skilled in the art should understand that the tracking error submodel ∑ t More or fewer parameters and equations / inequalities may be introduced as the rigid structure of the two-wheel travel system changes.

[0145] For example, the above formula (12b) is only the balanced error submodel ∑ b Of course, the balanced error submodel ∑ b It can also include more or fewer parameters, and formula (12b) is not a balanced error submodel ∑ b A person skilled in the art should understand that the balanced error submodel ∑ b More or fewer parameters and equations / inequalities may be introduced as the rigid structure of the two-wheel travel system changes.

[0146] Thus, the tracking error submodel and the balance error submodel can be used to determine whether the two-wheel driving system satisfies the balance constraint and the tracking constraint. For example, when the two-wheel driving system satisfies the balance constraint and the tracking constraint, it is determined that the two-wheel driving system can smoothly travel from the starting position to the target position along the candidate trajectory. When the two-wheel driving system does not satisfy the balance constraint and the tracking constraint, it is determined that the two-wheel driving system cannot smoothly travel from the starting position to the target position along the candidate trajectory.

[0147] Optionally, the use of the tracking error sub-model and the balance error sub-model to determine whether the two-wheel driving system satisfies the balance constraint and the tracking constraint also includes: using the tracking error sub-model to calculate the tracking error; and based on the tracking error and the range of the driving force provided by the rear-wheel drive component, determining whether the two-wheel driving system satisfies the tracking constraint; wherein the tracking constraint 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 candidate trajectory, and the error between the forward acceleration of the two-wheel driving system and the forward acceleration set by the candidate trajectory.

[0148] The ideal driving force provided by the rear-wheel drive component for controlling the convergence of the tracking error of the tracking error sub-model may be determined in various ways. The following uses the backstepping method as an example to explain one way of obtaining the ideal driving force provided by the rear-wheel drive component. Those skilled in the art should understand that the present disclosure is not limited to this.

[0149] In some embodiments, see Figure 3 , based on the tracking error and the range of the driving force provided by the rear-wheel drive component, determining whether the two-wheel driving system satisfies the tracking constraint condition also includes: based on the tracking error sub-model, using the backstepping method, determining the ideal driving force that controls the tracking error convergence of the tracking error sub-model; when the ideal driving force is within the range of the driving force provided by the rear-wheel drive component, determining that the two-wheel driving system satisfies the tracking constraint condition; and when the ideal driving force is outside the range of the driving force provided by the rear-wheel drive component, determining that the two-wheel driving system does not satisfy the tracking constraint condition; wherein the ideal driving force is positively correlated with the steering angular acceleration of the two-wheel driving system with respect to the yaw angle.

[0150] For example, according to formula (12a), when ψ e =0,x e =c1ωy e , where c1 is positive and constant, y e can be stabilized to zero. Therefore, through the backstepping method, the following variables are defined.

[0151]

[0152] According to formulas (12a) and (13), and The expression is:

[0153]

[0154] Formula (14) achieves the order reduction of the tracking error sub-model.

[0155] According to formula (14), we can design u v The driving force provided by the rear wheel drive assembly is the same as u v Directly proportional.

[0156] For the convenience of description, formula (15) is defined.

[0157]

[0158] Where c2 is a positive constant. Therefore, is expressed as (see formula (16)).

[0159]

[0160] definition Then u v is determined as (see formula (17)):

[0161]

[0162] Among them, c1, c2, and c3 are all positive constants. u ω is the steering angle acceleration of the two-wheel drive system for the yaw angle, for The derivative of .

[0163] If the above u v If there is a solution, and the torque of the rear-wheel drive assembly can provide the corresponding driving force, then at least at time t, the two-wheel driving system can smoothly drive from the starting position to the position (x d ,y d ), that is, the two-wheel driving system will not deviate too far from the candidate trajectory.

[0164] For the convenience of analysis, u is determined using formula (17) v To determine whether the stability of the driving error model / tracking error sub-model will be affected, the candidate Lyapunov function V of the tracking error sub-model is defined here: t .

[0165]

[0166] Combining formulas (12a), (14)-(18), we can get V t The derivative with respect to t is (see formula (19)):

[0167]

[0168] if is less than zero, the tracking error corresponding to the tracking error sub-model must converge. v The value of should be such that Therefore, in some embodiments, the candidate Lyapunov function of the error submodel is Less than zero can also be used as a tracking constraint or one of the balancing constraints.

[0169] Optionally, based on the above derivation, it can be determined that the mismatch interference of the tracking error submodel on the balancing error submodel is at least partially based on the steering angular velocity of the candidate trajectory and the error between the forward speed of the two-wheel driving system and the forward speed set by the candidate trajectory. For example, according to formula (12b), for ∑ b ,ω d v e It can be considered to be from ∑ t 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.

[0170] In some embodiments, see Figure 3 , the use of the tracking error sub-model and the balance error sub-model to determine whether the two-wheel travel system satisfies the balance constraint and the tracking constraint may also include: based on the range of the steering angular acceleration provided by the front handlebar steering assembly, using the balance error sub-model to determine whether the two-wheel travel system satisfies the balance constraint; wherein the balance constraint is that the balance error sub-model maintains a stable state, and the stability of the balance error sub-model is positively correlated with the dynamic balance of the two-wheel travel system during driving.

[0171] Optionally, determining whether the two-wheel travel system satisfies the balance constraint condition based on the range of the steering angular acceleration provided by the front handlebar steering assembly and using a balance error sub-model may also include: determining an ideal steering angular acceleration for controlling the stability of the balance error sub-model based on the balance error sub-model and using an optimal control method; determining that the two-wheel travel system satisfies the balance constraint condition when the ideal steering angular acceleration is within the range of the steering angular acceleration provided by the front handlebar steering assembly; and determining that the two-wheel travel system does not satisfy the balance constraint condition when the ideal steering angular acceleration is outside the range of the steering angular acceleration provided by the front handlebar steering assembly; wherein the steering angular acceleration provided by the front handlebar steering assembly is positively correlated with the component of the error between the contact point position of the rear wheel with the ground and the contact point position set by the candidate trajectory in a direction perpendicular to the forward direction.

[0172] It should be understood by those skilled in the art that for each fixed v d The corresponding ideal steering angular acceleration u provided by the front handlebar 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 how to obtain an example method of the steering angular acceleration that should be provided by the front handlebar steering assembly simulation. Those skilled in the art should understand that the present disclosure is not limited to this.

[0173] Based on the above derivation, using the optimal control method, u can be expressed as follows: ω .

[0174]

[0175] in,

[0176] μ and φ are any values ​​greater than zero, y e is 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 candidate trajectory in the direction perpendicular to the forward direction. Therefore, formula (12b) can be rewritten as formula (21).

[0177]

[0178] in, According to the optimal control method, can be designed as (see formula (22)):

[0179]

[0180] The matrix K can be obtained by solving the following Riccati formula (see formula (23)):

[0181]

[0182] in, Matrix R is the Riccati equation constructed based on matrices A, B, and D Parameters, P is the solution of the Riccati equation. AT is the transpose of matrix A, BT is the transpose of matrix B, Wherein, I4 and O4 are a four-dimensional unit matrix and a zero-point matrix respectively, Q=QT>0, and γ is a real number. As an example, γ is 1.5. Of course, γ can also be other values, and the present disclosure is not limited thereto.

[0183] If the above u ω If there is a solution, and the torque of the front handlebar steering assembly can provide the corresponding steering angular acceleration, then at least at time t, the two-wheel driving system can smoothly drive from the starting position to the position (x d ,y d ), that is, the two-wheel driving system will not deviate too far from the candidate trajectory.

[0184] For the convenience of analysis, u is determined using formula (20) ω To determine whether the stability of the driving error model / balance error sub-model will be affected, a candidate Lyapunov function V of the balance error sub-model is defined here: b , which is formula (24).

[0185] V b = x T Pχ (24)

[0186] According to optimal control theory, if formula (25) holds, the equilibrium error sub-model is stable.

[0187]

[0188] Next, based on the tracking error sub-model and the balancing error sub-model after adjusting parameters, it can be determined whether the two-wheel driving system can smoothly drive from the starting position to the target position along the candidate trajectory.

[0189] In order to make the candidate Lyapunov function V of the balanced error submodel b and the candidate Lyapunov function V of the tracking error submodel t All of them can make the above-mentioned balancing error sub-model, tracking error sub-model and driving error model stable, and the parameters that may be involved in the above-mentioned models need to be adjusted.

[0190] Two methods for adjusting the parameters in the driving error model are introduced below. Those skilled in the art should understand that there may be various ways to adjust the parameters in the driving error model, and the present disclosure does not limit this.

[0191] 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 the boundary of ω, M(u ω ) that is u ω The following describes a method 1 and a method 2 for adjusting the parameters in the driving error model in the two cases of ω≠0 and ω=0. The method 1 is applicable to ω≠0, and the method 2 is applicable to ω=0.

[0192] See also Figure 3 Method one includes: based on the tracking error submodel and the balance error submodel, determining a first gain of the tracking error submodel to the balance error submodel and a second gain of the balance error submodel to the tracking error submodel; based on the first gain and the second gain, determining a total gain of the driving driving force provided by the rear-wheel drive component and the steering angular acceleration provided by the front handlebar steering component for the driving error model, and adjusting parameters in the tracking error submodel and the balance error submodel based on the total gain; and determining whether the two-wheel driving system satisfies the balance constraint and the tracking constraint based on the tracking error submodel and the balance error submodel after adjusting the parameters.

[0193] In the case of ω≠0, ω≠0 means 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:

[0194]

[0195] because, and According to formula (26), the following inequality (27) can be obtained:

[0196]

[0197] in, and By using the following formula (28), we can ensure and

[0198]

[0199] Then, according to formula (15), the following inequality (29) can be obtained:

[0200]

[0201] also, and As a result, using formula (25), the following inequality (30) can be obtained:

[0202]

[0203] According to formula (27), from ∑ b to∑ t The gain can be calculated using formula (31), which is the second gain mentioned above:

[0204]

[0205] According to formula (30), from ∑ t to∑ b The gain can be calculated using formula (32), which is the first gain mentioned above:

[0206]

[0207] Among them, ω d ,v d and φ satisfy the following conditions (i.e., formula (33)):

[0208]

[0209] Therefore, if formula (28) is satisfied, the total gain g bt g tb <1. According to the small gain theory, at this point, the driving error system is asymptotically stable.

[0210] That is, by adjusting the parameters c1 and c2, and Among them, |ω|≤M(ω), |u ω |≤M(u ω ), |ω|>ρ>0, which can make the above-mentioned balance error sub-model, tracking error sub-model and driving error model asymptotically stable when ω≠0.

[0211] Of course, those skilled in the art will appreciate that the total gain g bt g tbAs the rigid structure of the two-wheel driving system changes, the corresponding expression can change accordingly. The present disclosure does not specifically limit the method of adjusting the parameters in the tracking error submodel and the balancing error submodel, as long as it can satisfy the total gain g bt g tb <1 will do.

[0212] If after attempts, parameters c1, c2 and c3 that meet the above conditions cannot be found, it means that there is a sampling point on the candidate trajectory that makes the balance error sub-model, tracking error sub-model and driving error model unstable, and thus the candidate trajectory is unqualified, that is, the two-wheel driving system cannot smoothly drive from the starting position to the target position along the candidate trajectory.

[0213] Continue to see Figure 3 Method 2 includes: based on the driving error model, determining a first stability analysis submodel and a second stability analysis submodel, wherein the first stability analysis submodel is cascaded with the second stability analysis submodel; adjusting parameters in the driving error model so that the first stability analysis submodel is input to a state stable and the second stability analysis submodel is locally exponentially low stable; based on the driving error model after adjusting parameters, determining the tracking error submodel and the balance error submodel; and based on the determined tracking error submodel and the balance error submodel, determining whether the two-wheel driving system satisfies the balance constraint and the tracking constraint.

[0214] In the case of ω = 0, according to the stability theorem (Lemma) of the nonlinear feedforward system (the driving error model is a typical nonlinear feedforward system): if the influencing variables in the nonlinear feedforward system are bounded (that is, |ω| ≤ M(ω) and |u ω |≤M(u ω )), then when the nonlinear feedforward system can be decomposed into two cascaded subsystems, and the lower subsystem of the cascade is input-state stable and the upper subsystem of the cascade is locally exponentially low-stable, the nonlinear feedforward system is globally asymptotically stable.

[0215] The stability theorem for nonlinear feedforward systems can be defined mathematically as follows.

[0216] If the nonlinear feedforward system defined by expression (34) has f(0)=0 and l(0)=0, and it is defined that: and G=g(0), then when the following two conditions are met, there exists μ * >0 and φ * > 0, so that for any μ∈(0,μ * ) and φ∈(0,φ *), the nonlinear feedforward system is globally gradual stable at the origin.

[0217]

[0218] Condition ①: is input-to-state stable (ISS) and It is locally exponentially stable (LES);

[0219] Condition ②: HW -1 G < 0. Locally exponentially stable (LES) can also be called locally asymptotically stable.

[0220] That is, there exists μ * >0 and φ * > 0, so that for any μ∈(0,μ * ) and φ∈(0,φ * ), the closed-loop system defined by the following formula (35) is globally gradual stable at the origin.

[0221]

[0222] When ω=0, When u is obtained in the above steps v and u ω , the driving error model in formula (12a) and formula (12b) can be written as follows, that is, formula (36):

[0223]

[0224] Among them, ∑ ξ This is the first stability analysis submodel. Remove Bu from formula (36) c The part after the component is the second stability analysis sub-model.

[0225] Definition ξ The candidate Lyapunov function is formula (37).

[0226]

[0227] Where a>0 and is a constant scalar. Consider u c =0, according to formula (36), It can be expressed as formula (38).

[0228]

[0229] If formula (33) is satisfied, it means:

[0230]

[0231] Therefore, there is So that:

[0232]

[0233] Formula (40) can derive the following inequality (41).

[0234]

[0235] Therefore, there exists a,λ>0 such that Therefore, when u c =0,∑ ξ The input is stable. At this time, ∑ ξ is ISS (that is, the first stability analysis submodel is input to the state stable), while the second stability analysis submodel is locally exponentially low stable. Therefore, condition ① holds for formula (36).

[0236] 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.

[0237] That is, by adjusting the parameters c1, c2 and c3, Among them, a satisfies the inequality and Any real number can make the above-mentioned balance error sub-model, tracking error sub-model and driving error model asymptotically stable when ω=0.

[0238] If after attempts, parameters c1, c2 and c3 that meet the above conditions cannot be found, it means that there is a sampling point on the candidate trajectory that makes the balance error sub-model, tracking error sub-model and driving error model unstable, and thus the candidate trajectory is unqualified, that is, the two-wheel driving system cannot smoothly drive from the starting position to the target position along the candidate trajectory.

[0239] Of course, those skilled in the art should understand that the first stability analysis submodel and the second stability analysis submodel can change with the change of the rigid structure of the two-wheel travel system, and their corresponding expressions can change accordingly. The present disclosure does not specifically limit the way to adjust the parameters in the tracking error submodel and the balance error submodel, as long as it can satisfy that the first stability analysis submodel is input to a stable state and the second stability analysis submodel is locally exponentially low stable. Once the parameters in the driving error model are adjusted, the first stability analysis submodel can be input to a stable state and the second stability analysis submodel is locally exponentially low stable, and the driving error model is stable / convergent when ω=0. At this time, the propulsion force and steering angular velocity of the determined two-wheel travel system can ensure that the two-wheel travel system accurately travels along the desired trajectory while ensuring the dynamic balance of the two-wheel travel system.

[0240] Therefore, the method for determining the driving trajectory of a two-wheel driving system provided by the present invention plans the driving path of the two-wheel driving system based on the balance constraint conditions, the starting position and the target position, thereby ensuring that the two-wheel driving system can smoothly drive to the target position according to the planned path.

[0241] Figure 4A 2 is an example of parameters of a two-wheel travel system according to at least one embodiment of the present disclosure. Figure 4B Based on Figure 4A A comparison curve diagram of the candidate trajectory of the two-wheel driving system determined by the parameters around the "circle-line" candidate trajectory and the simulated trajectory. Figure 4C Based on Figure 4A Schematic diagram of four different moments when the two-wheel driving system determined by the parameters of is driving around the "circle-line" candidate trajectory. Figure 4D Based on Figure 4A A comparison curve diagram of the candidate trajectory of the two-wheel driving system determined by the parameters traveling around the "8"-shaped candidate trajectory and the simulated trajectory. Figure 4E Based on Figure 4A Schematic diagram of four different moments when the two-wheel driving system determined by the parameters is driving around the "8"-shaped candidate trajectory.

[0242] See also Figure 4A , assuming Figure 1 and Figure 2B The two-wheel drive system 10 shown has the parameters shown in the parameter table of the two-wheel drive system, wherein the content shown in [] is the unit of the parameter.

[0243] The test was conducted with the following parameters to verify that the driving force provided by the rear-wheel drive assembly and the steering angular acceleration provided by the front handlebar steering assembly determined based on method 20 can ensure the dynamic balance of the two-wheel driving system while ensuring that the two-wheel driving system accurately travels along the desired trajectory.

[0244] Specifically, the parameters in the experiment were set as: 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.

[0245] Figure 4B The candidate trajectory of the "circle-line" shape is set (which is based on Figure 4B The radius of the circle in the candidate trajectory is 10 m. The two-wheel driving system 10 moves at a forward speed v d = 4m / s, trace the circle three times in the counterclockwise direction, and then proceed along the straight line shown by the dotted line. Figure 4B The horizontal axis of the graph (a) is the projection of the contact point between the rear wheel of the two-wheel travel system 10 and the ground in the X-axis direction in the basic three-dimensional coordinate system O-XYZ. Figure 4B The vertical axis of the curve graph (a) is the projection of the contact point between the rear wheel of the two-wheel travel system 10 and the ground in the Y-axis direction in the basic three-dimensional coordinate system O-XYZ.

[0246] 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 first 0.2 seconds, when the two-wheel travel system 10 accelerates from rest, the static balancing assembly 140 is used to balance the two-wheel travel system 10. Figure 4B In the curve diagram (a), the trajectory of the simulated driving of the two-wheel driving system 10 under the above-mentioned set parameters is represented by a solid line. It can be seen that the difference between the simulated trajectory of the two-wheel driving system 10 and the candidate trajectory is very small. That is, under this parameter, the two-wheel driving system can accurately drive along the desired trajectory.

[0247] Figure 4B The curve diagram (b) further shows the change of the horizontal component in the simulated trajectory and the horizontal component in the candidate trajectory over time. Specifically, Figure 4B The vertical axis of the curve graph (b) is the projection of the contact point between the rear wheel of the two-wheel travel system 10 and the ground in the X-axis direction in the basic three-dimensional coordinate system O-XYZ, and the unit is meter (m). Figure 4B The horizontal axis of the curve graph (b) is time, in seconds (s). The dotted line represents the candidate trajectory, and the solid line represents the simulated trajectory. It can be seen that the simulated trajectory x gradually converges to x d .

[0248] Figure 4B The curve diagram (c) further shows the change of the horizontal component in the simulated trajectory and the horizontal component in the candidate trajectory over time. Specifically, Figure 4BThe vertical axis of the curve graph (b) is the projection of the contact point between the rear wheel of the two-wheel travel system 10 and the ground in the Y-axis direction in the basic three-dimensional coordinate system O-XYZ, and the unit is meter (m). Figure 4B The horizontal axis of the curve (b) is time, in seconds (s). The dotted line represents the candidate trajectory, and the solid line represents the simulated trajectory. It can be seen that the simulated trajectory y gradually converges to y d .

[0249] Figure 4B The curve diagram (d) further shows the change of the roll angle θ in the simulated trajectory and the roll angle θ in the candidate trajectory over time. Specifically, Figure 4B The vertical axis of the graph (d) is the roll angle θ of the two-wheel travel system 10, with the unit being rad. Figure 4B The horizontal axis of the curve graph (d) is time, with the unit being seconds (s). Figure 4B In the curve diagram (d), when the two-wheel driving system 10 is traveling in the counterclockwise direction, it must balance its own roll angle θ to a negative value, at which time the gravity can be offset by the centrifugal force. When the two-wheel driving system 10 is traveling in a straight line, the required roll angle θ is zero. The dotted line represents the candidate trajectory, and the solid line represents the simulated trajectory. It can be seen that θ of the simulated trajectory converges asymptotically to the roll angle of the candidate trajectory.

[0250] Figure 4B The curve diagram (e) further shows the forward speed v in the simulated trajectory and the forward speed v in the candidate trajectory. d Changes over time. Specifically, Figure 4B The vertical axis of the curve graph (e) is the forward speed of the two-wheel travel system 10, and the unit is m / s. Figure 4B The horizontal axis of the curve graph (e) is time, with the unit being seconds (s). Figure 4B In the curve diagram (e), the dotted line represents the candidate trajectory and the solid line represents the simulated trajectory. It can be seen that the forward speed v of the simulated trajectory gradually converges to the forward speed v in the candidate trajectory. d .

[0251] Figure 4B The curve diagram (f) further shows the change of the steering angle in the simulated trajectory over time. Specifically, Figure 4B The vertical axis of the curve graph (f) is the steering angle of the two-wheel travel system 10, and the unit is rad. Figure 4B The horizontal axis of the curve graph (f) is time, and the unit is second (s).

[0252] Figure 4CSchematic diagram (a) shows a schematic diagram of the two-wheel travel system 10 traveling around the "circle-line" candidate trajectory at time t = 4.415. At this time, the contact point between the rear wheel of the two-wheel travel system 10 and the ground is located at x = -1.738, y = 8.311 in the basic three-dimensional coordinate system O-XYZ.

[0253] Figure 4C Schematic diagram (b) shows a schematic diagram of the two-wheel travel system 10 traveling around the "circle-line" candidate trajectory at time t = 8.415. At this time, the contact point between the rear wheel of the two-wheel travel system 10 and the ground is located at x = -8.014, y = -3.424 in the basic three-dimensional coordinate system O-XYZ.

[0254] Figure 4C Schematic diagram (c) shows a schematic diagram of the two-wheel travel system 10 traveling around the "circle-line" candidate trajectory at time t = 31.144. At this time, the contact point between the rear wheel of the two-wheel travel system 10 and the ground is located at x = 9.932, y = -1.085 in the basic three-dimensional coordinate system O-XYZ.

[0255] Figure 4C Schematic diagram (d) shows the schematic diagram of the two-wheel travel system 10 traveling around the "circle-line" candidate trajectory at time t = 57.586. At this time, the contact point between the rear wheel of the two-wheel travel system 10 and the ground is located at x = 10.390, y = 41.840 in the basic three-dimensional coordinate system O-XYZ.

[0256] visible Figure 4B The “circle-line” candidate trajectory is a qualified candidate trajectory.

[0257] Figure 4D The candidate trajectory of the "8" shape is set (which is based on Figure 4D The radius of the circle in the candidate trajectory is 10 m. The two-wheel driving system 10 moves at a forward speed v d =4m / s, and travels one circle in the right circle in the counterclockwise direction. Then, the two-wheel driving system 10 will travel one circle in the left circle in the clockwise direction at the same speed. Figure 4D The horizontal axis of the graph (a) is the projection of the contact point between the rear wheel of the two-wheel travel system 10 and the ground in the X-axis direction in the basic three-dimensional coordinate system O-XYZ. Figure 4D The vertical axis of the curve graph (a) is the projection of the contact point between the rear wheel of the two-wheel travel system 10 and the ground in the Y-axis direction in the basic three-dimensional coordinate system O-XYZ.

[0258] 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 first 0.2 seconds, when the two-wheel travel system 10 accelerates from rest, the static balancing assembly 140 is used to balance the two-wheel travel system 10. Figure 4D In the curve diagram (a), the trajectory of the simulated driving of the two-wheel driving system 10 under the above-mentioned set parameters is represented by a solid line. It can be seen that the difference between the simulated trajectory of the two-wheel driving system 10 and the candidate trajectory is very small. That is, under this parameter, the two-wheel driving system can accurately drive along the desired trajectory.

[0259] 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 candidate trajectory. After the two-wheel driving system 10 travels half a circle, or when the time t reaches infinity, the simulation trajectory will converge to the candidate trajectory again.

[0260] Figure 4D The curve diagram (b) further shows the change of the horizontal component in the simulated trajectory and the horizontal component in the candidate trajectory over time. Specifically, Figure 4D The vertical axis of the curve graph (b) is the projection of the contact point between the rear wheel of the two-wheel travel system 10 and the ground in the X-axis direction in the basic three-dimensional coordinate system O-XYZ, and the unit is meter (m). Figure 4D The horizontal axis of the curve graph (b) is time, in seconds (s). The dotted line represents the candidate trajectory, and the solid line represents the simulated trajectory. It can be seen that the simulated trajectory x gradually converges to x d .

[0261] Figure 4D The curve diagram (c) further shows the change of the horizontal component in the simulated trajectory and the horizontal component in the candidate trajectory over time. Specifically, Figure 4D The vertical axis of the curve graph (b) is the projection of the contact point between the rear wheel of the two-wheel travel system 10 and the ground in the Y-axis direction in the basic three-dimensional coordinate system O-XYZ, and the unit is meter (m). Figure 4D The horizontal axis of the curve (b) is time, in seconds (s). The dotted line represents the candidate trajectory, and the solid line represents the simulated trajectory. It can be seen that the simulated trajectory y gradually converges to y d .

[0262] Figure 4D The curve diagram (d) further shows the change of the roll angle θ in the simulated trajectory and the roll angle θ in the candidate trajectory over time. Specifically, Figure 4D The vertical axis of the graph (d) is the roll angle θ of the two-wheel travel system 10, with the unit being rad. Figure 4D The horizontal axis of the curve graph (d) is time, with the unit being seconds (s). Figure 4DIn the curve diagram (d), when the two-wheel driving system 10 is traveling in the counterclockwise direction, it must balance its own roll angle θ to a negative value, at which time the gravity can be offset by the centrifugal force. When the two-wheel driving system 10 is traveling in a straight line, the required roll angle θ is zero. The dotted line represents the candidate trajectory, and the solid line represents the simulated trajectory. It can be seen that θ of the simulated trajectory converges asymptotically to the roll angle of the candidate trajectory.

[0263] Figure 4D The curve diagram (e) further shows the forward speed v in the simulated trajectory and the forward speed v in the candidate trajectory. d Changes over time. Specifically, Figure 4D The vertical axis of the curve graph (e) is the forward speed of the two-wheel travel system 10, and the unit is m / s. Figure 4D The horizontal axis of the curve graph (e) is time, with the unit being seconds (s). Figure 4D In the curve diagram (e), the dotted line represents the candidate trajectory and the solid line represents the simulated trajectory. It can be seen that the forward speed v of the simulated trajectory gradually converges to the forward speed v in the candidate trajectory. d .

[0264] Figure 4D The curve diagram (f) further shows the change of the steering angle in the simulated trajectory over time. Specifically, Figure 4D The vertical axis of the curve graph (f) is the steering angle of the two-wheel travel system 10, and the unit is rad. Figure 4D The horizontal axis of the curve graph (f) is time, and the unit is second (s).

[0265] Figure 4E Schematic diagram (a) shows a schematic diagram of the two-wheel travel system 10 traveling around the candidate trajectory of the figure 8 at time t=4.367. At this time, the contact point between the rear wheel of the two-wheel travel system 10 and the ground is located at x=10.571, y=-10.429 in the basic three-dimensional coordinate system O-XYZ.

[0266] Figure 4E Schematic diagram (b) shows a schematic diagram of the two-wheel travel system 10 traveling around the candidate trajectory of the figure 8 at time t=12.317. At this time, the contact point between the rear wheel of the two-wheel travel system 10 and the ground is located at x=8.6661, y=9.908 in the basic three-dimensional coordinate system O-XYZ.

[0267] Figure 4E Schematic diagram (c) shows a schematic diagram of the two-wheel travel system 10 traveling around the candidate trajectory of the figure 8 at time t=31.144. At this time, the contact point between the rear wheel of the two-wheel travel system 10 and the ground is located at x=-7.100, y=-10.230 in the basic three-dimensional coordinate system O-XYZ.

[0268] Figure 4E Schematic diagram (d) shows a schematic diagram of the two-wheel travel system 10 traveling around the candidate trajectory of the figure 8 at time t=19.295. At this time, the contact point between the rear wheel of the two-wheel travel system 10 and the ground is located at x=-10.360, y=10.024 in the basic three-dimensional coordinate system O-XYZ.

[0269] visible Figure 4D The "8"-shaped candidate trajectory is a qualified candidate trajectory.

[0270] It can be seen that the method for determining the driving trajectory of a two-wheel driving system provided by the present disclosure plans the driving path of the two-wheel driving system based on the balance constraint condition, the starting position and the target position, thereby ensuring that the two-wheel driving system can smoothly drive to the target position according to the planned path.

[0271] Therefore, the present disclosure also provides a two-wheel driving system, which includes a front handlebar steering assembly and a rear-wheel drive assembly, wherein the front handlebar steering assembly and the rear-wheel drive assembly respectively form a contact point with the ground, and the driving trajectory of the two-wheel driving system is determined according to the aforementioned method 20.

[0272] like Figure 5 As shown, the operation terminal of the above 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 a computer readable code, and when the computer readable code is executed by the one or more processors 2010, the various methods described above can be executed.

[0273] The processor in the embodiments of the present disclosure may be an integrated circuit chip having the ability to process signals. The processor may 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 gates or transistor logic devices, discrete hardware components. The methods, steps and logic block diagrams disclosed in the embodiments of the present application may be implemented or executed. The general-purpose processor may be a microprocessor or the processor may be any conventional processor, etc., and may be an X86 architecture or an ARM architecture.

[0274] In general, various example embodiments of the present disclosure may be implemented in hardware or dedicated circuits, software, firmware, logic, or any combination thereof. Certain aspects may be implemented in hardware, while other aspects may be implemented in firmware or software that may be executed by a controller, microprocessor, or other computing device. When various aspects of the embodiments of the present disclosure are illustrated or described as block diagrams, flow charts, or using some other graphical representation, it will be understood that the blocks, devices, systems, techniques, or methods described herein may be implemented in hardware, software, firmware, dedicated circuits or logic, general purpose hardware or controllers or other computing devices, or some combination thereof as non-limiting examples.

[0275] For example, the method or device according to the embodiment of the present disclosure may also be Figure 6 The architecture of the computing device 3000 shown in FIG. Figure 6 As 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 device in the computing device 3000, such as the ROM 3030 or the hard disk 3070, may store various data or files used for processing and / or communication of the method for determining the driving risk of a vehicle provided by the present 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 only exemplary and can be omitted according to actual needs when implementing different devices. Figure 6 One or more components of a computing device are shown.

[0276] According to yet another aspect of the present disclosure, a computer-readable storage medium is provided. Figure 7 A schematic diagram of a storage medium 4000 according to the present disclosure is shown.

[0277] like Figure 7As shown, the computer storage medium 4020 stores computer-readable instructions 4010. When the computer-readable instructions 4010 are executed by the processor, the various methods described with reference to the above figures according to the embodiments of the present disclosure can be executed. The computer-readable storage medium in the embodiments of the present disclosure can be a volatile memory or a non-volatile memory, or can include both volatile and non-volatile memories. The non-volatile memory can be a read-only memory (ROM), a programmable read-only memory (PROM), an erasable programmable read-only memory (EPROM), an electrically erasable programmable read-only memory (EEPROM), or a flash memory. The volatile memory can be a 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 connection dynamic random access memory (SLDRAM) and direct memory bus random access memory (DR RAM). It should be noted that memory of the methods described herein is intended to include, but is not limited to, these and any other suitable types of memory. It should be noted that memory of the methods described herein is intended to include, but is not limited to, these and any other suitable types of memory.

[0278] The embodiments of the present disclosure also provide a computer program product or a computer program, which includes a computer instruction stored in a computer-readable storage medium. The processor of the computer device reads the computer instruction from the computer-readable storage medium, and the processor executes the computer instruction, so that the computer device executes each method according to the embodiments of the present disclosure.

[0279] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the possible architecture, functions and operations of the systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each box in the flowchart or block diagram can represent a module, a program segment, or a part of a code, and the module, program segment, or a part of the code contains one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of boxes in the block diagram and / or flowchart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0280] In general, various example embodiments of the present disclosure may be implemented in hardware or dedicated circuits, software, firmware, logic, or any combination thereof. Certain aspects may be implemented in hardware, while other aspects may be implemented in firmware or software that may be executed by a controller, microprocessor, or other computing device. When various aspects of the embodiments of the present disclosure are illustrated or described as block diagrams, flow charts, or using some other graphical representation, it will be understood that the blocks, devices, systems, techniques, or methods described herein may be implemented in hardware, software, firmware, dedicated circuits or logic, general purpose hardware or controllers or other computing devices, or some combination thereof as non-limiting examples.

[0281] The exemplary embodiments of the present disclosure described in detail above are merely illustrative and not restrictive. It should be understood by those skilled in the art that various modifications and combinations may be made to these embodiments or their features without departing from the principles and spirit of the present disclosure, and such modifications should fall within the scope of the present disclosure.

Claims

1. A method for determining a driving trajectory of a two-wheel driving system, wherein: The two-wheel driving system comprises a front handlebar steering assembly and a rear wheel driving assembly, and the method comprises: Determining a set of candidate trajectories of the two-wheel travel system based on a starting position and a target position of the two-wheel travel system; For each candidate trajectory in the candidate trajectory set, Based on the candidate trajectory, determining a tracking constraint condition for the two-wheel driving system to travel along the candidate trajectory, and a balance constraint condition for the two-wheel driving system to maintain dynamic balance during the travel along the candidate trajectory; and Based on the balance constraint and the tracking constraint, determining whether the two-wheel driving system can smoothly drive from the starting position to the target position along the candidate trajectory; The tracking constraint condition is determined based on the kinematic characteristic quantity of the two-wheel travel system and the candidate trajectory, and the balance constraint condition is determined based on the dynamic characteristic quantity and kinematic characteristic quantity of the two-wheel travel system. Among them, the tracking constraint condition is the convergence of the tracking error, and the tracking error includes: the error between the forward speed of the two-wheel driving system and the forward speed set by the candidate trajectory, and the error between the forward acceleration of the two-wheel driving system and the forward acceleration set by the candidate trajectory.

2. The method of claim 1, wherein: The kinematic characteristic quantities and the dynamic characteristic quantities of the two-wheel driving system are associated with the performance parameters of the front handlebar steering assembly and the rear-wheel drive assembly. The performance parameters of the front handlebar steering assembly at least include the range of the steering angular acceleration provided by the front handlebar steering assembly, and the performance parameters of the rear-wheel drive assembly at least include the range of the driving force provided by the rear-wheel drive assembly.

3. The method of claim 2, wherein: The determining, based on the balance constraint and the tracking constraint, whether the two-wheel driving system can smoothly drive from the starting position to the target position along the candidate trajectory further includes: Determining a driving error model based on the balance constraint and the tracking constraint; Based on the driving error model, determining a tracking error sub-model and a balancing error sub-model; Determining whether the two-wheel driving system satisfies the balance constraint condition and the tracking constraint condition by using the tracking error sub-model and the balance error sub-model; Under the condition that the two-wheel driving system satisfies the balance constraint condition and the tracking constraint condition, determining that the two-wheel driving system can smoothly drive from the starting position to the target position along the candidate trajectory; When the two-wheel driving system does not satisfy the balance constraint condition and the tracking constraint condition, it is determined that the two-wheel driving system cannot smoothly drive from the starting position to the target position along the candidate trajectory.

4. The method of claim 3, wherein: The determining whether the two-wheel driving system satisfies the balance constraint condition and the tracking constraint condition by using the tracking error sub-model and the balance error sub-model further comprises: Calculating the tracking error using the tracking error sub-model; and Based on the tracking error and the range of the driving force provided by the rear wheel drive assembly, it is determined whether the two-wheel drive system satisfies the tracking constraint condition.

5. The method of claim 3, wherein: The determining whether the two-wheel driving system satisfies the balance constraint condition and the tracking constraint condition by using the tracking error sub-model and the balance error sub-model further comprises: Based on the range of steering angular acceleration provided by the front handlebar steering assembly, using a balance error sub-model, determining whether the two-wheel travel system satisfies the balance constraint condition; The balance constraint condition is that the balance error sub-model maintains a stable state, and the stability of the balance error sub-model is positively correlated with the dynamic balance of the two-wheel driving system during driving.

6. The method of claim 3, wherein: in, The mismatched interference of the tracking error sub-model to the balancing error sub-model is based at least in part on the steering angle velocity of the candidate trajectory and the error between the forward speed of the two-wheel drive system and the forward speed set by the candidate trajectory.

7. The method of claim 4, wherein: Based on the tracking error and the range of the driving force provided by the rear wheel drive assembly, determining whether the two-wheel driving system satisfies the tracking constraint condition further includes: Based on the tracking error sub-model, using a backstepping method, determining an ideal driving force for controlling the tracking error convergence of the tracking error sub-model; determining that the two-wheel drive system satisfies the tracking constraint condition when the ideal driving force is within the range of the driving force provided by the rear-wheel drive assembly; and determining that the two-wheel drive system does not satisfy the tracking constraint condition when the ideal driving force is outside the range of the driving force provided by the rear-wheel drive assembly; The ideal driving force is positively correlated with the steering angle acceleration of the two-wheel drive system with respect to the yaw angle.

8. The method of claim 7, wherein: The determining whether the two-wheel travel system satisfies the balance constraint condition based on the range of the steering angular acceleration provided by the front handlebar steering assembly and using the balance error sub-model further comprises: Based on the balance error sub-model, using an optimal control method, determining an ideal steering angle acceleration for controlling the balance error sub-model to maintain a stable state; determining that the two-wheel travel system satisfies the balance constraint condition when the ideal steering angular acceleration is within the range of the steering angular acceleration provided by the front handlebar steering assembly; and In a case where the ideal steering angular acceleration is outside the range of the steering angular acceleration provided by the front handlebar steering assembly, determining that the two-wheel travel system does not satisfy the balance constraint condition; The steering angular acceleration provided by the front handlebar steering assembly is positively correlated with a component of an error between a contact point position of the rear wheel with the ground and a contact point position set by the candidate trajectory in a direction perpendicular to the forward direction.

9. The method of claim 3, wherein: The use of the tracking error sub-model and the balance error sub-model to determine whether the two-wheel driving system satisfies the balance constraint condition and the tracking constraint condition: Based on the tracking error sub-model and the balancing error sub-model, determining a first gain of the tracking error sub-model to the balancing error sub-model and a second gain of the balancing error sub-model to the tracking error sub-model; Based on the first gain and the second gain, 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 for the driving error model, Based on the total gain, adjusting parameters in the tracking error sub-model and the balancing error sub-model; as well as Based on the tracking error sub-model and the balancing error sub-model after adjusting parameters, it is determined whether the two-wheel driving system satisfies the balancing constraint condition and the tracking constraint condition.

10. The method of claim 8, wherein: The determining whether the two-wheel driving system satisfies the balance constraint condition and the tracking constraint condition by using the tracking error sub-model and the balance error sub-model further comprises: Based on the driving error model, determining a first stability analysis sub-model and a second stability analysis sub-model, wherein the first stability analysis sub-model is cascaded with the second stability analysis sub-model; Adjusting parameters in the driving error model so that the first stability analysis submodel is input-to-state stable and the second stability analysis submodel is locally exponentially low stable; Determining the tracking error sub-model and the balancing error sub-model based on the driving error model after adjusting the parameters; and Based on the determined tracking error sub-model and the balancing error sub-model, it is determined whether the two-wheel driving system satisfies the balancing constraint condition and the tracking constraint condition.

11. The method of claim 7, wherein: The ideal driving force is determined as the ideal forward acceleration u of the two-wheel drive system at time t. v Proportional, Among them, u v Determined as in, Among them, c1, c2, and c3 are all positive constants. u ω is the ideal steering angular acceleration, for The derivative of in, u v,d The forward acceleration set for the candidate trajectory; ω is the simulated steering angular velocity of the two-wheel travel system at time t; y e is the component of the error between the simulated contact point position of the rear wheel and the ground at time t and the contact point position set by the candidate trajectory in the perpendicular direction to the forward direction, v e is the error between the simulated forward speed of the two-wheel driving system at time t and the forward speed set by the candidate trajectory, v d The forward speed set for the candidate trajectory at time t, ψ e is the error between the simulated yaw angle of the two-wheel travel system at time t and the yaw angle set for the candidate trajectory at time t; x e It is the component of the error in the forward direction between the simulated contact point position of the rear wheel and the ground at time t and the contact point position set by the candidate trajectory.

12. The method of claim 8, wherein: The ideal steering angular acceleration u at time t ω Determined to be in, u ω,d The steering angular acceleration at time t set for the candidate trajectory, ε>0, matrix R is the Riccati equation constructed based on matrices A, B, and D Parameters, P is the solution of the Riccati equation, A T is the transpose of matrix A, B T is the transpose of matrix B, Among them, I4 and 04 are the four-dimensional unit matrix and zero-point matrix respectively, Q = Q T >0, γ is a real number, μ and φ are any values ​​greater than zero, y e is the component of the error between the simulated contact point position of the rear wheel and the ground at time t and the contact point position set by the candidate trajectory in the perpendicular direction to the forward direction, ψ e is the error between the simulated yaw angle of the two-wheel driving system at time t and the yaw angle set at time t by the candidate trajectory, η 1,e represents the error between the roll angle of the two-wheel driving system at time t and the roll angle set by the candidate trajectory, η 2,e represents the error between the parameter associated with the roll angle of the two-wheel drive system at time t and the parameter associated with the roll angle of the candidate trajectory setting, ω e is the error between the simulated steering angular velocity of the two-wheel travel system at time t and the steering angular velocity set for the candidate trajectory at time t, v d is the forward speed set for the candidate trajectory at time t, m is the total mass of the two-wheel travel system, h is the height of the center of mass of the two-wheel travel system, I is the moment of inertia of the two-wheel travel system, g is the acceleration of gravity, and b is the horizontal distance between the contact point of the rear wheel with the ground and the center of mass of the two-wheel travel system.

13. The method of claim 1, wherein: The front handlebar steering assembly comprises: a front wheel, a front handlebar, and a steering motor; The rear wheel drive assembly includes: a rear wheel, and a drive motor; The two-wheel travel system further comprises: a frame crossbeam; The simulated driving state parameters associated with the dynamic characteristic quantity or the kinematic characteristic quantity include the roll angle of the two-wheel driving system and one or more of the following items: the steering angle of the front handlebar, the angle between the center axis of the front handlebar 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 mass 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 center axis of the front handlebar and 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 center of mass height of the two-wheel driving system.

14. A two-wheel driving system, comprising a front handlebar steering assembly and a rear wheel drive assembly, wherein: The driving trajectory of the two-wheel drive system is determined according to the method according to any one of claims 1-13.

15. A computer-readable storage medium having computer-readable instructions stored thereon, wherein when a computer executes the instructions, the method according to any one of claims 1 to 13 is executed.

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