Self-balancing motion control method of a double-wheel vertical robot

Abstract

This invention belongs to the field of robot motion control technology and discloses a self-balancing motion control method for a two-wheeled upright robot, comprising the following steps: First, considering the mass, moment of inertia, length, and wheel-ground resistance coefficient of the two-wheeled upright robot, a differential equation is constructed to describe the dynamic characteristics of the robot's pitch angle and wheel rotation angle; Second, error variables are designed based on the pitch angle, pitch velocity, wheel rotation angle, wheel speed, and desired wheel rotation angle and desired wheel speed; Third, a control input with adaptive parameters and time-varying gain is designed; Fourth, an update law for the adaptive parameters and time-varying gain is designed; Fifth, the calculated control input is allocated to the left and right wheels. This invention completes the design of a self-balancing motion controller with adaptive parameters and time-varying gain, reducing the difficulty of development and debugging for engineers.

Description

Technical Field

[0001] This invention belongs to the field of robot motion control technology, and particularly relates to a self-balancing motion control method for a two-wheeled upright robot. Background Technology

[0002] In daily life, such as Figure 2 The two-wheeled upright robot shown has many applications, such as short-distance freight within the park and self-balancing vehicles for carrying people.

[0003] Currently, the main control methods for this type of robot are Linear Quadratic Regulator (LQR) and Model Predictive Control (MPC). Both methods require precise acquisition of parameters such as the robot's actual weight, length, and moment of inertia to calculate controller parameters or control inputs. However, in the aforementioned freight and passenger transport applications, the weight of personnel and goods, as well as their standing and placement positions, introduce uncertainties in weight and moment of inertia into the robot model, adversely affecting the control performance of LQR and MPC. Although these controllers have a certain robustness to uncertainties in weight and moment of inertia, from a safety perspective, before carrying passengers or goods, operators must pre-test the weight and position distribution to ensure the robot will not experience accidents. This also increases the application cost of this type of robot. Furthermore, due to issues with controller parameter selection, the controller's tolerance for uncertainties in weight and moment of inertia may be overly conservative, resulting in the robot's inability to complete certain freight or passenger transport tasks, necessitating the return to the factory to modify controller parameters, leading to additional economic expenses.

[0004] Therefore, for transportation scenarios such as freight and passenger transport, there is an urgent need to develop a self-balancing motion control algorithm from a safety perspective. This algorithm can adaptively adjust control parameters online to address uncertainties such as mass, moment of inertia, length, and drag coefficient, thereby reducing the debugging workload of the robot before it can perform tasks, increasing the working range that the robot can cover, reducing application costs, and exploring the application potential of this type of robot. Summary of the Invention

[0005] The technical problem to be solved by this invention is: how to achieve adaptive adjustment of control parameters of a two-wheeled upright robot online.

[0006] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0007] A self-balancing motion control method for a two-wheeled upright robot includes the following steps:

[0008] The first step is to consider the mass, moment of inertia, length, and wheel-ground drag coefficient of the two-wheeled upright robot, and construct differential equations to describe the dynamic characteristics of the pitch angle and wheel rotation angle of the two-wheeled upright robot.

[0009] The second step is to design error variables based on pitch angle, pitch rate, wheel angle, wheel speed, and desired wheel angle and desired wheel speed.

[0010] The third step is to design a control input with adaptive parameters and time-varying gain.

[0011] The fourth step is to design the update law for adaptive parameters and time-varying gain;

[0012] The fifth step is to distribute the calculated control inputs to the left and right wheels.

[0013] Furthermore, the differential equation constructed in the first step is as follows:

[0014]

[0015] in, It is the pitch angle of the two-wheeled upright robot. It is the pitch angular velocity of the two-wheeled upright robot. It is the distance the two-wheeled upright robot moves in its forward direction. It is the linear velocity of the two-wheeled upright robot in its forward direction. It is the resultant torque of the two wheels. , , and This includes unknown parameters such as robot length, total weight, moment of inertia, and drag coefficient.

[0016] Furthermore, in the second step, the specific error variables are as follows:

[0017]

[0018] in, It is pitch angle error. It is the pitch angular velocity error. It is the wheel angle error. Wheel speed error It is the distance that the expected two-wheeled upright robot will travel in its forward direction. It is the linear velocity of the expected two-wheeled upright robot moving in its forward direction.

[0019] Furthermore, in the third step, the specific control inputs are as follows:

[0020]

[0021] in, It is an intermediate variable. Yes Adaptive parameters, , , and It is a time-varying gain.

[0022] Furthermore, in the fourth step, the specific update law is as follows:

[0023]

[0024] in, , , , , and It is a positive adjustable parameter.

[0025] Furthermore, in the fifth step, the calculated control inputs are distributed to the left and right wheels, as follows:

[0026]

[0027] in, and These are the actual control torques for the left and right wheels, respectively.

[0028] The present invention has the following advantages:

[0029] (1) The present invention designs a self-balancing motion control method for a two-wheeled upright robot, which enables the two-wheeled upright robot to track the desired motion trajectory while ensuring that the two-wheeled upright robot can maintain balance, that is, the pitch angle is near 0 degrees.

[0030] (2) The method proposed in this invention can be applied to the field of load transportation, and does not require precise measurement of the load weight and installation location, which greatly simplifies the preparation work before load transportation, reduces labor and measurement equipment expenditures, and has broad application prospects and application value.

[0031] (3) The method proposed in this invention can adjust the motion characteristics of the two-wheeled upright robot by adjusting the adjustable parameters, which makes it easier for engineers to optimize the motion characteristics of the robot according to actual application needs and has good scalability. Attached Figure Description

[0032] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0033] Figure 2 This is a schematic diagram of a two-wheeled upright robot.

[0034] Figure 3 A schematic diagram illustrating the pitch angle tracking error of traditional control methods under variable load;

[0035] Figure 4 A schematic diagram illustrating the position tracking error of traditional control methods under variable load;

[0036] Figure 5 A schematic diagram illustrating the pitch angle tracking error of the method of the present invention under variable load;

[0037] Figure 6 A schematic diagram illustrating the position tracking error of the method of the present invention under variable load;

[0038] Figure 7 This is a schematic diagram of time-varying gain under varying load.

[0039] Figure 8 This is a schematic diagram of adaptive parameters under varying load. Detailed Implementation

[0040] To better understand the purpose, structure, and function of this invention, the invention will be described in further detail below with reference to the accompanying drawings.

[0041] This embodiment considers an upright robot with parallel left and right wheels. To meet the motion control requirements of maintaining the robot's upright balance and tracking the desired trajectory, a self-balancing motion controller with adaptive parameters and time-varying gain was designed to reduce the development and debugging difficulties for engineers and improve the application capability of the two-wheeled upright robot in the field of load transportation.

[0042] like Figure 1 As shown in the figure, the self-balancing motion control method of the two-wheeled upright robot in this embodiment is illustrated in the flowchart below. Figure 1 As shown, it includes the following steps:

[0043] The first step is to consider unknown parameters such as the mass, moment of inertia, length, and wheel-ground drag coefficient of the two-wheeled upright robot, and construct differential equations to describe the dynamic characteristics of the pitch angle and wheel rotation angle of the two-wheeled upright robot.

[0044] The second step is to design error variables based on pitch angle, pitch rate, wheel angle, wheel speed, and desired wheel angle and desired wheel speed.

[0045] The third step is to design a control input with adaptive parameters and time-varying gain.

[0046] The fourth step is to design the update law for adaptive parameters and time-varying gain;

[0047] The fifth step is to distribute the calculated control inputs to the left and right wheels.

[0048] The first step considers unknown parameters such as the mass, moment of inertia, length, and wheel-ground drag coefficient of the two-wheeled upright robot, and constructs differential equations to describe the dynamic characteristics of the robot's pitch angle and wheel rotation angle. The specific equations are as follows:

[0049]

[0050] Among them, the pitch angle of the two-wheeled upright robot Pitch angular velocity of a two-wheeled upright robot The distance traveled by the two-wheeled upright robot in its forward direction The linear velocity of the two-wheeled upright robot in its forward direction , It is the resultant torque of the two wheels. , , and These are unknown parameters including robot length, total weight, moment of inertia, and drag coefficient.

[0051] In the second step, error variables are designed based on pitch angle, pitch rate, wheel angle, wheel speed, and desired wheel angle and desired wheel speed. The specific error variables are as follows:

[0052]

[0053] Among them, the expected distance the two-wheeled upright robot moves in its forward direction is... , For time, the expected linear velocity of the two-wheeled upright robot moving in its forward direction. ;

[0054] The third step involves designing a control input with adaptive parameters and time-varying gain. The specific control input is as follows:

[0055]

[0056] in, Yes Adaptive parameters, , , and It is a time-varying gain;

[0057] The fourth step involves designing the update law for the adaptive parameters and time-varying gain. The specific update law is as follows:

[0058]

[0059] in, , , , , and It is a positive adjustable parameter.

[0060] The fifth step involves distributing the calculated control inputs to the left and right wheels, as follows:

[0061]

[0062] in, and These are the actual control torques for the left and right wheels, respectively.

[0063] To further verify the above example, simulations were performed using MATLAB. The differential equations were solved numerically using the fourth-order Runge-Kutta method, with a calculation step size of 0.01 seconds and a simulation duration of 150 seconds. The initial value of the time-varying gain was designed as follows: , , and The initial values ​​of the adaptive parameters are designed as follows: Unknown parameters include robot length, total weight, moment of inertia, and drag coefficient. , , and for:

[0064]

[0065] Simulation results are attached. Figure 3-8 As shown. Among them, Figure 3 and Figure 4 The LQR control method described in the paper [Klemm V, Morra A, Gulich L, et al. LQR-assisted whole-body control of a wheeled bipedal robot with kinematic loops[J]. IEEE Robotics and Automation Letters, 2020, 5(2):3745-3752] was used. This method pre-sets the control gain by measuring the robot's parameters. However, from Figure 3 and Figure 4It can be observed that when the robot's parameters change, the originally set parameters can no longer guarantee system stability, and the system is in a state of oscillation and divergence. Figures 5-8 In this study, the self-balancing motion control method designed in this invention was used. It can be seen that the time-varying gain and adaptive parameters begin to adaptively adjust in the early stages of the control algorithm's operation. The adjusted parameters can adapt to changes in parameters, ensuring that the two-wheeled upright robot can achieve the desired self-balancing and motion characteristics.

[0066] The simulation results above verify the effectiveness of this method and its beneficial effects.

[0067] Although embodiments of the present invention have been described in conjunction with the accompanying drawings, those skilled in the art will be able to make various modifications and improvements without departing from the principles of the present invention, and these modifications and improvements should also be considered to fall within the scope of protection of the present invention.

Claims

1. A self-balancing motion control method of a two-wheel upright robot, characterized by, The method comprises the following steps: In the first step, differential equations are constructed to describe the dynamics of the pitch angle and the wheel angle of the bioradial robot, considering the mass, moment of inertia, length and wheel-ground friction coefficient of the bioradial robot; In the second step, error variables are designed based on the pitch angle, pitch angle velocity, wheel angle, wheel velocity and expected wheel angle and expected wheel velocity, and the error variables are as follows: wherein, is a pitch angle error, is a pitch angle velocity error, is a wheel rotation angle error, is a wheel rotation velocity error, is a distance that the desired two-wheeled upright robot moves in its direction of travel, is a linear velocity that the desired two-wheeled upright robot moves in its direction of travel; is a pitch angle of the two-wheeled upright robot, is a pitch angle velocity of the two-wheeled upright robot, is a distance that the two-wheeled upright robot moves in its direction of travel, is a linear velocity that the two-wheeled upright robot moves in its direction of travel; In the third step, control inputs with adaptive parameters and time-varying gains are designed, and the control inputs are as follows: wherein is the resultant moment of the two wheels, is an intermediate variable, is an adaptive parameter to , , , and are time-varying gains; In the fourth step, an updating law of the adaptive parameters and the time-varying gains is designed; In the fifth step, the calculated control inputs are distributed to the left and right wheels.

2. The self-balancing motion control method of a dual-wheel upright robot according to claim 1, wherein, In the first step, the constructed differential equations are as follows: wherein, is the resultant moment of the two wheels, , , and are unknown parameters including the length of the robot, the total weight, the moment of inertia, the drag coefficient.

3. The self-balancing motion control method of a dual-wheel upright robot according to claim 2, wherein, In the fourth step, the updating law is as follows: wherein , , , , and are positive adjustable parameters.

4. The self-balancing motion control method of the dual-wheel upright robot according to claim 3, wherein, In the fifth step, the calculated control inputs are distributed to the left and right wheels, and the distribution is as follows: wherein, and are the actual control torques for the left and right wheels, respectively.

Images