A method for open-loop posture control of mobile robots

Abstract

This invention discloses an open-loop posture control method for a mobile robot. This method eliminates the need for sensor feedback to adjust the robot's posture. The method controls the desired posture over multiple cycles. Within each cycle, the target posture increment is converted into the robot's velocity using an open-loop posture trajectory planning algorithm. This is then converted into the robot's wheel speed based on the robot's model. The entire control method is rigorous, highly accurate, and highly adaptable.

Description

Technical Field

[0001] The present invention belongs to the field of control of fully constrained wheeled mobile robots, and in particular relates to an open-loop posture control method for a mobile robot. Background Art

[0002] Robots have been widely used in industries such as industrial production and medical electronics. By eliminating manual labor during production, they effectively improve production efficiency, save labor costs and production management expenses, and significantly reduce costs. Furthermore, some working environments are harmful to the human body. Robots play a vital role in freeing up labor and increasing productivity.

[0003] Traditional mobile robots use a velocity-based control strategy, using sensor feedback to form a closed-loop control system for robot posture control. This traditional control approach introduces numerous engineering inconveniences and is also costly. Open-loop posture control eliminates the need for feedback adjustments and achieves posture control unaffected by the environment map. Summary of the Invention

[0004] Existing mobile robots use closed-loop control systems based on sensor feedback to control their position and posture. This control method is inconvenient in engineering implementation and is also costly.

[0005] The technical solution adopted by the present invention is: a mobile robot open-loop posture control method, the method comprising:

[0006] The pose of a mobile robot is described as a position (x, y) and a rotation φ. The motion control of a mobile robot is to subdivide the desired target pose into multiple control cycles according to a given period T, and convert the pose increment into the movement speed of the mobile robot in each cycle.

[0007] The change of vehicle posture in a single cycle is expressed in the form of a coordinate system as follows: Figure 1 As shown; the control algorithm includes the mobile robot coordinate system {B} and the fixed world coordinate system {S}. The mobile robot is located at q at time k-1. k-1 Point, the vehicle body coordinate system corresponding to this moment is {B k-1}, the corresponding instantaneous generalized velocity of the mobile robot is The three elements in the brackets of the generalized velocity represent the k-1 moment coordinate system {B k-1}, the velocity in the x direction, the coordinate system at time k-1 {B k-1}, the velocity in the y direction, the coordinate system at time k-1 {B k-1}The rotation speed under the condition of The three elements in the brackets in the pose represent the k-1 moment coordinate system {B k-1}X-axis coordinate value, k-1 moment coordinate system {B k-1}The y-axis coordinate value, k-1 moment coordinate system {B k-1}; after the cycle ends, that is, at time k, it is at q k Point, the corresponding mobile robot coordinate system at this time is {B k}, the corresponding instantaneous speed of the mobile robot is The posture is Assume that the mobile robot moves from q k-1 to q k The process is uniform motion,

[0008] From k-1 time point at q k-1 The body coordinate system of point {B k-1}Look, in the k-1 Click to q k During the movement of a point, its velocity changes with time as follows:

[0009]

[0010] Integrating the above formula within one cycle gives the coordinate system {B k-1}, ω≠0:

[0011]

[0012] Where T represents the period and τ represents the time constant;

[0013] When ω = 0, that is, the mobile robot has no rotation but only translation, the position increment of the mobile robot is obtained:

[0014]

[0015] Since the open-loop posture control of the mobile robot is based on the known desired posture increment in the mobile robot coordinate system {B} k-1 Δq=[ k-1 Δx, k-1 Δy, k-1 Δφ] T Calculate the speed of the mobile robot corresponding to the period T; when ω≠0, calculate according to formula (2):

[0016]

[0017] According to formula (4), the required speed of the mobile robot in the period T is calculated as:

[0018]

[0019] When ω = 0, the speed is calculated directly according to formula (3):

[0020]

[0021] The calculation results of formula (5) and formula (6) are the final control results obtained by the open-loop posture control method of the mobile robot.

[0022] Combining the open-loop posture control algorithm design of the mobile robot obtained in the above steps with a specific mobile robot can obtain the open-loop posture control method of the mobile robot of the present invention. Figure 2 shown. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 is the change of vehicle body posture within a single cycle;

[0024] Figure 2 This is the open-loop attitude control block diagram;

[0025] Figure 3 Provide mathematical modeling diagram for the kinematics of mobile robots;

[0026] Figure 4 is the moving speed of the mobile robot;

[0027] Figure 5 is the angular velocity of the mobile robot wheel;

[0028] Figure 6 Control effect for mobile robots. DETAILED DESCRIPTION

[0029] In order to explain the technical content, algorithm features, and purpose and effect of the present invention in detail, the following detailed description of the method operation process will be given in conjunction with specific implementation methods. The mobile robot of the present invention can be driven in a variety of ways, as long as there is a clear correspondence between the speed of the mobile robot's posture change and the wheel speed. The embodiment herein uses a Mecanum wheeled mobile robot. The control method of the present invention can be implemented using a traditional PC or an ordinary single-chip microcomputer in combination with a motor driver and a motor.

[0030] First, a mathematical model of the Mecanum wheeled mobile robot is constructed. In this embodiment, a mobile robot with four Mecanum wheels is used, and all four Mecanum wheels are driving wheels. Each Mecanum wheel is driven by a motor, which can be a servo motor or a stepper motor, determined according to the control accuracy and stability requirements. In this embodiment, a stepper motor is used. The four Mecanum wheels of the mobile robot have certain installation requirements. The present invention selects an installation method to perform kinematic mathematical modeling of the Mecanum wheeled mobile robot. Figure 3 As shown in Figure 2, a coordinate system {B} is established at the geometric center of the mobile robot.

[0031] Taking a single wheel as the research object, such as the right front wheel, the linear velocity of the roller and the linear velocity of the wheel together provide the velocity of the wheel in the mobile robot coordinate system {B}, then:

[0032] v wix =v i +v ni cosα (7)

[0033] v wiy =v ni sinα (8)

[0034] Where v wi is the speed of the i-th wheel in coordinate system {B}.

[0035] Since the entire vehicle body is a rigid body and the motion of the OMV is planar motion, the relationship between the wheel speeds in the mobile robot coordinate system is as follows:

[0036]

[0037] Where v B represents the absolute velocity of the mobile robot in the coordinate system, Represents the position vector from the wheel to the geometric center of the mobile robot, ω x 、ω y 、ω z Represents the angular velocity of rotation around the x-axis, y-axis, and z-axis respectively, x i 、y i 、z i Represent the distance vectors from the wheel to the geometric center of the mobile robot in the x-, y-, and z-directions respectively.

[0038] Since the mobile robot only has an angular velocity around the z-axis, And assuming that the mobile robot does not move around the z axis, z i =0. Substituting into formula (9) we have:

[0039]

[0040] The combined equations (7)(8)(10) are:

[0041] v i +v ni cosα=v Bx -y i ω z (11)

[0042] v ni sinα=v By +x i ω z (12)

[0043] Define the angle between the rollers of the left front wheel and the right rear wheel and the wheel axis as +45°, and the angle between the rollers of the right front wheel and the left rear wheel and the wheel axis as -45°. According to the established vehicle body coordinate system {B}, the center coordinates of the right front wheel, left front wheel, left rear wheel, and right rear wheel are (L, -W), (L, W), (-L, W), (-L, -W), respectively. Then:

[0044]

[0045] Where v1, v1, v1, and v1 represent the rotational linear velocities of the right front wheel, left front wheel, left rear wheel, and right rear wheel, respectively; W represents the distance from the wheel to the x-axis in the mobile robot coordinate system {B}, and L represents the distance from the wheel to the y-axis in the mobile robot coordinate system {B}.

[0046] According to formula (13), the rotation angular velocity of the four wheels corresponding to the mobile robot can be calculated:

[0047]

[0048] In the formula, ω1, ω2, ω3, and ω4 represent the rotational angular velocities of the right front wheel, left front wheel, left rear wheel, and right rear wheel respectively; r represents the radius of the wheel.

[0049] Assume the target position of the mobile robot in the world coordinate system is (1000, 1000) in mm; the target rotation posture is 2π in rad. The period T = 200ms, that is, in this implementation, the mobile robot has both translation and rotation. Assume the position increment Δq in the world coordinate system within a single period = [20, 20, π / 25]. According to the control method of the present invention:

[0050] ①Convert the pose increment in the world coordinate system into the pose increment in the mobile robot coordinate system;

[0051] ②According to the formula Convert the position increment of the mobile robot into the speed of the mobile robot along the x-axis and y-axis, as well as the rotational angular velocity in its coordinate system;

[0052] ③ According to the mobile robot model, the formula Get the angular velocity of the four wheels of the mobile robot.

[0053] According to the above control method, the real-time control data is calculated and the actual posture data is analyzed. The corresponding moving speed of the mobile robot in the x-direction and y-direction in its own coordinate system is as follows: Figure 4 As shown; the corresponding four wheel angular velocities required for mobile robot control are as follows Figure 5 As shown; the final control quantity in the world coordinate system is as follows Figure 6 shown.

[0054] Finally, a motion control chip can be used for motor control. The angular velocity of the robot's four wheels within a single cycle is converted into pulses and directions for motor control, achieving the desired open-loop posture control effect.

Claims

1. A method for open-loop posture control of a mobile robot, the method comprising: The pose of the mobile robot is described as the position (x, y) and the rotation φ; The motion control of a mobile robot is to subdivide the desired target posture into multiple control cycles according to a given period T, and convert the posture increment into the moving speed of the mobile robot in each cycle; The control algorithm includes the mobile robot coordinate system {B} and the fixed world coordinate system {S}. The mobile robot is located at q at time k-1. k-1 Point, the vehicle body coordinate system corresponding to this moment is {B k-1 }, the corresponding instantaneous generalized velocity of the mobile robot is The three elements in the brackets of the generalized velocity represent the k-1 moment coordinate system {B k-1 }, the velocity in the x direction, the coordinate system at time k-1 {B k-1 }, the velocity in the y direction, the coordinate system at time k-1 {B k-1 }The rotation speed under the condition of The three elements in the brackets in the pose represent the k-1 moment coordinate system {B k-1 }X-axis coordinate value, k-1 moment coordinate system {B k-1 }The y-axis coordinate value, k-1 moment coordinate system {B k-1 }; after the cycle ends, that is, at time k, it is at q k Point, the corresponding mobile robot coordinate system at this time is {B k }, the corresponding instantaneous speed of the mobile robot is The posture is Assume that the mobile robot moves from q k-1 to q k The process is uniform motion, From k-1 time point at q k-1 The body coordinate system of point {B k-1 }Look, in the k-1 Click to q k During the movement of a point, its velocity changes with time as follows: Integrating the above formula within one cycle gives the coordinate system {B k-1 }, ω≠0: Where T represents the period and τ represents the time constant; When ω = 0, that is, the mobile robot has no rotation but only translation, the change in the mobile robot's posture is obtained: Since the open-loop posture control of the mobile robot is based on the known k-1 }The pose change under k-1 Δq=[ k-1 Δx, k-1 Δy, k-1 Δφ] T Calculate the speed of the mobile robot corresponding to the period T; when ω≠0, calculate according to formula (2): According to formula (4), the required speed of the mobile robot in the period T is calculated as: When ω = 0, the speed is calculated directly according to formula (3): The calculation results of formula (5) and formula (6) are the final control results obtained by the open-loop posture control method of the mobile robot.

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