CN117445929A - Track tracking control method based on two-wheel differential drive - Google Patents
Track tracking control method based on two-wheel differential drive Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
- B60W30/00—Purposes of road vehicle drive control systems not related to the control of a particular sub-unit, e.g. of systems using conjoint control of vehicle sub-units
- B60W30/18—Propelling the vehicle
- B60W30/18009—Propelling the vehicle related to particular drive situations
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
- B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B60—VEHICLES IN GENERAL
- B60W—CONJOINT CONTROL OF VEHICLE SUB-UNITS OF DIFFERENT TYPE OR DIFFERENT FUNCTION; CONTROL SYSTEMS SPECIALLY ADAPTED FOR HYBRID VEHICLES; ROAD VEHICLE DRIVE CONTROL SYSTEMS FOR PURPOSES NOT RELATED TO THE CONTROL OF A PARTICULAR SUB-UNIT
- B60W50/00—Details of control systems for road vehicle drive control not related to the control of a particular sub-unit, e.g. process diagnostic or vehicle driver interfaces
- B60W2050/0001—Details of the control system
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- B60W2050/0011—Proportional Integral Differential [PID] controller
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Abstract
A track tracking control method based on two-wheel differential drive is characterized in that a coordinate system is established by taking a starting point of a two-wheel differential robot as an origin, a target track at each moment and a motion track of the two-wheel differential robot are decomposed according to an X axis and a Y axis, deviation and angle deviation of the target track and the motion track on the two axes are obtained, two PID position controllers are respectively established on the X axis and the Y axis, the linear speed of the vehicle body center at the next moment is obtained through deviation control, and meanwhile, a PID gesture controller is established according to the angle deviation to obtain the angular speed of the vehicle body center at the next moment. And finally, decoupling the central line speed and the angular speed of the vehicle body according to the analysis of the two-wheel differential mathematical model to obtain the speeds of the left wheel and the right wheel at the next moment, and continuously correcting the speeds of the two wheels so as to realize track tracking. The invention greatly saves the cost, and the method is simple and easy to realize and has good tracking effect.
Description
Technical Field
The invention relates to the field of two-wheel differential drive control, in particular to a track tracking control method without external navigation.
Background
Two-wheel differential drive is a common control method and is widely applied to various types of vehicles, including automobiles, trucks, engineering machinery, AGV robots and the like. The two-wheel differential drive control mode can enable the vehicle to be more stable and flexible in the running process, and control performance and efficiency of the vehicle are improved. The two-wheel differential control comprises two major types of mechanical differential and electronic differential. The mechanical differential uses a mode that a driving motor is connected with a speed reducer and then wheels are driven, and the differential steering of the vehicle is realized by changing the speeds of two inner and outer wheels driven by the motor. The electronic differential speed completely adopts an electronic and software control mode to control the rotating speed of each travelling wheel, so that the wheels rotate at different speeds during steering, and a mechanical transmission device with a complicated steering wheel control is not needed for mechanical steering. The electronic differential saves the traditional mechanical components such as a clutch, a speed reducer, a transmission bridge and the like, not only reduces the mass of the whole automobile body, but also ensures the real-time performance of the electronic differential. Therefore, the electronic differential is gradually replacing the traditional mechanical differential, and is increasingly applied to steering control of various electric vehicles.
The two-wheel differential system is most widely applied to electric balance cars, AGV robots and the like, and utilizes an electronic differential steering mode to move from a departure place to a destination according to a planned path under the action of a navigation system. At present, track tracking is commonly used in two modes of GPS navigation and radar navigation. GPS navigation is generally used in outdoor occasions with wide opening and fewer obstacles, and cannot be suitable for robots working indoors. Although the radar navigation is suitable for indoor environment, the positioning accuracy of the radar is related to the installation position of the radar, and the position data of the radar in the whole robot needs to be measured in advance in the process of drawing and positioning to be used as the basis of path planning in the subsequent navigation. Meanwhile, good track tracking effect can be achieved by combining information of the gesture sensors such as the IMU mounted on the vehicle body. Therefore, it is a practical need to develop a simple trajectory tracking control method without using an expensive navigation device such as GPS and radar.
The patent application number is 202111243441.0, and the invention provides a control method for realizing track tracking by carrying out real-time fuzzy control on the angular speed and the linear speed of an AGV at the next moment according to the position and the angle deviation returned in real time and the built two-wheel differential AGV deviation correction model. However, the different selection of the fuzzy rule in the method has great influence on the tracking effect. The patent application number is 201810285908.X, the invention is named as a two-wheel speed control method based on a Z-axis gyroscope and a wheel speed difference, and a PID feedback channel between two independent control loops is constructed by mainly utilizing the information of the Z-axis gyroscope, so that the two-wheel speed control error is compensated and corrected, and the track tracking is realized. According to the method, the angle measurement is carried out by means of the attitude sensor, the requirement on the measurement accuracy of the sensor is high, the attitude sensor is greatly influenced by the external environment, and the serious zero drift problem exists.
Disclosure of Invention
In order to overcome the defects of the existing navigation-free track tracking control method based on two-wheel differential control, the track tracking control method based on two-wheel differential drive is provided, the relation between the motion position, the motion angle and the two-wheel speed of a robot is established in real time by combining the structure and the kinematic relation of the two-wheel differential robot without an external navigation device, and the motion pose of the two-wheel differential robot is corrected by constructing a PID controller of the position and the pose of the two-wheel differential robot, so that simple track tracking is realized.
The technical scheme adopted by the invention for solving the problems is as follows:
a track following control method based on two-wheel differential drive, the method comprising the steps of:
s1: according to the structure and the motion characteristics of the two-wheel differential robot, a motion model is established;
s2: establishing a three-loop PID tracking model of a given track by a two-wheel differential robot model;
s3: decomposing the X axis of the tracking track, making a difference with the motion component of the X axis of the two-wheel differential robot, obtaining the distance deviation of the X axis, and obtaining the motion speed of the X axis of the two-wheel differential robot at the next moment by adopting a PID control strategy;
s4: decomposing a tracking track on a Y axis, differencing the Y axis motion component of the two-wheel differential robot, obtaining Y axis distance deviation, adopting a PID control strategy, obtaining the Y axis motion speed of the two-wheel differential robot at the next moment, and carrying out vector synthesis with the obtained X axis speed to obtain the total motion speed;
s5: according to the course angle deviation of the two-wheel differential robot, a gesture PID control strategy is adopted to obtain the angular speed of the robot motion at the next moment;
s6: and (3) according to the robot angle correction amount and the two-wheel differential control amount, carrying out gesture calculation to obtain the speed control amounts of the left and right wheels and the running track of the X axis and the Y axis at the next moment, and repeating the step (S3) until the running track of the two-wheel differential robot tracks the given track.
Further, the process of step S1 is as follows:
let the center point of two wheels of the two-wheel differential robot be O respectively 1 And O 2 The radius of the wheels is R respectively r And R is l The angular speeds of the left motor and the right motor are omega respectively r And omega l Thereby obtaining the linear velocity v of the two driving wheels r And v l The expression is:
in the formula, v r The linear speed of the right driving wheel of the two-wheel differential robot is v l The linear speed of the driving wheel at the left side of the two-wheel differential robot is equal to that of the driving wheel at the left side of the two-wheel differential robot. Taking the midpoint of the connecting line of two driving wheels of the two-wheel differential robot as the centroid O c And centroid O c The coordinates in the world coordinate system XOY are (x c ,y c ) The mass center O of the two-wheel differential robot can be obtained by the method (1) c The linear velocity calculation formula of (2) is:
taking the midpoint distance of two driving wheels of the two-wheel differential robot as l, and the rotation center of the two-wheel differential robot as O r Center of rotation O r To centroid O c The distance of the two-wheel differential robot is the rotation radius R, so that the mass center angular speed of the two-wheel differential robot is obtained as follows:
meanwhile, the rotation radius R is obtained by combining the formula (2) and the formula (3):
is provided withWherein x, y and θ are respectively the abscissa, the ordinate and the course angle under the world coordinate system when the two-wheel differential robot moves, so that when the driving wheel of the two-wheel differential robot contacts with the ground to be in pure rolling, the kinematic model of the two-wheel differential robot is expressed as:
when v r Greater than v l When the two-wheel differential robot is used, the linear speed of the right driving wheel is higher than that of the left driving wheel, and the robot turns leftwards; when v r Equal to v l When the driving linear speeds of the left side and the right side of the robot are equal, the robot keeps straight running along the positive direction or the negative direction; while when v r Less than v l When the robot turns right, the linear speed of the driving wheel on the right side of the robot is smaller than that of the driving wheel on the left side of the robot. From this, it is understood that by controlling the left and right linear velocities v of the robot r 、ν l The forward, backward and turning functions of the two-wheel differential robot can be realized.
In step S2, the tracking track is analyzed, the controlled quantity of the two-wheel differential robot is the pose of the robot, the controlled quantity is the rotation speed of the left wheel and the right wheel, and the robot needs to meet three constraint conditions according to the requirement that the robot reaches the target point according to the designated track:
1) The distance deviation from the target point is 0.
2) The deviation from the posture of the target point is 0.
3) The distance deviation from the target track during traveling is 0.
The physical quantity directly related to the 3 constraint conditions is the linear speed and the angular speed of the robot, the linear speed can be controlled to reduce the distance deviation with the target point, the angular speed can be controlled to reduce the gesture deviation with the target point, and the deviation with the target track in the driving process can be corrected;
let two-wheel differential robot real-time pose as P (x, y, θ) and target position as Q (x) g ,y g ,θ g ) The real-time distance d between the robot and the target point can be easily obtained err And angle difference theta err The method comprises the following steps of:
two parallel PID controllers are designed according to the formula (6) and the formula (7), and the line speed v is obtained according to the formula (2) and the formula (3) c Angular velocity omega c Then resolving the left wheel speed and the right wheel speed to a machine for execution; the controller can control the robot to continuously move towards the target, when the distance is smaller than a certain value, namely the robot moves into a circle taking the target as a circle center and tau as a radius, namely d err And when tau is less than or equal to tau, judging that the robot reaches the target position, and completing the motion control process.
Further, considering that the initial gesture and the target gesture of the robot are different, the convergence speed of the motion track to the target track is also different; when the attitude deviation angle is an obtuse angle, the attitude angle and the distance control can converge towards the target track together, and when the attitude angle is an acute angle, the motion also accords with the distance feedback control rate according to the original attitude of the robot, so that the target track cannot be converged rapidly; the good tracking effect cannot be realized only by means of distance control and angle control with the target point, because the control target and the motion track do not establish a more direct relation, and the distance deviation only focuses on the position of the arrival target and does not focus on the arrival process; the final pose is controlled, and the movement process of the robot is restrained; therefore, the reference track not only needs to contain gesture information, but also needs to contain time information, the gesture of the robot at each moment is determined, the reference track is respectively projected to the X-axis direction, the Y-axis direction and the gesture angle of the reference track, which changes along with time, two groups of positions and time and a group of gesture and time functions are obtained, three PID controllers are designed to track the X-axis direction track, the Y-axis direction track and the angle track respectively, and finally, the linear speed and the angular speed of the robot are fused, the left wheel speed and the right wheel speed are calculated, and the purpose of tracking the given track to reach the designated position is achieved.
Further, in the step S3, the X-axis component of the reference trajectory at the time t is set as the target in the X-direction to be X gt According to formula (5):
from (8), the real-time distance deviation d between the robot and the target point on the X-axis can be easily obtained xerr The method comprises the following steps:
d xerr ＝x gt -x t (9)
according to the formula (9), the PID controller in the X direction can be designed, and the input is d xerr Output is the linear velocity v in the X direction xt See the input distance error d xerr Determining the linear velocity v xt I.e. the farther the distance the greater the speed, the closer the distance the lesser the speed; therefore, attention is paid to the continuity of the speed, so the output of the PID is firstly limited and then smoothed, namely limited v xpidout ||≤v xmax Smoothing v x(t-1) -v xpidout The I is less than or equal to sigma, and finally v is output xt ＝v xpidout 。
Further, in the step S4, the Y-axis component of the reference trajectory at the time t is set as the target in the Y-direction to be Y gt According to formula (5):
from (10), the real-time distance deviation d between the robot and the target point on the Y axis is easily obtained yerr ：
d yerr ＝y gt -y t (11)
According to the formula (11), a PID controller in the Y direction can be designed, and the input is d yerr Output is the linear velocity v in the Y direction yt The method comprises the steps of carrying out a first treatment on the surface of the Can see the input distance error d yerr Determining the linear velocity v yt I.e. the longer the distance is, the smaller the distance is, the continuity of the speed is noted, so the PID output is limited first and then smoothed, i.e. limited v ypidout ||≤v ymax Smoothing v y(t-1) -v ypidout Zeta is not more than zeta and is the given error band, and finally v is output yt ＝v ypidout Simultaneous v xt And v yt Obtaining the central speed v of the robot along with the change of time ct The method comprises the following steps:
further, in the step S5, the angle of the reference track is set as the target given angle θ g According to formula (7):
inputting theta according to (12) design angle PID control err Outputting the central angular velocity omega of the robot changing along with time ct Namely, the deflection angle error determines the rotating speed, positively deflects left, and negatively deflects right; the rotation is more rapid, the rotation is less rapid; attention should be paid to the problem of the boundary crossing caused by the angle calculation mode, and the calculated theta err If it is greater or less than pi, it is normalized to (-pi, pi)]I.e. θ err Greater than pi minus 2 pi; less than or equal to-pi, plus 2 pi.
In the step S6Calculating the previous steps to obtain the linear velocity v of the robot center ct Angular velocity omega ct Combining the wheel distance l of two driving wheels of the mobile robot, and obtaining the left wheel speed v through pose calculation l Right wheel speed v r ：
And (3) repeating the steps S3 to S6 to gradually track the given track through continuously correcting the movement speed and the movement angle of the robot, and finally reaching the specified target.
The beneficial effects of the invention are mainly shown in the following steps: (1) In the track tracking control, the motion state of the robot is not required to be adjusted in real time by virtue of a navigation system such as a radar, the position and the gesture of the robot at the next moment can be calculated by combining the left and right wheel speeds of the robot, a system model and the like, and the track tracking is realized by carrying out closed-loop control on the gesture of the robot, so that the system cost is reduced. (2) The three-ring parallel control is designed, and the relation between time and the pose of the robot is established, so that the motion control of the robot is more real-time, and the tracking effect is more accurate.
Drawings
Fig. 1 shows a schematic diagram of a two-wheeled differential robot motion model.
Fig. 2 shows an embodiment for tracking a given trajectory based on two-wheel differential control.
FIG. 3 shows a block diagram of a tricyclic PID control that tracks a given track based on two-wheel differential control.
FIG. 4 shows a simulation flow diagram for tracking a given trajectory based on two-wheel differential control.
Fig. 5 shows a pose effect graph with an initial angle of 0rad, tracking a given trajectory.
Fig. 6 shows a pose effect graph with an initial angle of 0.5rad, tracking a given trajectory.
Detailed Description
The following detailed description of the embodiments of the invention is exemplary and is provided merely to illustrate the invention and is not to be construed as limiting the invention. The following describes in detail a track following control method based on differential driving of two wheels according to the present invention with reference to the accompanying drawings.
Referring to fig. 1, a track following control method based on two-wheel differential driving, the method includes the steps of:
s1: according to the structure and the motion characteristics of the two-wheel differential robot, a motion model is established;
s2: establishing a three-loop PID tracking model of a given track by a two-wheel differential robot model;
s3: decomposing the X axis of the tracking track, making a difference with the motion component of the X axis of the two-wheel differential robot, obtaining the distance deviation of the X axis, and obtaining the motion speed of the X axis of the two-wheel differential robot at the next moment by adopting a PID control strategy;
s4: decomposing a tracking track on a Y axis, differencing the Y axis motion component of the two-wheel differential robot, obtaining Y axis distance deviation, adopting a PID control strategy, obtaining the Y axis motion speed of the two-wheel differential robot at the next moment, and carrying out vector synthesis with the obtained X axis speed to obtain the total motion speed;
s5: according to the course angle deviation of the two-wheel differential robot, a gesture PID control strategy is adopted to obtain the angular speed of the robot motion at the next moment;
s6: and (3) according to the robot angle correction amount and the two-wheel differential control amount, carrying out gesture calculation to obtain the speed control amounts of the left and right wheels and the running track of the X axis and the Y axis at the next moment, and repeating the step (S3) until the running track of the two-wheel differential robot tracks the given track.
According to the structure and the motion characteristics of the two-wheel differential robot, a robot rotary motion model is established, and the relation between the positions of the two-wheel differential robot, the left wheel speed, the right wheel speed and the angle is obtained:
in the model, it can be seen that the left wheel and the right wheel of the robot move coaxially, and the axis passes through the center of the robot, so that the robot has the same angular velocity as the axis, the rotation center during turning is the same rotation center, and the relationship between the left wheel speed and the right wheel speed and the movement center of the robot is established for more convenient description:
by knowing the kinematic relationship, a basic simulation block diagram of the two-wheel differential robot can be built, and three control indexes of track tracking are analyzed to obtain the control scheme of FIG. 2. The reference track is decomposed according to the X axis, the Y axis and the gesture, the reference track is differenced with the position gesture of the two-wheel differential robot at the current moment to obtain the deviation at the current moment, the deviation is sent to three PID controllers to obtain the linear speed and the angular speed of the center of the vehicle body at the next moment, the left wheel speed and the right wheel speed are obtained according to the kinematic relation between the two-wheel speed and the center of the robot, the left wheel speed and the right wheel speed are integrated to obtain the gesture of the vehicle body at the next moment, and the gesture is fed back to the reference track end to continue the deviation control.
In this embodiment, three PID parallel control is adopted, and as shown in fig. 3, the X-axis Y-axis speed controller performs clipping processing on the speed output in order to avoid excessive speed change. Maximum limiting value v in this example max ＝0.6m/s，v min -0.6m/s; to avoid excessive angular velocity changes, the angular velocity output needs to be limited, the maximum limiting omega max =0.1 rad/s, minimum limiting value ω min ＝-0.1rad/s。
In this embodiment, the tracking track is set as a straight line, the overall control flow chart is as shown in fig. 4, the starting point is first set as initpos= [2,3], the target point is gold= [22,28], the tracking track is y=1.25x+0.5, the tracking angle is 53 °, x is a function of time t, and x= 2+t may be set, so the total time is 20s, and the update step of time t is 0.1s. In this example, the two-wheeled differential robot starts to run from the set start point, coinciding with the start point of the set trajectory. In order to distinguish from the tracking track gesture, the initial angle of the two-wheeled differential robot is set to be 0rad and 0.5rad, and the tracking effect of different initial angles is slightly different, and only the initial angle of 0rad and the initial angle of 0.5rad are used for illustration. The simulation results are shown in fig. 5. The motion angle of the two-wheel differential robot gradually approaches to the direction of a given track, the angle value is 0.92rad, the converted angle value is 53 degrees, and the angle is the same as the angle of the given track. Meanwhile, the positions of the two-wheel differential robot are gradually overlapped with the given track. After tracking a given trajectory, the robot will continue to move because the given target has not been reached, and will not stop until the target point is eventually reached. It can be seen from fig. 6 that the two-wheeled differential robot also has a good tracking effect in the case of an initial angle of 0.5 rad.
The matters described in the examples of this specification are merely illustrative of the manner in which the inventive concepts may be implemented. The scope of the invention should not be considered limited to the particular forms set forth in this example, as such, and equivalents thereof will suggest themselves to those of ordinary skill in the art in view of the present teachings.
Claims (7)
1. The track tracking control method based on the two-wheel differential drive is characterized by comprising the following steps of:
s1: according to the structure and the motion characteristics of the two-wheel differential robot, a motion model is established;
s2: establishing a three-loop PID tracking model of a given track by a two-wheel differential robot model;
s3: decomposing the X axis of the tracking track, making a difference with the motion component of the X axis of the two-wheel differential robot, obtaining the distance deviation of the X axis, and obtaining the motion speed of the X axis of the two-wheel differential robot at the next moment by adopting a PID control strategy;
s4: decomposing a tracking track on a Y axis, differencing the Y axis motion component of the two-wheel differential robot, obtaining Y axis distance deviation, adopting a PID control strategy, obtaining the Y axis motion speed of the two-wheel differential robot at the next moment, and carrying out vector synthesis with the obtained X axis speed to obtain the total motion speed;
s5: according to the course angle deviation of the two-wheel differential robot, a gesture PID control strategy is adopted to obtain the angular speed of the robot motion at the next moment;
s6: and (3) according to the robot angle correction amount and the two-wheel differential control amount, carrying out gesture calculation to obtain the speed control amounts of the left and right wheels and the running track of the X axis and the Y axis at the next moment, and repeating the step (S3) until the running track of the two-wheel differential robot tracks the given track.
2. The track following control method based on two-wheel differential driving according to claim 1, wherein the process of step S1 is as follows:
let the center point of two wheels of the two-wheel differential robot be O respectively 1 And O 2 The radius of the wheels is R respectively r And R is l The angular speeds of the left motor and the right motor are omega respectively r And omega l Thereby obtaining the linear velocity v of the two driving wheels r And v l The expression is:
in the formula, v r The linear speed of the right driving wheel of the two-wheel differential robot is v l For the linear speed of the left driving wheel of the two-wheel differential robot, taking the midpoint of the connecting line of the two driving wheels of the two-wheel differential robot as the centroid O c And centroid O c The coordinates in the world coordinate system XOY are (x c ,y c ) The mass center O of the two-wheel differential robot can be obtained by the method (1) c The linear velocity calculation formula of (2) is:
taking the midpoint distance of two driving wheels of the two-wheel differential robot as l, and the rotation center of the two-wheel differential robot as O r Center of rotation O r To centroid O c The distance of the two-wheel differential robot is the rotation radius R, so that the mass center angular speed of the two-wheel differential robot is obtained as follows:
meanwhile, the rotation radius R is obtained by combining the formula (2) and the formula (3):
is provided withWherein x, y and θ are respectively the abscissa, the ordinate and the course angle under the world coordinate system when the two-wheel differential robot moves, so that when the driving wheel of the two-wheel differential robot contacts with the ground to be in pure rolling, the kinematic model of the two-wheel differential robot is expressed as:
when v r Greater than v l When the two-wheel differential robot is used, the linear speed of the right driving wheel is higher than that of the left driving wheel, and the robot turns leftwards; when v r Equal to v l When the driving linear speeds of the left side and the right side of the robot are equal, the robot keeps straight running along the positive direction or the negative direction; while when v r Less than v l When the robot turns right, the linear speed of the driving wheel on the right side of the robot is smaller than that of the driving wheel on the left side of the robot.
3. The track following control method based on two-wheel differential driving according to claim 1 or 2, wherein in the step S2, the following track is analyzed, the controlled quantity of the two-wheel differential robot is the pose of the robot, the controlled quantity is the left and right wheel rotation speeds, and the robot needs to meet three constraint conditions according to the appointed track to reach the target point:
1) The distance deviation from the target point is 0;
2) The deviation from the posture of the target point is 0;
3) The distance deviation between the target track and the driving process is 0;
the physical quantity directly related to the 3 constraint conditions is the linear speed and the angular speed of the robot, the linear speed can be controlled to reduce the distance deviation with the target point, the angular speed can be controlled to reduce the gesture deviation with the target point, and the deviation with the target track in the driving process can be corrected;
let two-wheel differential robot real-time pose as P (x, y, θ) and target position as Q (x) g ,y g ,θ g ) The real-time distance d between the robot and the target point can be easily obtained err And angle difference theta err The method comprises the following steps of:
two parallel PID controllers are designed according to the formula (6) and the formula (7), and the line speed v is obtained according to the formula (2) and the formula (3) c Angular velocity omega c Then resolving the left wheel speed and the right wheel speed to a machine for execution; the controller can control the robot to continuously move towards the target, when the distance is smaller than a certain value, namely the robot moves into a circle taking the target as a circle center and tau as a radius, namely d err And when tau is less than or equal to tau, judging that the robot reaches the target position, and completing the motion control process.
4. The track following control method based on two-wheel differential driving according to claim 1 or 2, wherein in the step S3, X is given by taking the X-axis component of the reference track at the time t as the target in the X direction gt According to formula (5):
from (8), the real-time distance deviation d between the robot and the target point on the X-axis can be easily obtained xerr The method comprises the following steps:
d xerr ＝x gt -x t (9)
according to the formula (9), the PID controller in the X direction can be designed, and the input is d xerr Output is the linear velocity v in the X direction xt See the input distance error d xerr Determining the linear velocity v xt I.e. the farther the distance the greater the speed, the closer the distance the lesser the speed; therefore, attention is paid to the continuity of the speed, so the output of the PID is firstly limited and then smoothed, namely limited v xpidout ||≤v xmax Smoothing v x(t-1) -v xpidout The I is less than or equal to sigma, and finally v is output xt ＝v xpidout 。
5. The track following control method based on two-wheel differential driving according to claim 1 or 2, wherein in the step S4, Y is given by taking the Y-axis component of the reference track at the time t as the target in the Y direction gt According to formula (5):
from (10), the real-time distance deviation d between the robot and the target point on the Y axis is easily obtained yerr ：
d yerr ＝y gt -y t (11)
According to the formula (11), a PID controller in the Y direction can be designed, and the input is d yerr Output is the linear velocity v in the Y direction yt The method comprises the steps of carrying out a first treatment on the surface of the Can see the input distance error d yerr Determining the linear velocity v yt I.e. the longer the distance is, the smaller the distance is, the continuity of the speed is noted, so the PID output is limited first and then smoothed, i.e. limited v ypidout ||≤v ymax Smoothing v y(t-1) -v ypidout Zeta is not more than zeta and is the given error band, and finally v is output yt ＝v ypidout Simultaneous v xt And v yt Obtaining the central speed v of the robot along with the change of time ct The method comprises the following steps:
6. the track following control method based on two-wheel differential driving as claimed in claim 5, wherein in said step S5, the angle of the reference track is set as a target given angle θ g According to formula (7):
inputting theta according to (12) design angle PID control err Outputting the central angular velocity omega of the robot changing along with time ct Namely, the deflection angle error determines the rotating speed, positively deflects left, and negatively deflects right; the rotation is more rapid, the rotation is less rapid; attention should be paid to the problem of the boundary crossing caused by the angle calculation mode, and the calculated theta err If it is greater or less than pi, it is normalized to (-pi, pi)]I.e. θ err Greater than pi minus 2 pi; less than or equal to-pi, plus 2 pi.
7. The method for tracking and controlling a track based on differential driving of two wheels as claimed in claim 6, wherein in said step S6, the linear velocity v of the center of the robot is calculated from the previous steps ct Angular velocity omega ct Combining the wheel distance l of two driving wheels of the mobile robot, and obtaining the left wheel speed v through pose calculation l Right wheel speed v r ：
And (3) repeating the steps S3 to S6 to gradually track the given track through continuously correcting the movement speed and the movement angle of the robot, and finally reaching the specified target.
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