CN112180944B - Rope-tied wheel type mobile robot motion control system and method - Google Patents

Rope-tied wheel type mobile robot motion control system and method Download PDF

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Publication number
CN112180944B
CN112180944B CN202011137137.3A CN202011137137A CN112180944B CN 112180944 B CN112180944 B CN 112180944B CN 202011137137 A CN202011137137 A CN 202011137137A CN 112180944 B CN112180944 B CN 112180944B
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tether
control
wheel
rope
speed
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CN112180944A (en
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王小涛
王邢波
张家友
韩亮亮
张玉花
陈金宝
王飞宇
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Nanjing University of Aeronautics and Astronautics
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Nanjing University of Aeronautics and Astronautics
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory
    • G05D1/0223—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory involving speed control of the vehicle
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
    • G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
    • G05D1/02—Control of position or course in two dimensions
    • G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
    • G05D1/0276—Control of position or course in two dimensions specially adapted to land vehicles using signals provided by a source external to the vehicle

Abstract

The invention discloses a motion control system and method for a rope-tied wheel type mobile robot. The invention fully considers the disturbance factors such as local terrain change of extreme terrain and the like, and actively compensates the disturbance; the organic matching of the driving torque of the wheels and the tether tension is comprehensively considered, so that the power consumption of the system is reduced; the robot is moved along a predetermined trajectory while maintaining the tether tension constraint.

Description

Rope-tied wheel type mobile robot motion control system and method
Technical Field
The invention belongs to the field of motion control of mobile robots, and particularly relates to a motion control system and method of a rope-tied wheel type mobile robot.
Background
Many regions of exploration value of the planet surface tend to be in extreme terrains of the type of steep slopes, ravines, and the like. Most of the existing robots can only operate and work on relatively flat rock terrain with slopes of less than 30 degrees, and are not suitable for exploring the aforementioned extreme terrain areas. The traction force of the patrol device can be weakened by the steep slope, and the terrain trafficability is greatly reduced; with conventional rocker arm bogie configurations, slip on steep slopes can increase significantly and certain areas cannot be entered at all; ravines are very dangerous for the rover, which may also fall over rough terrain.
In order to overcome the limitation caused by the extreme terrain areas, a rope-based mobile robot is a tour device designed for terrains such as steep slopes and ravines, and the rope-based mobile robot can reach the steep slopes and ravines which cannot be passed, entered or fixedly detected at fixed points by a common wheel-based robot by providing tension or supporting force through a rope with one end fixed to a parent robot or an anchor point, so that the detection of the extreme terrain areas becomes possible.
The tethered mobile robot can be applied to many fields in addition to planetary surface exploration due to the ability to explore extreme terrain. High-risk terrain areas, such as areas near volcanoes, can be explored autonomously and remotely. In addition, the rope-tied mobile robot does not need a terrain surface to provide support for descending, so that the rope-tied mobile robot can descend into a pit hole and can be used for searching and rescuing tasks of dangerous areas in mine accidents.
Although many methods for motion control of a general wheeled mobile robot have been proposed, they are basically directed to a non-tethered robot. Along with the proposal of the rope-tied wheel type mobile robot, a corresponding reasonable motion control technology is urgently needed to reasonably control the driving moment of the wheels and the pulling force of the tied rope, so that the robot can move according to an expected track through the obstacle that the common wheel type mobile robot cannot pass through; meanwhile, the system can quickly respond to interference, sliding and falling caused by local change of extreme terrains, and reduces the power consumption of the system.
Disclosure of Invention
In order to solve the technical problems mentioned in the background art, the invention provides a motion control system and method for a rope-tied wheeled mobile robot.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a motion control system of a rope-tied wheel type mobile robot comprises a controller, a left wheel driver, a right wheel driver, a tied rope winch driver, a tied rope tension sensor, a tied rope, a rope-tied wheel type mobile mechanism and a navigation positioning device; the rope wheel type moving mechanism comprises a left driving wheel, a right driving wheel, a winch, a central shaft body and a caster arm; the left driving wheel and the right driving wheel are connected to the left side and the right side of the central shaft body through bearings, the caster arms are fixedly connected with the central shaft body, the winch is installed in the center of the central shaft body through bearings, the tether is wound on the winch, the tether tension sensor is fixed on the winch or installed on the caster arms, the tether penetrates through the tether tension sensor, the tether tension sensor measures the tension of the tether and converts the tension into an electric signal to be sent to the controller, the navigation positioning device detects the speed and the pose information of the robot and sends the information to the controller, the controller comprises a kinematics control module, a dynamics control module, an interference observer module and a tether tension control module, the controller processes the information sent by the tether tension sensor and the navigation positioning device to obtain the expected torque of the left wheel driver and the right wheel driver and the expected tether length of the tether winch driver, the left wheel driver and the right wheel driver control the left driving wheel and the right driving wheel to move according to the expected torque, and the tether winch driver controls the winch to retract and release the tether according to the expected tether retraction length, so that the motion control of the robot is realized.
The control method based on the rope-tied wheel type mobile robot motion control system comprises the following steps:
(1) comparing a difference value between an expected pose output by the upper trajectory planning system and an actual pose of the tethered wheel type mobile robot, and converting the difference value into a robot body coordinate system to obtain a pose error;
(2) calculating expected speed and azimuth angle speed by a kinematics control module through a kinematics control law according to the pose error;
(3) comparing the difference between the expected speed and the azimuth speed and the actual speed and the azimuth speed of the rope-tied wheeled mobile robot to obtain a speed deviation and an azimuth speed deviation;
(4) interference, velocity bias and azimuthal velocity bias estimated from the interference observer moduleDifference and dynamics control law, the dynamics control module calculates the optimal tether tension F based on the minimum energy consumption principle*Calculating to obtain expected left wheel control torque and right wheel control torque through a dynamics control law, and respectively transmitting the expected left wheel control torque and right wheel control torque to a left wheel driver and a right wheel driver for double-wheel control;
(5) according to the actual speed and azimuth speed of the rope-tied wheeled mobile robot, the double-wheel control moment and the optimal rope-tied tension F*The disturbance observer module estimates the uncertainty and disturbance of the system and outputs the uncertainty and disturbance to the dynamics control module for compensation;
(6) according to the optimum tether tension F*And tether tension measured by the tether tension sensor, the tether tension control module calculating an expected tether retraction length and transmitting the expected tether retraction length to the tether winch drive for winch control.
Further, in step (2), the kinematic control law is as follows:
vc＝k1xe+vdcosθe
Figure BDA0002737046850000031
in the above formula, k0,k1,k2For controlling gain, and has k0＞0,k1＞0,k2＞0；vc、ωcRespectively desired velocity and azimuthal velocity, vd、ωdRespectively representing the expected speed and the azimuth angle speed in the robot body coordinate system; x is the number ofe、ye、θeRespectively an abscissa error, an ordinate error and an azimuth error in the pose error.
Further, in step (4), the dynamics control law is as follows:
Figure BDA0002737046850000032
in the above formula, τlrFor two-wheeled control of torque, taulr＝[τl τr]T，τlAnd τrThe left wheel control moment and the right wheel control moment are respectively, and the superscript T represents transposition;
Figure BDA0002737046850000033
m (q) is a positive definite inertia matrix in a system dynamics model, S is a shorthand form of S (q), q ═ x y θ]TX, y represent the current position of the robot, and theta represents the current azimuth angle of the robot;
Figure BDA0002737046850000041
g (q) is a gravity term in a system dynamics model;
Figure BDA0002737046850000042
a point above the letter represents the first derivative of the parameter; kτA positive definite control gain matrix; u. ofc＝[vc ωc]T，u＝[v ω]TV, ω are the actual velocity and the azimuth velocity of the robot;
Figure BDA00027370468500000411
is an estimate of system uncertainty and interference;
Figure BDA0002737046850000043
Figure BDA0002737046850000044
Figure BDA0002737046850000045
Figure BDA0002737046850000046
Figure BDA0002737046850000047
wherein r is the radius of the driving wheel, L is half of the distance between the two driving wheels, a is the length of the caster arm, and alpha is the included angle between the tether and the axis of the caster arm shaft.
Further, in step (4), the optimal tether tension F*The following were used:
Figure BDA0002737046850000048
in the above formula, y1、y2、z1、z2Defining:
Figure BDA0002737046850000049
Figure BDA00027370468500000410
further, in step (5), the expression of the disturbance observer module is as follows:
Figure BDA0002737046850000051
Figure BDA0002737046850000052
in the above formula, K3And K4An observer gain adjustment matrix;
Figure BDA0002737046850000053
is an estimate of the x-ray intensity,
Figure BDA0002737046850000054
Figure BDA0002737046850000055
in order for the speed to track the error,
Figure BDA0002737046850000056
b (q) τ is the generalized force experienced by the system:
Figure BDA0002737046850000057
adopt the beneficial effect that above-mentioned technical scheme brought:
the invention can realize that the extreme terrain moves along a preset track; energy consumption is reduced by comprehensively considering the energy consumption minimum optimization method of double-wheel moment and tether tension; under the interference factors such as local terrain change of extreme terrain, the interference is actively compensated through an interference observer, and stable track tracking is realized; meanwhile, the tension of the tether is kept in a proper range, the abrasion of the tether is reduced, and the service life of the tether is prolonged. The robot can be further applied to a rope system mobile robot which provides supporting force through a rope system with one end fixed at the anchoring position of the parent robot, and the robot can be used in the fields of planet surface detection, disaster relief and emergency rescue and the like, so that the robot has wide application prospect.
Drawings
FIG. 1 is a system composition diagram of the present invention;
FIG. 2 is a motion control block diagram of the present invention;
FIG. 3 is a schematic diagram for describing the pose of the two-wheel differential drive mobile robot;
FIG. 4 is a schematic view of pose error definition;
fig. 5 is a force-bearing schematic diagram of the tethered wheeled mobile robot.
Description of reference numerals: 1. a controller; 2. a left wheel drive; 3. a right wheel drive; 4. a tether winch drive; 5. a tether tension sensor; 6. a tether; 7. a rope-tied wheel type moving mechanism; 8. a navigation positioning device; 9. a left drive wheel; 10. a right drive wheel; 11. a winch; 12. a central shaft body; 13. a caster arm.
Detailed Description
The technical scheme of the invention is explained in detail in the following with the accompanying drawings.
As shown in fig. 1, a motion control system of a tethered wheel-type mobile robot includes: the device comprises a controller 1, a left wheel driver 2, a right wheel driver 3, a tether winch driver 4, a tether tension sensor 5, a tether 6, a tether wheel type moving mechanism 7 and a navigation positioning device 8. The rope wheel type moving mechanism 7 comprises a left driving wheel 9, a right driving wheel 10, a winch 11, a central shaft body 12 and a caster arm 13, wherein the left driving wheel 9 and the right driving wheel 10 are connected to the left side and the right side of the central shaft body 12 through bearings, and the caster arm 13 is fixedly connected with the central shaft body 12. Winch 11 passes through the bearing and installs in central axis body 12 central authorities, and tether 6 one end is fixed in on winch 11, and the other end of tether 6 is fixed in on mother's robot or a fixed anchor point through truckle arm central axis hole. Before deployment, the tether 6 is wound on the winch 11, and by rotating the winch 11, retraction and winding of the tether 6 can be achieved. The tether tension sensor 5 is fixed to the winch 11 or mounted on the caster arm 13, the tether 6 passes through the tether tension sensor 5, and the tether tension sensor 5 measures the tether 6 tension and converts it into an electrical signal to be sent to the controller 1. The navigation positioning device 8 can determine the speed and the pose of the robot and send the speed and the pose to the controller 1 for processing uniformly to realize a control function.
The controller 1 comprises a kinematic control module, a dynamic control module, a disturbance observer module, and a tether tension control module. The controller 1 receives a tether tension F, a robot speed, and robot posture information from the tethered wheeled mobile robot. The tether tension is measured by a tether tension sensor 5, and the robot speed and the robot posture information can be determined by a navigation positioning device. The expected torque output by the dynamics control module is output to a left wheel driver 2 and a right wheel driver 3, the left wheel driver and the right wheel driver comprise motors and related motor control components, and the left wheel driver and the right wheel driver are driven to move according to the expected torque input by the controller 1; meanwhile, the controller 1 sends the expected tether retracting length delta x to the tether winch driver 4, so that the winch 11 rotates in the expected direction, the tether tension is controlled by retracting the tether 6, and the tether tension control and the movement are realized in cooperation with the left driving wheel and the right driving wheel. Wherein the tether winch drive 4 comprises a motor and associated motor control and the like.
As shown in fig. 2, the control method based on the motion control system of the tethered wheeled mobile robot includes the following steps:
step 1, comparing an expected pose x output by an upper locus planning system by a comparatord,yd,θdThe difference between the actual pose x, y and theta of the rope wheel type mobile robot system is converted into a robot body coordinate system to obtain a pose error xe,ye,θe；
Step 2, according to the pose error xe,ye,θeThe desired control speed v is calculated by a kinematic control module through a kinematic control lawc,ωc；
Step 3, comparing the expected control speed v by a comparatorc,ωcObtaining the speed and azimuth angle speed deviation v and omega from the difference between the speed and the azimuth angle speed v and omega of the actual rope-tied wheeled mobile robote,ωe；
Step 4, according to the interference estimated by the interference observer module
Figure BDA0002737046850000071
Velocity and azimuthal velocity deviation ve,ωeAnd a dynamics control law, wherein the dynamics control module calculates the optimal tether tension F based on the minimum energy consumption principle*(ii) a Expected left wheel control torque and right wheel control torque are further obtained through calculation of a dynamics control law, and the control torques are respectively transmitted to a left wheel driver and a right wheel driver to control the two wheels;
step 5, according to the actual speed and the azimuth angle speed v, omega of the rope-tied wheeled mobile robot and the double-wheel control moment and the rope-tied tension F output by the dynamic control module*The disturbance observer module estimates the uncertainty and disturbance of the system
Figure BDA0002737046850000072
And output to the dynamics control module for compensation;
step 6, controlling the tether tension according to the optimal tether tension F*And the tether tension output by the tether tension sensor calculates the tether retraction length, and transmits the tether retraction length to a tether winch driver to control a winch, so that tether tension control is realized.
The specific implementation of each module in the controller is as follows:
1) kinematic control module
A mobile robot operating on a relatively flat road surface generally reduces the road surface to a two-dimensional plane, and a specific case of a differentially driven two-wheeled robot is shown in fig. 3. The mobile robot has three degrees of freedom at this time, and the pose is described as q ═ x y θ]TWherein x and y represent the current position of the robot, and theta represents the current azimuth angle of the robot, namely the included angle between the advancing direction of the robot and the positive direction of the x axis; since the robot is driven differentially in two wheels, the robot has two degrees of freedom in common and is written as u ═ v ω]TWhere v denotes a velocity of the geometric center of the robot in the robot advance direction, and ω denotes a rotational angular velocity of the geometric center of the robot about the z-axis (perpendicular to the xy-plane).
At this time, the kinematic equation of the mobile robot is:
Figure BDA0002737046850000081
wherein the transformation matrix is:
Figure BDA0002737046850000082
as shown in fig. 4, the pose error of a wheeled mobile robot in the robot coordinate system is defined as:
Figure BDA0002737046850000083
wherein x isd,yd,θdThe expected pose track output by the upper track planning system is represented, and x, y and theta areActual pose, x, of the mobile robote,ye,θeAnd representing the pose error.
The kinematic control law is as follows:
vc＝k1xe+vdcosθe
Figure BDA0002737046850000084
wherein k is0,k1,k2For controlling gain, and has k0＞0,k1＞0,k2＞0；vc,ωcIs the desired control speed.
2) Dynamics control module
For a wheeled mobile robot system, the dynamic model is as follows:
Figure BDA0002737046850000085
wherein, M (q) is a positive definite inertia matrix of the system dynamics model; g (q) is a gravity term;
Figure BDA0002737046850000086
representing a set of uncertainties and interferences;
Figure BDA0002737046850000087
for centrifugal and coriolis force terms, a (q) λ represents a constraining force vector, where:
A(q)＝[sinθ -cosθ 0]T
since the tethered wheeled mobile robot needs to keep the tether in tension during extreme terrain movements, it is subjected to the tether tension in addition to the two-wheel input torque, as shown in fig. 5.
The generalized forces experienced by the system from FIG. 5 can be:
Figure BDA0002737046850000091
wherein, taul,τrThe driving torque of the left wheel and the driving torque of the right wheel are respectively, F is the tension of the tether, a is the length of the caster arm, alpha is an included angle between the tether and the axis of the caster arm shaft, r is the wheel radius, and 2L is the distance between the two driving wheels.
From the above formula, one can obtain:
Figure BDA0002737046850000092
Figure BDA0002737046850000093
wherein the content of the first and second substances,
Figure BDA0002737046850000094
Figure BDA0002737046850000095
for simplicity and clarity, part of S (q) is abbreviated as S. From the dynamic equation of the actual rope-tied wheeled mobile robot,
Figure BDA0002737046850000096
thus, the term is removed from the formula.
In the case of a tethered mobile robot, because the presence of the tether additionally subjects the robot to a tether tension, the tether tension must be kept within a suitable constraint range by taking into account the combined effect of the tether tension, and reasonable control of the tether tension is achieved mainly by taking into account the combination of the two-wheel moment and the minimum energy consumption required by the tether tension. The generalized input force is now decomposed as follows:
Figure BDA0002737046850000097
wherein, taulr＝[τl τr]TIs 2 x 1 dimensional inputMoment of force, BτIs a 2 x 2 dimensional double-wheel torque input matrix, BFThe method is a 2 multiplied by 1 dimension rope tension input matrix, and specifically comprises the following steps:
Figure BDA0002737046850000098
setting the optimal tether tension to F*The dynamics control module adopts the following control laws:
Figure BDA0002737046850000101
wherein, KτIn order to positively determine the control gain matrix,
Figure BDA0002737046850000102
is the disturbance estimate output by the disturbance observer module,
Figure BDA0002737046850000103
Figure BDA0002737046850000104
Figure BDA0002737046850000105
in addition, considering that the energy consumption is minimized for the three control input forces/moments, the energy function is defined here as:
Figure BDA0002737046850000106
the control law of the dynamics control module can be further written as:
Figure BDA0002737046850000107
wherein:
Figure BDA0002737046850000108
Figure BDA0002737046850000109
will taul、τrIs shown as F*The expression of (c) is substituted into the energy function, from E min,
Figure BDA00027370468500001010
the optimum rope tension F can be obtained*：
Figure BDA00027370468500001011
Will find F*And substituting the expected input torque into a control law of a dynamics control module, and further calculating the expected input torque of the corresponding left and right driving wheels.
3) Interference observer module
The disturbance observer is:
Figure BDA0002737046850000111
Figure BDA0002737046850000112
wherein, K3And K4In order to be an observer gain matrix,
Figure BDA0002737046850000113
in order to make an estimate of f,
Figure BDA0002737046850000114
representing a set of uncertainties and disturbances in a system dynamics model;
Figure BDA0002737046850000115
in order to evaluate the value of x,
Figure BDA0002737046850000116
Figure BDA0002737046850000117
for velocity tracking error, defined as:
Figure BDA0002737046850000118
according to τ and ucAnd the estimation value of the interference f can be obtained, and the estimation value of the interference is input into a dynamic control module and is used for interference active compensation.
4) Tether tension control module
The tether tension control module system expression is as follows:
Figure BDA0002737046850000119
wherein, KPF，KDFParameters are controlled for tether tension PD.
Through proper mechanism parameters, a corresponding parameter matrix can be determined; further according to specific performance index requirements, corresponding controller parameters may be determined. The following is a set of relevant parameter settings for the specific implementation example.
The specific extreme terrain is steep slope terrain, and the inclination angle of the slope relative to the horizontal plane is thetasThe parameters of a rope-based two-wheeled robot are shown in table 1, and are substituted into the following formula to obtain the corresponding parameter values of the kinetic equation:
Figure BDA0002737046850000121
Figure BDA0002737046850000122
Figure BDA0002737046850000123
Figure BDA0002737046850000124
wherein m is the total mass of the robot, r is the wheel radius, 2L is the wheel spacing,
Figure BDA0002737046850000125
the caster arm is a light thin rod for the moment of inertia of the central shaft body around the coordinate axis oz, so the mass and the moment of inertia are ignored,
Figure BDA0002737046850000126
and
Figure BDA0002737046850000127
the moment of inertia of the wheel about the coordinate axes oy and oz, respectively.
TABLE 1
Configuration parameter Numerical value Unit of
Radius of wheel 225 mm
Wheel spacing 980 mm
Mass of single wheel 1.5 kg
Center shaft body mass 17 kg
Radius of central shaft body 110 mm
The controller of the rope wheel type mobile robot system consists of an embedded single board computer and a data acquisition module; and the control of the wheels and the ropes is realized by combining a motor drive controller.
And adjusting the control parameters of the kinematics control module and the dynamics control module according to the structural parameters. According to the actual measurement, the coordinate of the anchor point of the tether is (5.0,4.8) m, thetas45 degrees, the control parameter of the kinematic control module is k0＝2.5,k1＝0.6,k20.9, kinetic controller parameter Kτ＝diag[20 10]Observer parameter K3＝diag[5 5]，K4＝diag[10 10]Control parameter K of tether tension PDPF＝15，K DF10. The system realized by the method of the invention obtains good performance and can move along a preset track; energy consumption is reduced by comprehensively considering the energy consumption minimum optimization method of double-wheel moment and tether tension; under the interference factors such as local terrain change of extreme terrain, the interference can be actively compensated through the interference observer, and stable track tracking is realized; while maintaining the tether tension within a suitable range, reducingThe wear of the tether increases its life.
The method can be further applied to a rope system mobile robot which provides supporting force through a rope system with one end fixed at the anchoring position of the parent robot, and the robot can be used for planetary surface detection, disaster relief and emergency rescue, so the implementation method has wide application prospect.
The embodiments are only for illustrating the technical idea of the present invention, and the technical idea of the present invention is not limited thereto, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the scope of the present invention.

Claims (1)

1. The control method is based on a rope-tied wheel type mobile robot motion control system, and the rope-tied wheel type mobile robot motion control system comprises a controller, a left wheel driver, a right wheel driver, a tied rope winch driver, a tied rope tension sensor, a tied rope, a rope-tied wheel type mobile mechanism and a navigation positioning device; the rope wheel type moving mechanism comprises a left driving wheel, a right driving wheel, a winch, a central shaft body and a caster arm; the left driving wheel and the right driving wheel are connected to the left side and the right side of the central shaft body through bearings, the caster arms are fixedly connected with the central shaft body, the winch is installed in the center of the central shaft body through bearings, the tether is wound on the winch, the tether tension sensor is fixed on the winch or installed on the caster arms, the tether penetrates through the tether tension sensor, the tether tension sensor measures the tension of the tether and converts the tension into an electric signal to be sent to the controller, the navigation positioning device detects the speed and the pose information of the robot and sends the information to the controller, the controller comprises a kinematics control module, a dynamics control module, an interference observer module and a tether tension control module, the controller processes the information sent by the tether tension sensor and the navigation positioning device to obtain the expected torque of the left wheel driver and the right wheel driver and the expected tether length of the tether winch driver, the left wheel driver and the right wheel driver control the left driving wheel and the right driving wheel to move according to the expected torque, and the tether winch driver controls the winch to receive and release the tether according to the expected tether receiving and releasing length, so that the motion control of the robot is realized;
the control method is characterized by comprising the following steps:
(1) comparing a difference value between an expected pose output by the upper trajectory planning system and an actual pose of the tethered wheel type mobile robot, and converting the difference value into a robot body coordinate system to obtain a pose error;
(2) calculating expected speed and azimuth angle speed by a kinematics control module through a kinematics control law according to the pose error; the kinematic control law is as follows:
vc＝k1xe+vdcosθe
Figure FDA0003243268460000011
in the above formula, k0,k1,k2For controlling gain, and has k0＞0,k1＞0,k2＞0；vc、ωcRespectively desired velocity and azimuthal velocity, vd、ωdRespectively representing the expected speed and the azimuth angle speed in the robot body coordinate system; x is the number ofe、ye、θeRespectively representing an abscissa error, an ordinate error and an azimuth error in the pose errors;
(3) comparing the difference between the expected speed and the azimuth speed and the actual speed and the azimuth speed of the rope-tied wheeled mobile robot to obtain a speed deviation and an azimuth speed deviation;
(4) according to the interference, the speed deviation, the azimuth speed deviation and the dynamics control law estimated by the interference observer module, the dynamics control module calculates the optimal tether tension F based on the minimum energy consumption principle*Calculating to obtain expected left wheel control torque and right wheel control torque through a dynamics control law, and respectively transmitting the expected left wheel control torque and right wheel control torque to a left wheel driver and a right wheel driver for double-wheel control; the dynamics control law is as follows:
Figure FDA0003243268460000021
in the above formula, τlrFor two-wheeled control of torque, taulr＝[τl τr]T，τlAnd τrThe left wheel control moment and the right wheel control moment are respectively, and the superscript T represents transposition;
Figure FDA0003243268460000022
m (q) is a positive definite inertia matrix in a system dynamics model, S is a shorthand form of S (q), q ═ x y θ]TX, y represent the current position of the robot, and theta represents the current azimuth angle of the robot;
Figure FDA0003243268460000023
g (q) is a gravity term in a system dynamics model;
Figure FDA0003243268460000024
a point above the letter represents the first derivative of the parameter; kτA positive definite control gain matrix; u. ofc＝[vc ωc]T，u＝[v ω]TV, ω are the actual velocity and the azimuth velocity of the robot;
Figure FDA0003243268460000025
is an estimate of system uncertainty and interference;
Figure FDA0003243268460000026
Figure FDA0003243268460000027
Figure FDA0003243268460000028
Figure FDA0003243268460000031
Figure FDA0003243268460000032
wherein r is the radius of the driving wheel, L is half of the distance between the two driving wheels, a is the length of the caster arm, and alpha is the included angle between the tether and the axis of the caster arm;
the optimal tether tension F*The following were used:
Figure FDA0003243268460000033
in the above formula, y1、y2、z1、z2Defining:
Figure FDA0003243268460000034
Figure FDA0003243268460000035
(5) according to the actual speed and azimuth speed of the rope-tied wheeled mobile robot, the double-wheel control moment and the optimal rope-tied tension F*The disturbance observer module estimates the uncertainty and disturbance of the system and outputs the uncertainty and disturbance to the dynamics control module for compensation; the expression of the disturbance observer module is as follows:
Figure FDA0003243268460000036
Figure FDA0003243268460000037
in the above formula, K3And K4An observer gain adjustment matrix;
Figure FDA0003243268460000038
is an estimate of the x-ray intensity,
Figure FDA0003243268460000039
Figure FDA00032432684600000310
in order for the speed to track the error,
Figure FDA00032432684600000311
b (q) τ is the generalized force experienced by the system:
Figure FDA00032432684600000312
(6) according to the optimum tether tension F*And tether tension measured by the tether tension sensor, the tether tension control module calculating an expected tether retraction length and transmitting the expected tether retraction length to the tether winch drive for winch control.
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