CN108098770A - A kind of Trajectory Tracking Control method of mobile robot - Google Patents
A kind of Trajectory Tracking Control method of mobile robot Download PDFInfo
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- CN108098770A CN108098770A CN201711343115.0A CN201711343115A CN108098770A CN 108098770 A CN108098770 A CN 108098770A CN 201711343115 A CN201711343115 A CN 201711343115A CN 108098770 A CN108098770 A CN 108098770A
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B25—HAND TOOLS; PORTABLE POWER-DRIVEN TOOLS; MANIPULATORS
- B25J—MANIPULATORS; CHAMBERS PROVIDED WITH MANIPULATION DEVICES
- B25J9/00—Programme-controlled manipulators
- B25J9/16—Programme controls
- B25J9/1656—Programme controls characterised by programming, planning systems for manipulators
- B25J9/1664—Programme controls characterised by programming, planning systems for manipulators characterised by motion, path, trajectory planning
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
- G05B2219/00—Program-control systems
- G05B2219/30—Nc systems
- G05B2219/40—Robotics, robotics mapping to robotics vision
- G05B2219/40519—Motion, trajectory planning
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Abstract
The invention discloses a kind of Trajectory Tracking Control methods of mobile robot, the data that this method is detected according to the coefficient that trackslips, the motion mathematical model expression formula of slip rate and GPS INS, expected path, desired speed and the expectation yaw velocity information provided again according to mobile robot decision-making level, calculate the numerical value of the coefficient that trackslips, slip rate, then it is counter to be updated in the kinematics model of mobile robot, the vehicle wheel rotational speed for realizing track following is compensated and calculated, achievees the purpose that accurately to track desired trajectory.It is an advantage of the invention that：Slippage of trackslipping can constantly be calculated, more really, accurately describes and characterize the motion state of mobile robot reality, so as to effectively accurately follow desired trajectory.
Description
Technical field：
The present invention relates to mobile robot technology fields, are especially a kind of Trajectory Tracking Control side of mobile robot
Method.
Background technology：
The track following of mobile robot is basis and the guarantee that mobile robot performs task, and then mobile robot exists
Under the complex environment of field during operation, ground environment is complicated, such as sandy soil, muddy road surface, ground are wet and slippery, operating mode icy on road, this
It inevitably results from trackslipping and sliding between mobile robot and ground under environment, and parameter is slid using zero slip at this time
The Trajectory Tracking Control method of estimation can not realize accurate Trajectory Tracking Control.
The content of the invention：
The technical problem to be solved by the present invention is to, slippage of trackslipping can constantly be calculated by providing one kind, more really,
The motion state of mobile robot reality is accurately described and characterizes, so as to effectively accurately follow the path of desired trajectory
Tracking and controlling method.
The technical solution of the present invention is to provide a kind of Trajectory Tracking Control method of mobile robot, this method bag
Include following steps：
Step 1：The desired trajectory of mobile robot decision-making level planning and desired trajectory tracking velocity signal are received, setting is just
Beginning preview distance d chooses to be used as the point of preview distance d with mobile robot distance in expected path and takes aim at point q in advanced, read
The mobile robot current status data of GPS-INS integrated positioning systems acquisition；
Step 2：Foundation is trackslipped based on wheels of mobile robot, the kinematics model of car body sliding：
The earth inertial coodinate system ∑ I, bodywork reference frame ∑ b are defined,
Pose of the car body under inertial coodinate system：qI=[xI yI θI]T
Pose of the car body under bodywork reference frame：qb=[xb yb θb]T
And θI=θb=θ is mobile robot course angle,
Rate conversion relation between inertial coodinate system and bodywork reference frame is：
If
Then
Under mobile robot coordinate system, it is longitudinal direction x to define length of wagon direction, and vehicle-body width direction is transverse direction y, left vehicle
The coefficient that trackslips of wheel is sI,
The coefficient that trackslips of right wheel is sr, radius of wheel r, car body left side wheel rotational speed omegal, linear velocity vl, car body right side
Vehicle wheel rotational speed ωr, linear velocity vr, mobile robot longitudinal velocity is vbx, mobile robot yaw velocity be ω, wheel center
Width is 2L,
The slip coefficient of vehicle sliding is i, and mobile robot lateral velocity is vby,
It establishes under inertial coodinate system, the moveable robot movement model based on sliding of trackslipping：
Step 3：According to the moveable robot movement model based on sliding of trackslipping, the coefficient s that trackslips of left wheel is solvedl,
Right wheel trackslips
Coefficient srExpression formula：
Step 4：Establish the track following error model under mobile robot coordinate：
I.e.
Wherein,Represent the trajectory error under bodywork reference frame,It represents in the inertial coodinate system next period
It hopes the pose of tracing point, i.e., takes aim at point q in advancedPose, the pose q of desired trajectorydIt is provided by decision system；It represents to move
Mobile robot pose current under inertial coodinate system；
Step 5：Derivation is carried out to tracking error model, draws tracking error state equation：
Step 6：According to the track following error state equation of step 5, using based on trackslip, the track following of slip coefficient
The control law of control：
Wherein, v1It is inputted for the speed control of right wheel, v2It is inputted for the speed control of left wheel,
Wherein control gain coefficient k1、k：、k3、k4More than zero and there is a upper bound；
Step 7：According to the input of the control rate of step 6, then control mobile robot traveling is detected according to GPS-INS
And the data recorded obtain current pose of the mobile robot under inertial coodinate systemThat is qc=ql, inertial coordinate
Speed under systemThe yaw velocity ω of car body measures left and right vehicle wheel rotational speed ω according to encoderl、ωr, it is described
Encoder be relative encoder；
Step 8：According to the v under bodywork reference framebx、vbyWith v under inertial coodinate systemIx、vIyRelation：
Calculate vbx、vbyAnd slip rateAnd Then by i,ωl、ωr、Substitute into the s in step 3l、srCalculation formula calculates sl、sr；
Step 9：The s that will be calculated in step 8l、sr, desired speed vd, it is expected yaw velocity ωdIt substitutes into step 6
Control lawIn, and selected control gain coefficient k1、k2、k3, by calculatingSubstitution step 2 solve driving wheel in cunning
Turn the required control mobile robot both sides vehicle wheel rotational speed under sliding coupling estimationIt is denoted asWherein desired speed vd
And it is expected yaw velocity ωdIt is the data exported by decision-making level.
Step 10：The mobile robot both sides vehicle wheel rotational speed calculated according to step 9Entire car controller arrives calculating
Obtained wheel rotation speed signals send the actuator of driving wheel and wheel controlled to be moved with this speed；
Step 11：Action of the step 4 to step 10 is repeated, it is final to realize that desired speed accurately tracks expected path.
The beneficial effects of the invention are as follows：
The 1st, the coefficient that trackslips of mobile robot, slip rate model are introduced to the kinematics model of mobile robot, more can
Really, accurately describe and characterize the motion state of mobile robot reality；
2nd, the moveable robot movement model established based on sliding coupling estimation of trackslipping, cunning can be solved by the model
Transfer from one department to another number, the mathematical relationship expression formula of slip rate, therefore, the calculating for the coefficient that trackslips, slip rate provides model；
3rd, the Trajectory Tracking Control method based on sliding coupling estimation of trackslipping proposed, according to the coefficient that trackslips, slip rate
The data that mathematic(al) representation and GPS-INS are detected, then provide according to mobile robot decision-making level expected path, it is expected speed
Degree and expectation yaw velocity information, can calculate the numerical value of the coefficient that trackslips, slip rate, then counter to be updated to mobile robot
Kinematics model in, compensate and calculate realize track following vehicle wheel rotational speed, achieve the purpose that accurately to track desired trajectory.
4th, the Trajectory Tracking Control method proposed by the present invention based on sliding coupling estimation of trackslipping, computing go out moving machine
Device people sliding, the truth of wheel slip, improve the environmental suitability of mobile Robot, such as ice and snow, it is sliding it is wet,
Soft slippery road surface still can accurately track expected path, and therefore, which greatlys improve movement
Tracking accuracy of the robot under complicated road environment.
Description of the drawings：
Fig. 1 is the coordinate representation schematic diagram in the present invention；
Fig. 2 is the tracking error model schematic diagram in the present invention；
Fig. 3 is the sliding model schematic diagram in the present invention；
Fig. 4 is the control block schematic diagram of the present invention.
Specific embodiment：
A kind of Trajectory Tracking Control method of mobile robot of the present invention is made in the following with reference to the drawings and specific embodiments into
One step explanation：
Mobile robot involved in the present invention is independent full driving, and wheel is without active steering degree of freedom, and car body homonymy
The identical mobile robot of vehicle wheel rotational speed, this mobile robot includes GPS-INS integrated positioning systems, for gathering wheel
The encoder of rotary speed data and the entire car controller that driving motor rotating speed is sent to entire car controller.
As shown in Figure 1, Figure 2, Figure 3 and Figure 4, a kind of mobile robot path based on sliding coupling estimation of trackslipping of the present invention
Tracking and controlling method, this method comprise the following steps：
Step 1：The desired trajectory of mobile robot decision-making level planning and desired trajectory tracking velocity signal are received, setting is just
Beginning preview distance d chooses to be used as the point of preview distance d with mobile robot distance in expected path and takes aim at point q in advanced, read
The mobile robot current status data of GPS-INS integrated positioning systems acquisition；
Step 2：Foundation is trackslipped based on wheels of mobile robot, the kinematics model of car body sliding：
The earth inertial coodinate system ∑ I, bodywork reference frame ∑ b are defined,
Pose of the car body under inertial coodinate system：qI=[xI yI θI]T
Pose of the car body under bodywork reference frame：qb=[xb yb θb]T
And θI=θb=θ is mobile robot course angle,
Rate conversion relation between inertial coodinate system and bodywork reference frame is：
If
Then
Under mobile robot coordinate system, it is longitudinal direction x to define length of wagon direction, and vehicle-body width direction is transverse direction y, left vehicle
The coefficient that trackslips of wheel is sl,
The coefficient that trackslips of right wheel is sr, radius of wheel r, car body left side wheel rotational speed omegal, linear velocity vl, car body right side
Vehicle wheel rotational speed ωr, linear velocity vr, mobile robot longitudinal velocity is vbx, mobile robot yaw velocity be ω, wheel center
Width is 2L,
The slip coefficient of vehicle sliding is i, and mobile robot lateral velocity is vby,
It establishes under inertial coodinate system, the moveable robot movement model based on sliding of trackslipping：
Step 3：According to the moveable robot movement model based on sliding of trackslipping, the coefficient s that trackslips of left wheel is solvedl,
Right wheel trackslips
Coefficient srExpression formula：
Step 4：Establish the track following error model under mobile robot coordinate：
I.e.
Wherein,Represent the trajectory error under bodywork reference frame,It represents in the inertial coodinate system next period
It hopes the pose of tracing point, i.e., takes aim at point q in advancedPose, the pose q of desired trajectorydIt is provided by decision system；It represents to move
Mobile robot pose current under inertial coodinate system；
Step 5：Derivation is carried out to tracking error model, draws tracking error state equation：
Step 6：According to the track following error state equation of step 5, using based on trackslip, the track following of slip coefficient
The control law of control：
Wherein, vlIt is inputted for the speed control of right wheel, v2It is inputted for the speed control of left wheel,
Wherein control gain coefficient k1、k2、k3、k4More than zero and there is a upper bound；
Step 7：According to the input of the control rate of step 6, then control mobile robot traveling is detected according to GPS-INS
And the data recorded obtain current pose of the mobile robot under inertial coodinate systemThat is qc=qI, inertial coordinate
Speed under systemThe yaw velocity ω of car body measures left and right vehicle wheel rotational speed ω according to encoderl、ωr, it is described
Encoder be relative encoder；
Step 8：According to the v under bodywork reference framebx、vbyWith v under inertial coodinate systemlx、vlyRelation：
Calculate vbx、vbyAnd slip rateMesh Then by i,ωl、ωr、Substitute into the s in step 3l、srCalculation formula calculates sl、sr；
Step 9：The s that will be calculated in step 8l、sr, desired speed vd, it is expected yaw velocity ωdIt substitutes into step 6
Control lawIn, and selected control gain coefficient k1、k2、k3, by calculatingSubstitution step 2 solve driving wheel in cunning
Turn the required control mobile robot both sides vehicle wheel rotational speed under sliding coupling estimationIt is denoted asWherein desired speed vd
And it is expected yaw velocity ωdIt is the data exported by decision-making level.
Step 10：The mobile robot both sides vehicle wheel rotational speed calculated according to step 9Entire car controller arrives calculating
Obtained wheel rotation speed signals send the actuator of driving wheel and wheel controlled to be moved with this speed；
Step 11：Action of the step 4 to step 10 is repeated, it is final to realize that desired speed accurately tracks expected path.
Embodiment described above is only that the preferred embodiment of the present invention is described, not to the scope of the present invention
It is defined, on the premise of design spirit of the present invention is not departed from, those of ordinary skill in the art are to technical scheme
The various modifications made and improvement should all be fallen into the protection domain that claims of the present invention determines.
Claims (1)
1. a kind of Trajectory Tracking Control method of mobile robot, it is characterised in that：This method comprises the following steps：
Step 1：The desired trajectory of mobile robot decision-making level planning and desired trajectory tracking velocity signal are received, setting is initial pre-
Distance d is taken aim at, chooses to be used as the point of preview distance d with mobile robot distance in expected path and takes aim at point q in advanced, read GPS-INS
The mobile robot current status data of integrated positioning system acquisition；
Step 2：Foundation is trackslipped based on wheels of mobile robot, the kinematics model of car body sliding：
The earth inertial coodinate system ∑ I, bodywork reference frame ∑ b are defined,
Pose of the car body under inertial coodinate system：qI=[xI yI θI]T
Pose of the car body under bodywork reference frame：qb=[xb yb θb]T
And θI=θb=θ is mobile robot course angle,
Rate conversion relation between inertial coodinate system and bodywork reference frame is：
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Rotational speed omegar, linear velocity vr, mobile robot longitudinal velocity isMobile robot yaw velocity be ω, wheel center width
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<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>sin</mi>
<mi>&theta;</mi>
<mo>+</mo>
<mi>i</mi>
<mi>cos</mi>
<mi>&theta;</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
<mtd>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>s</mi>
<mi>l</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>sin</mi>
<mi>&theta;</mi>
<mo>+</mo>
<mi>i</mi>
<mi>cos</mi>
<mi>&theta;</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>s</mi>
<mi>r</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mi>L</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mo>-</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>s</mi>
<mi>l</mi>
</msub>
</mrow>
<mo>)</mo>
</mrow>
<mo>/</mo>
<mi>L</mi>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>r</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>l</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Step 3：According to the moveable robot movement model based on sliding of trackslipping, the coefficient s that trackslips of left wheel is solvedl, right wheel
Trackslip
Coefficient srExpression formula：
<mrow>
<msub>
<mi>s</mi>
<mi>r</mi>
</msub>
<mo>=</mo>
<mn>1</mn>
<mo>-</mo>
<mfrac>
<mrow>
<mi>L</mi>
<mover>
<msub>
<mi>&theta;</mi>
<mi>I</mi>
</msub>
<mo>&CenterDot;</mo>
</mover>
</mrow>
<mrow>
<msub>
<mi>r&omega;</mi>
<mi>r</mi>
</msub>
</mrow>
</mfrac>
<mo>-</mo>
<mfrac>
<mover>
<msub>
<mi>x</mi>
<mi>I</mi>
</msub>
<mo>&CenterDot;</mo>
</mover>
<mrow>
<msub>
<mi>r&omega;</mi>
<mi>r</mi>
</msub>
<mrow>
<mo>(</mo>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mi>&theta;</mi>
<mo>-</mo>
<mi>i</mi>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</mrow>
<mrow>
<msub>
<mi>q</mi>
<mi>e</mi>
</msub>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&theta;</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mi>&theta;</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mi>&theta;</mi>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mi>&theta;</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mi>&theta;</mi>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mrow>
<mo>(</mo>
<msub>
<mi>q</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
<msub>
<mi>q</mi>
<mi>c</mi>
</msub>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mi>&theta;</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>s</mi>
<mi>i</mi>
<mi>n</mi>
<mi>&theta;</mi>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<mo>-</mo>
<mi>sin</mi>
<mi>&theta;</mi>
</mrow>
</mtd>
<mtd>
<mrow>
<mi>c</mi>
<mi>o</mi>
<mi>s</mi>
<mi>&theta;</mi>
</mrow>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
</mtr>
<mtr>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>0</mn>
</mtd>
<mtd>
<mn>1</mn>
</mtd>
</mtr>
</mtable>
</mfenced>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>x</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>c</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>y</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>c</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&theta;</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mi>c</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Step 4：Establish the track following error model under mobile robot coordinate：
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&theta;</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>x</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
<msub>
<mi>x</mi>
<mi>c</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>y</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
<msub>
<mi>y</mi>
<mi>c</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&theta;</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&theta;</mi>
<mi>c</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
I.e.
<mrow>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&theta;</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mi>S</mi>
<mrow>
<mo>(</mo>
<mi>&theta;</mi>
<mo>)</mo>
</mrow>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<msub>
<mi>x</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
</mtd>
<mtd>
<msub>
<mi>x</mi>
<mi>c</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>y</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
</mtd>
<mtd>
<msub>
<mi>y</mi>
<mi>c</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&theta;</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
</mtd>
<mtd>
<msub>
<mi>&theta;</mi>
<mi>c</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein,Represent the trajectory error under bodywork reference frame,Expression it is expected rail under inertial coodinate system
The pose of mark point takes aim at point q in advancedPose, the pose q of desired trajectorydIt is provided by decision system；Represent moving machine
Device people pose current under inertial coodinate system；
Step 5：Derivation is carried out to tracking error model, draws tracking error state equation：
<mrow>
<mover>
<mi>qe</mi>
<mo>.</mo>
</mover>
<mo>=</mo>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mover>
<msub>
<mi>x</mi>
<mi>e</mi>
</msub>
<mo>.</mo>
</mover>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mover>
<mi>y</mi>
<mo>.</mo>
</mover>
<mi>e</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mover>
<msub>
<mi>&theta;</mi>
<mi>e</mi>
</msub>
<mo>.</mo>
</mover>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<msub>
<mi>v</mi>
<mi>d</mi>
</msub>
<mi>cos</mi>
<msub>
<mi>&theta;</mi>
<mi>e</mi>
</msub>
<mo>-</mo>
<msub>
<mi>iv</mi>
<mi>d</mi>
</msub>
<mi>sin</mi>
<msub>
<mi>&theta;</mi>
<mi>e</mi>
</msub>
<mo>-</mo>
<msub>
<mi>v</mi>
<mi>bx</mi>
</msub>
<mo>+</mo>
<msub>
<mi>&omega;</mi>
<mi>c</mi>
</msub>
<msub>
<mi>y</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>v</mi>
<mi>d</mi>
</msub>
<mi>sin</mi>
<msub>
<mi>&theta;</mi>
<mi>e</mi>
</msub>
<mo>+</mo>
<msub>
<mi>iv</mi>
<mi>d</mi>
</msub>
<mi>cos</mi>
<msub>
<mi>&theta;</mi>
<mi>e</mi>
</msub>
<mo>-</mo>
<msub>
<mi>iv</mi>
<mi>bx</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>c</mi>
</msub>
<msub>
<mi>x</mi>
<mi>e</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>d</mi>
</msub>
<mo>-</mo>
<msub>
<mi>&omega;</mi>
<mi>c</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Step 6：According to the track following error state equation of step 5, using based on trackslip, the Trajectory Tracking Control of slip coefficient
Control law：
<mrow>
<mover>
<msub>
<mi>v</mi>
<mi>C</mi>
</msub>
<mo>-</mo>
</mover>
<mo>=</mo>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<msub>
<mi>v</mi>
<mn>1</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>v</mi>
<mn>2</mn>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<mi>&omega;</mi>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open='[' close=']'>
<mtable>
<mtr>
<mtd>
<mfrac>
<mrow>
<msub>
<mi>v</mi>
<mi>c</mi>
</msub>
<mo>+</mo>
<mn>2</mn>
<mi>L</mi>
<msub>
<mi>&omega;</mi>
<mi>c</mi>
</msub>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>s</mi>
<mi>r</mi>
</msub>
</mrow>
</mfrac>
</mtd>
</mtr>
<mtr>
<mtd>
<mfrac>
<mrow>
<msub>
<mi>v</mi>
<mi>c</mi>
</msub>
<mo>-</mo>
<mn>2</mn>
<mi>L</mi>
<msub>
<mi>&omega;</mi>
<mi>c</mi>
</msub>
</mrow>
<mrow>
<mn>1</mn>
<mo>-</mo>
<msub>
<mi>s</mi>
<mi>l</mi>
</msub>
</mrow>
</mfrac>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>c</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
</mrow>
Wherein, v1It is inputted for the speed control of right wheel, v2It is inputted for the speed control of left wheel,
<mrow>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<msub>
<mi>v</mi>
<mi>c</mi>
</msub>
</mtd>
</mtr>
<mtr>
<mtd>
<msub>
<mi>&omega;</mi>
<mi>c</mi>
</msub>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>=</mo>
<mfenced open = "[" close = "]">
<mtable>
<mtr>
<mtd>
<mrow>
<msub>
<mi>v</mi>
<mi>d</mi>
</msub>
<msub>
<mi>cos&theta;</mi>
<mi>e</mi>
</msub>
<mo>-</mo>
<msub>
<mi>iv</mi>
<mi>d</mi>
</msub>
<msub>
<mi>sin&theta;</mi>
<mi>e</mi>
</msub>
<mo>+</mo>
<msub>
<mi>k</mi>
<mn>1</mn>
</msub>
<msub>
<mi>x</mi>
<mi>e</mi>
</msub>
<msup>
<mi>sin</mi>
<mn>2</mn>
</msup>
<msub>
<mi>&theta;</mi>
<mi>e</mi>
</msub>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd>
<mrow>
<msub>
<mi>&omega;</mi>
<mi>d</mi>
</msub>
<mo>+</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>+</mo>
<msup>
<mi>i</mi>
<mn>2</mn>
</msup>
</mrow>
<mo>)</mo>
</mrow>
<msub>
<mi>k</mi>
<mn>2</mn>
</msub>
<msub>
<mi>v</mi>
<mi>d</mi>
</msub>
<msub>
<mi>y</mi>
<mi>e</mi>
</msub>
<mo>+</mo>
<msub>
<mi>ik</mi>
<mn>1</mn>
</msub>
<msub>
<mi>k</mi>
<mn>2</mn>
</msub>
<msub>
<mi>x</mi>
<mi>e</mi>
</msub>
<msub>
<mi>y</mi>
<mi>e</mi>
</msub>
<msub>
<mi>sin&theta;</mi>
<mi>e</mi>
</msub>
<mo>+</mo>
<msub>
<mi>k</mi>
<mn>3</mn>
</msub>
<msub>
<mi>sin&theta;</mi>
<mi>e</mi>
</msub>
<mo>+</mo>
<msub>
<mi>k</mi>
<mn>4</mn>
</msub>
<msub>
<mi>y</mi>
<mi>e</mi>
</msub>
<msub>
<mi>cos&theta;</mi>
<mi>e</mi>
</msub>
</mrow>
</mtd>
</mtr>
</mtable>
</mfenced>
<mo>,</mo>
</mrow>
Wherein control gain coefficient k1、k2、k3、k4More than zero and there is a upper bound；
Step 7：According to the input of the control rate of step 6, then control mobile robot traveling is detected and remembered according to GPS-INS
The data of record obtain current pose of the mobile robot under inertial coodinate systemThat is qc=qI, under inertial coodinate system
SpeedThe yaw velocity ω of car body measures left and right vehicle wheel rotational speed ω according to encoder1、ωr, the coding
Device is relative encoder；
Step 8：According under bodywork reference frameWith under inertial coodinate systemRelation：
It calculatesAnd slip rateAnd
Then by i,ωl、ωr、Substitute into the s in step 3l、srCalculation formula calculates sl、sr；
Step 9：The s that will be calculated in step 8l、sr, desired speed vd, it is expected yaw velocity ωdSubstitute into the control in step 6
RuleIn, and selected control gain coefficient k1、k2、k3, by calculatingSubstitution step 2 solve driving wheel in cunning of trackslipping
Move the required control mobile robot both sides vehicle wheel rotational speed under coupling estimationIt is denoted asWherein desired speed vdAnd
It is expected yaw velocity ωdIt is the data exported by decision-making level.
Step 10：The mobile robot both sides vehicle wheel rotational speed calculated according to step 9Entire car controller is obtained what is calculated
To wheel rotation speed signals send driving wheel actuator and control wheel with this speed move；
Step 11：Action of the step 4 to step 10 is repeated, it is final to realize that desired speed accurately tracks expected path.
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Cited By (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN107901917A (en) * | 2017-11-16 | 2018-04-13 | 中国科学院合肥物质科学研究院 | A kind of automatic driving vehicle path tracking control method based on sliding coupling estimation of trackslipping |
| CN109189079A (en) * | 2018-11-05 | 2019-01-11 | 南京理工大学 | Mobile Robotics Navigation control method based on GPS positioning |
| CN109739094A (en) * | 2019-02-28 | 2019-05-10 | 哈尔滨理工大学 | A kind of mobile robot trace tracking new method based on adaptive sliding-mode observer |
| CN110160527A (en) * | 2019-05-06 | 2019-08-23 | 安徽红蝠智能科技有限公司 | A kind of Mobile Robotics Navigation method and apparatus |
| CN110989350A (en) * | 2019-12-11 | 2020-04-10 | 安徽理工大学 | Method and device for realizing pose optimization of underground mobile robot based on membrane calculation |
| CN111994169A (en) * | 2020-09-08 | 2020-11-27 | 北京北特圣迪科技发展有限公司 | Motion control method of independently driven and steered performance trolley based on position compensation |
| CN112157651A (en) * | 2020-08-21 | 2021-01-01 | 深圳市优必选科技股份有限公司 | Pose determination method and device and robot |
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| CN112925323B (en) * | 2021-01-28 | 2022-03-15 | 北京科技大学 | Rule-based mobile robot speed adjusting method and system |
| CN113211456A (en) * | 2021-04-09 | 2021-08-06 | 江苏大学 | Anti-idling high-performance track tracking control method for sand blasting and rust removing parallel robot moving platform |
| CN113341960A (en) * | 2021-05-26 | 2021-09-03 | 重庆大学 | Automatic driving automobile steering control method based on supervised DQN algorithm |
| CN113341989A (en) * | 2021-06-18 | 2021-09-03 | 广州蓝胖子移动科技有限公司 | Wheeled mobile robot, control point model establishing method and device and storage medium |
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