CN113211456B - Track tracking control method for sand blasting and rust removing parallel robot moving platform - Google Patents
Track tracking control method for sand blasting and rust removing parallel robot moving platform Download PDFInfo
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- B—PERFORMING OPERATIONS; TRANSPORTING
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Abstract
The invention discloses an anti-idle high-performance track tracking control method for a moving platform of a sand blasting and rust removing parallel robot. Then, the actual acceleration value of the vehicle body is obtained by measuring the vehicle-mounted accelerometer, the wheel rotation speed value is obtained by measuring the encoder, and the slip rate error lambda is calculated by the two measured values e And judging whether the mobile platform idles or not. According to the idling condition of the mobile platform, different control methods are adopted to realize the high-performance track tracking motion control of the mobile platform. Finally, the control method is applied to a sand blasting rust removal parallel robot control system, so that the mobile platform moves according to a desired track. The anti-idling high-performance track tracking control method for the sandblasting rust removing parallel robot mobile platform provided by the invention can not only realize accurate tracking of the expected track, but also effectively avoid idling of wheels.
Description
Technical Field
The invention relates to the field of track tracking of a mobile platform under a low-adhesion pavement, in particular to an anti-idling high-performance track tracking control method for a mobile platform of a sand blasting and rust removing parallel robot, which aims at solving the idling problem of track tracking of a low-adhesion steel grit pavement of the mobile platform.
Background
In order to realize sand blasting and rust removal of the steel box girder, a steel sand rust removal parallel robot is developed and consists of a tail end spray gun, a Stewart type six-degree-of-freedom parallel operating mechanism, a lifting mechanism and a moving platform. The mobile platform has the advantages of strong bearing performance, good maneuverability and the like. However, from the control point of view, due to factors such as low adhesiveness of the steel grit accumulation ground, excessive steering of the car-like mobile robot (CLMR) type mobile platform and the like, the mobile platform is extremely easy to generate an idling phenomenon when tracking the track, and the track tracking precision is affected. In order to realize the running stability and accuracy of the steel grit rust removal parallel robot moving platform, the anti-idle track tracking control technology of the steel grit rust removal parallel robot moving platform is necessary to be researched.
The literature (Bei Xuying and the like, china mechanical engineering.2018) discloses a method for tracking and controlling the track of a wheeled mobile robot in a longitudinal slip state, which establishes a kinematic model with slip parameters, estimates the slip parameters by a slip model observer, and compensates the slip distance on the basis of track tracking. The method only compensates the sliding distance from the kinematic angle as external disturbance, only realizes track tracking control under the condition of smaller sliding rate, and has an unsatisfactory track tracking effect when the sliding rate is larger than the optimal sliding rate.
The literature (Ge Yinghui, et al, university of Jiangnan, 2004) refers to the slip ratio as a control target to ensure that the slip ratio is near the optimal slip ratio when the electric vehicle is accelerated, and to obtain the optimal road surface adhesion. The method only adopts slip rate control to solve the slip problem, and does not consider track tracking error, so that the track tracking precision of the vehicle body is not high.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention provides an anti-idling high-performance track tracking control method for a steel grit rust removal parallel robot moving platform, aiming at the steel grit rust removal parallel robot moving platform, so as to solve the idling problem of low-adhesion steel grit pavement track tracking of the moving platform.
The technical scheme of the invention is as follows: a method for controlling anti-idle high-performance track tracking of a sand blasting and rust removing parallel robot mobile platform comprises the following steps:
1) According to the sand blasting process requirements of the sand blasting and derusting parallel robot, and by fully considering the running stability of the mobile platform, designing a grating sand blasting path and an S curve acceleration and deceleration as an expected track of the mobile platform; defining an expected slip rate according to a steel grit slip characteristic curve;
2) According to the physical characteristics of the steel grit, a bekker pressure-bearing model of the driving wheel is built, the 'weakening amount' of the slip rate to the driving force in the model is calculated according to a slip characteristic curve, and therefore a dynamic model of the sand blasting rust removal parallel robot is built, wherein the slip characteristic of the steel grit piled pavement and the resistance of the slip characteristic are considered;
3) Based on the model in the step 2), a method for controlling anti-idle high-performance track tracking of a moving platform of a sand blasting rust removing parallel robot is designed, wherein in the method, an actual acceleration value of a vehicle body is measured by a vehicle-mounted accelerometer, a wheel rotating speed value is measured by an encoder, and a slip rate error lambda is calculated by the two measured values e Judging whether the mobile platform idles or not, and adopting different control methods according to the condition of the mobile platform idles so as to realize high-performance track tracking motion control of the mobile platform; the mobile platform does not idle (lambda) e When the system is=0), the system performs steel grit resistance input compensation tracking error smooth sliding mode track tracking control; full idle (lambda) occurs e When the system is in the condition of being 1), the system determines the optimal slip rate according to the slip characteristic curve of the steel grit pavement, and performs slip rate error control; after occurrence of incomplete idle rotation (0<λ e When the weight coefficient is less than 1), the system carries out composite control of steel grit resistance input compensation tracking error smooth sliding mode track tracking control and slip ratio error control by using a variable fuzzy weight coefficient;
4) Adopting an upper computer and lower computer structure to construct a sand blasting rust removing parallel robot control system;
5) And sending the calculated driving wheel control instruction to each motor driver to enable the sand blasting and rust removing parallel robot moving platform to move according to the expected track.
Further, in the step 2), it is calculated from the slip characteristic curve that the slip ratio λ is greater than the optimum slip ratio λ max When the "weakening amount" of the driving force is:
c in the formula 1 、C 2 、C 3 Is the slip characteristic parameter of the steel grit, F p max Is the corresponding driving force under the optimal slip rate;
the driving resistance of the steel grit pavement is calculated by a driving wheel bekker pressure-bearing model and is as follows:
wherein r is the radius of the wheel, b is the width of the wheel, sigma m Maximum stress, θ is the wheel angle, θ m For the wheel angle corresponding to the maximum stress, θ 1 Is the maximum wheel angle;
thus, a dynamic model of the mobile platform is established by considering the sliding property and the resistance of the steel grit accumulation pavement:
in the method, in the process of the invention,
is a velocity vector and an acceleration vector under a world coordinate system of a mobile platform, and the units are m/s and m/s 2 ；τ x The unit is N, which is the weakening amount of the moment; τ is a moment input vector, and the unit is N; m and C are respectively a mass matrix and a centrifugal force matrix; b, inputting a transformation matrix; f (F) B The steel grit resistance is given in N.
Further, in the step 3), when the idle running (λ) of the mobile platform does not occur e When=0), the system performs steel grit resistance input compensation tracking error smooth sliding mode track tracking control, and the design control law is:
wherein K is control gain, S is slip-form surface,
for the expected acceleration of the mobile platform in the world coordinate system, the unit is m/s 2 ,/>
The unit is m, which is the differentiation of the track tracking error;
when moving flatThe table is fully idle (lambda) e When=1), the system performs slip rate error control, and the design control law is:
wherein k is control gain, s is a sliding mode surface, m is wheel mass, and the unit is kg; v is the wheel speed in m/s, lambda i The slip ratio of the wheel is J, the rotational inertia of the wheel is represented by N.m, eta is an adhesion coefficient, g is a gravitational acceleration constant, and T B The influence of steel grit accumulation resistance on the moment of the wheel is shown;
when the movable platform runs incompletely idle (0<λ e When the weight coefficient is less than 1), the system performs composite control of steel grit resistance input compensation tracking error smooth sliding mode track tracking control and slip rate error control with variable fuzzy weight coefficient, and designs a composite control law as follows:
aT mi +(1-a)T ni (0＜a＜1) (6)
wherein a is a fuzzy weight coefficient.
The slip rate error and the derivative thereof are taken as input, the composite control weight coefficient is taken as output, and the fuzzy rule of the designed weight coefficient is as follows: when the slip ratio error is small, the weight coefficient a is taken to be large, the system mainly performs smooth sliding mode track tracking control of tracking error, and the slip ratio error control is used as moment compensation; when the slip ratio error is medium, the weight coefficient a takes a value medium, and the system equally performs smooth sliding mode track tracking control and slip ratio error control of the tracking error; when the slip rate error is large, the weight coefficient a is small, the system mainly performs slip rate error control, and the smooth sliding mode track tracking control of the tracking error is used as moment compensation.
The invention provides a control method combining a bekker pressure-bearing model, a sliding characteristic, a fuzzy control technology and a smooth sliding mode control technology for the first time, which realizes the high-performance anti-idle track tracking control of a steel grit rust removal parallel robot moving platform and has the following characteristics and beneficial effects:
1) The method comprises the steps of establishing a bekker pressure-bearing model of a driving wheel according to the physical characteristics of steel grit, calculating the weakening amount of the slip rate to the driving force in the model according to the slip characteristic curve, and establishing a dynamic model of the mobile platform taking the slip characteristic of the steel grit accumulation pavement and the resistance thereof into consideration.
2) The method for controlling the track of the steel grit resistance input compensation smooth sliding mode with strong robustness is provided, and can realize high-performance track tracking control under the condition that the mobile platform does not idle.
3) The control system can adopt steel grit resistance input compensation smooth sliding mode track tracking control, slip rate control or SSCSSC and SC compound control according to whether the mobile platform has idling or not, and can realize the anti-idling high-performance track tracking motion control of the mobile platform.
Drawings
Fig. 1 is a block diagram of the overall structure of the sand blasting rust removing parallel robot.
Fig. 2 is a schematic structural view of a large steel box Liang Changjian.
FIG. 3 is a bekker pressure model and a slip characteristic diagram; (a) is a pressure-bearing model; (b) is a slip characteristic curve.
Fig. 4 is a diagram of the forward and backward directions of the moving platform of the sand blasting and rust removing parallel robot.
Fig. 5 is a top view of the structure of the moving platform of the sand blasting rust removing parallel robot.
FIG. 6 is a schematic general diagram of an anti-idle high-performance track tracking control method for a moving platform of a sand blasting and rust removing parallel robot
FIG. 7 shows that no idling (lambda) e And (0) a schematic diagram of a steel grit resistance input compensation tracking error smooth sliding mode track tracking control method.
FIG. 8 shows that full idle (. Lambda.) occurs e Schematic diagram of slip ratio control method at time of=1).
FIG. 9 shows that incomplete idle (0<λ e Schematic diagram of SSCSSC and SC composite control method when < 1).
FIG. 10 shows a control system structure of an anti-idle high-performance track tracking control method for a sand blasting rust removal parallel robot moving platform.
Detailed Description
The following describes the embodiments of the present invention further with reference to the drawings.
The overall structure diagram of the sand blasting rust removing parallel robot shown in fig. 1 comprises a 1-movable carrier, a 2-lifting frame, a 3-Stewart type six-degree-of-freedom parallel mechanism, a 4-steel sand conveying hose and a 5-straight rigid clamping lever 6-sand blasting gun.
Firstly, determining an expected motion track of a mobile platform according to a sand blasting path of a sand blasting and derusting parallel robot and defining an expected slip rate according to a steel grit slip characteristic curve; then, a bekker pressure-bearing model of the driving wheel is built according to the physical characteristics of the steel grit, and the 'weakening amount' of the slip rate to the driving force in the model is calculated according to a slip characteristic curve, so that a dynamic model of a mobile platform considering the slip characteristics of the steel grit piled pavement and the resistance thereof is built; next, a method for controlling anti-idle high-performance track tracking of the moving platform of the sand blasting rust removing parallel robot is designed. In the method, the actual acceleration value of the vehicle body is measured by an on-vehicle accelerometer, the wheel rotation speed value is measured by an encoder, and the slip rate error lambda is calculated from the two measured values e And judging whether the mobile platform idles or not. According to the idling condition of the mobile platform, different control methods are adopted to realize the high-performance track tracking motion control of the mobile platform. The mobile platform does not idle (lambda) e When the system is=0), the system performs steel grit resistance input compensation tracking error smooth sliding mode track tracking control; full idle (lambda) occurs e When the system is in the condition of being 1), the system determines the optimal slip rate according to the slip characteristic of the steel grit pavement, and performs slip rate error control; after occurrence of incomplete idle rotation (0<λ e When the weight coefficient is less than 1), the system carries out composite control of steel grit resistance input compensation tracking error smooth sliding mode track tracking control and slip ratio error control by using a variable fuzzy weight coefficient; further, a distributed structure, namely an upper computer and a lower computer structure is adopted to construct a sand blasting rust removing parallel robot control system; finally, the calculated driving wheel momentAnd the control instruction is sent to each motor driver, so that the moving platform of the sand blasting and rust removing parallel robot moves according to the expected track. The specific method comprises the following steps:
1. the structural schematic diagram of the large steel box Liang Changjian determines the expected motion track of the moving platform according to the sand blasting path of the sand blasting and rust removing parallel robot and defines the expected slip rate according to the steel grit slip characteristic curve.
According to the sand blasting process requirements of the sand blasting and derusting parallel robot, the running stability of the mobile platform is fully considered, and a grating sand blasting path and an S-curve acceleration and deceleration are designed to be used as the expected track of the mobile platform. Thereby determining the expected motion trail q= (x) of the mobile platform under the generalized coordinate system r ，y r ，θ r ) T Wherein x is r ，y r ，θ r The expected pose components in the x, y and theta directions under the world coordinate system are respectively shown, wherein the units of the x and y are m, and the units of the theta are rad; according to the slip characteristic curve of the steel grit, an expected slip rate lambda is defined d ＝0.17。
2. And (3) establishing a bekker pressure-bearing model of the driving wheel according to the physical characteristics of the steel grit, and calculating the 'weakening amount' of the slip rate to the driving force in the model according to the slip characteristic curve, thereby establishing a dynamic model of the mobile platform taking the slip characteristic of the steel grit piled pavement and the resistance thereof into consideration.
Establishing a horizontal and vertical stress balance equation and a torque balance equation which do not consider steel grit resistance:
wherein m is the wheel mass (in kg); v is the wheel speed (in m/s); f (F) p And F Z Dividing the tangential force (unit is N) generated by the wheels; η is the adhesion coefficient; t (T) m Is the driving torque (unit is N); j is the moment of inertia (unit is N.s) of the wheel; w is the wheel angular velocity (in rad/s);
calculating that the slip rate lambda is greater than the optimal slip rate lambda from the slip characteristic curve max When the "weakening amount" of the driving force is:
the driving resistance F is obtained by a driving wheel bekker pressure-bearing model and a series of linearization treatment B ：
Finally, a dynamic model of the mobile platform, which takes the sliding property and the resistance of the steel grit accumulation pavement into consideration, of the steel grit accumulation pavement is obtained:
3. a method for controlling anti-idle high-performance track tracking of a moving platform of a sand blasting and rust removing parallel robot is designed. In the method, the actual acceleration value of the vehicle body is measured by an on-vehicle accelerometer, the wheel rotation speed value is measured by an encoder, and the slip rate error lambda is calculated from the two measured values e And judging whether the mobile platform idles or not. According to the idling condition of the mobile platform, different control methods are adopted to realize the high-performance track tracking motion control of the mobile platform. The mobile platform does not idle (lambda) e When the system is=0), the system performs steel grit resistance input compensation tracking error smooth sliding mode track tracking control; full idle (lambda) occurs e When the system is in the condition of being 1), the system determines the optimal slip rate according to the slip characteristic of the steel grit pavement, and performs slip rate error control; after occurrence of incomplete idle (0 < lambda e <1) And when the system performs composite control of steel grit resistance input compensation tracking error smooth sliding mode track tracking control and slip rate error control by using the variable fuzzy weight coefficient.
Firstly, designing a slip rate error control law:
defining slip ratio of each drive wheel
Wherein w is i Wheel speed (in rad/s) of each driving wheel, r is wheel radius (in m), and v is running speed of the mobile platform.
Designing a smooth sliding mode slip rate control law when the driving wheel idles:
wherein k is control gain, s is slip-form surface, lambda i The slip ratio of the wheel, g is gravity acceleration, and TB is the influence of steel grit accumulation resistance on the moment of the wheel (the unit is N.s).
Secondly, designing a smooth sliding mode track tracking control law of tracking errors as follows:
and 2) calculating a smooth sliding mode track tracking control law of steel grit resistance input compensation tracking error by the dynamic model established in the step 2), wherein the smooth sliding mode track tracking control law is as follows:
wherein K is control gain, S is slip-form surface,
is the expected acceleration (in m/s) of the world coordinate system of the mobile platform 2 ),/>
F is the differentiation of the track following error B The running resistance (unit is N) of the road surface is piled up for the steel grit of the mobile platform.
The actual acceleration value of the vehicle body is measured by an on-board accelerometer, and the wheel is measured by an encoderThe rotation speed value and the slip rate error lambda are calculated from the two measured values e And judging whether the mobile platform idles or not. According to the idling condition of the mobile platform, different control methods are adopted to realize the high-performance track tracking motion control of the mobile platform. The mobile platform does not idle (lambda) e When the system is=0), the system performs steel grit resistance input compensation tracking error smooth sliding mode track tracking control; full idle (lambda) occurs e When the system is in the condition of being 1), the system determines the optimal slip rate according to the slip characteristic of the steel grit pavement, and performs slip rate error control;
finally, to achieve that in the event of incomplete idle (0 < lambda e <1) When the system is used, the variable fuzzy weight coefficient can be used for carrying out composite control of steel grit resistance input compensation tracking error smooth sliding mode track tracking control and slip rate error control, and a fuzzy rule which takes slip rate error and derivative thereof as input and takes composite control weight coefficient as output is designed. The composite control law for SSCSS and SC is:
aT mi +(1-a)T ni (0＜a＜1) (9)
wherein T is mi T is slip rate error control law ni And (3) inputting a tracking error compensating smooth sliding mode track tracking control law for steel grit resistance, wherein a is a weight coefficient. When the slip ratio error is small, the weight coefficient a is taken to be large, the system mainly performs smooth sliding mode track tracking control of tracking error, and the slip ratio error control is used as moment compensation; when the slip ratio error is medium, the weight coefficient a takes a value medium, and the system equally performs smooth sliding mode track tracking control and slip ratio error control of the tracking error; when the slip rate error is large, the weight coefficient a is small, the system mainly performs slip rate error control, and the smooth sliding mode track tracking control of the tracking error is used as moment compensation.
4. And a distributed structure, namely an upper computer and a lower computer structure is adopted to construct the sand blasting rust removing parallel robot control system.
The anti-idling high-performance track tracking control system of the parallel robot moving platform for sand blasting and rust removal is constructed by taking the ohm dragon CK3M multi-axis motion controller as a core control unit, and the control system adopts a distributed structure of an upper computer industrial personal computer and a lower computer ohm dragon CK3M multi-axis motion controller.
5. And sending the calculated driving wheel control instruction to each motor driver to enable the sand blasting and rust removing parallel robot moving platform to move according to the expected track.
And (3) according to the control quantity of the driving wheels of the mobile platform calculated in the step (7), the formula (8) and the formula (9), the control quantity is sent to a motor driver of the mobile platform of the sand blasting rust removing parallel robot through a control system by programming an upper computer so as to drive a mechanism to move according to a desired track.
One embodiment of the invention is provided below:
example 1
The control method is mainly applied to an anti-idling high-performance track tracking control method for the moving platform of the sand blasting and rust removing parallel robot, and aims to solve the idling problem of the moving platform of the sand blasting and rust removing parallel robot when the moving platform of the sand blasting and rust removing parallel robot runs on a low-adhesion steel grit pavement. The specific implementation mode of the control method is as follows:
1. the sand blasting and rust removing parallel robot structure diagram shown in fig. 1 and the large steel box Liang Changjian structure diagram shown in fig. 2 are used for off-line planning of a sand blasting path of the sand blasting and rust removing parallel robot according to actual engineering application, so that a desired motion track of a mobile platform is obtained, and a desired slip rate is defined according to a steel grit slip characteristic curve.
Determining the expected motion track q= (x) of the moving platform under a generalized coordinate system according to the grating-type sand blasting track of the sand blasting rust removing robot and the acceleration and deceleration of an S curve r ，y r ，θ r ) T During actual sand blasting movement, the mobile platform mainly moves in the x direction, and the specific expression is as follows:
y＝0 (11)
z＝0 (12)
as can be seen from the slip characteristic diagram shown in fig. 3, when λ=0.17, the driving wheel obtains the maximum driving force, so the set periodSlip ratio lambda d ＝0.17。
2. And (3) establishing a bekker pressure-bearing model of the driving wheel according to the physical characteristics of the steel grit, and calculating the 'weakening amount' of the slip rate to the driving force in the model according to the slip characteristic curve, thereby establishing a dynamic model of the mobile platform taking the slip characteristic of the steel grit piled pavement and the resistance thereof into consideration.
From the driving wheel bekker pressure model of the left diagram of fig. 3, first, a steel grit resistance F is established without consideration B Horizontal, vertical force balance equations and torque balance equations:
as shown in the right hand graph of fig. 3, the mobile platform obtains a maximum traction force when the slip ratio is at the peak position, and when the slip ratio is greater than the optimal slip ratio, the driving force is severely "impaired", ultimately resulting in lost motion.
Since the highest speed of the longitudinal movement of the mobile platform is 0.14m/s, the moment of inertia can be ignored, and the relation between the moment of the motor of the driving wheel and the traction force of the driving wheel of the mobile platform is obtained:
the above equation holds when no spin occurs, and when spin occurs, the actual values of the wheel traction force at different slip rates are obtained from the slip characteristic curves shown in the right diagram of fig. 3. The slip characteristic can be approximated as:
when lambda takes 0.17 as the optimal slip rate lambda max Neglecting motor bearing friction, driving the wheel motor moment F under the optimal slip rate pmax The relation with the traction force of the driving wheel of the movable platform satisfies the formula (15). Thereby making it possible to
Obtain a slip ratio lambda greater than the optimumSlip ratio lambda max The "weakening amount" of the driving force is:
secondly, solving the running resistance F of the steel grit pavement of the moving platform of the rust removing parallel robot by using a driving wheel bekker pressure-bearing model B ：
The normal stress sigma of the ground particles is from theta 0 =0 to maximum value θ m Then go to theta 1 The stress formula for the two intervals is given by =0:
wherein k is c The cohesive modulus of the steel sand; k (k) φ Friction modulus for steel grit; n is the deformation index of the steel grit.
The piecewise function of equation (17) is too complex and is simplified and approximated for ease of post-control:
approximation 1: when the wheel is a driving wheel, θ m At theta 1 Near the midpoint. But is approximated to obtain theta m ＝(θ 0 +θ 1 )。
Approximation 2: the piecewise function described above may be linearized to yield:
for further simplicity, θ can be reduced by approximating symmetry 0 To theta 1 Is regarded as twice the stress of theta 0 To theta m Is a stress of (a). At this time, steel grit resistance can be obtained:
carrying out dynamic stress analysis on the moving platform by using a force diagram of the moving platform of the sand blasting and derusting parallel robot in fig. 4 in the forward and backward directions and a top view of the moving platform of the sand blasting and derusting parallel robot in fig. 5:
obtaining a Lagrange dynamics model of the mobile platform:
in the middle of
Combining the formula (16) and the formula (19), and establishing a moving platform dynamics model of the steel grit accumulation pavement combined with the slip characteristic:
3. based on the model in the step 2), an anti-idle high-performance track tracking control method for the moving platform of the sand blasting rust removing parallel robot is designed. In the method, the actual acceleration value of the vehicle body is measured by an on-board accelerometer, the wheel rotation speed value is measured by an encoder, and the slip is calculated by the two measured valuesRate error lambda e And judging whether the mobile platform idles or not. According to the idling condition of the mobile platform, different control methods are adopted to realize the high-performance track tracking motion control of the mobile platform. The mobile platform does not idle (lambda) e When the system is=0), the system performs input compensation tracking error smooth sliding mode track tracking control; full idle (lambda) occurs e When=1), slip ratio error control is performed; after occurrence of incomplete idle (0 < lambda e <1) And when the system uses a variable fuzzy weight coefficient to carry out composite control of steel grit resistance input compensation tracking error smooth sliding mode track tracking control slip rate error control, and the control block diagrams are shown in fig. 6, 7, 8 and 9.
Firstly, designing a slip rate error control law:
defining slip ratio of each drive wheel
Solving a differential equation of the slip rate lambda: instead of
Design slip plane s=λ - λ d Obtaining a control law of a smooth slip-form slip ratio when each driving wheel idles:
secondly, designing a smooth sliding mode track tracking control law of tracking errors:
regarding steel grit resistance as external disturbance F d Defining an upper bound for external disturbances:
F d ＜η (26)
designing a sliding die surface:
taking the constant-speed approach rate, and obtaining the control law as follows:
considering the steel grit resistance as an external disturbance, this results in a large switching gain K, which can be directly compensated for using an input control approach, since the disturbance is known to be constant. The upper bound of the disturbance is defined at this time as:
the obtained steel grit resistance input compensation sliding mode track tracking control law is as follows:
in order to weaken the buffeting of the sliding mode control, a continuous function S (t) is used for replacing sgn (S), and the tracking control law of the steel grit resistance input compensation smooth sliding mode track is obtained as follows:
then, the actual acceleration value of the vehicle body is obtained by measuring the vehicle-mounted accelerometer, the wheel rotation speed value is obtained by measuring the encoder, and the slip rate error lambda is calculated by the two measured values e And judging whether the mobile platform idles or not. According to the idling condition of the mobile platform, different control methods are adopted to realize the high-performance track tracking motion control of the mobile platform. The mobile platform does not idle (lambda) e When the system is=0), the system performs steel grit resistance input compensation tracking error smooth sliding mode track tracking control; full idle (lambda) occurs e When the system is=1), the system determines the optimal slip rate according to the slip characteristic of the steel grit pavement, and performs slip rate error control.
Finally, to achieve that in the event of incomplete idle (0 < lambda e <1) When the system is used, the variable fuzzy weight coefficient can be used for carrying out composite control of steel grit resistance input compensation tracking error smooth sliding mode track tracking control and slip rate error control, and a fuzzy rule which takes slip rate error and derivative thereof as input and takes composite control weight coefficient as output is designed. The composite control law for SSCSSC and SC is:
aT mi +(1-a)T ni (0＜a＜1) (32)
wherein T is mi T is slip rate error control law ni And (3) inputting a tracking error compensating smooth sliding mode track tracking control law for steel grit resistance, wherein a is a weight coefficient. When the slip ratio error is small, the weight coefficient a is taken to be large, the system mainly performs smooth sliding mode track tracking control of tracking error, and the slip ratio error control is used as moment compensation; when the slip ratio error is medium, the weight coefficient a takes a value medium, and the system equally performs smooth sliding mode track tracking control and slip ratio error control of the tracking error; when the slip rate error is large, the weight coefficient a is small, the system mainly performs slip rate error control, and the smooth sliding mode track tracking control of the tracking error is used as moment compensation. The design fuzzy rule table is as follows:
4. sand blasting rust removing parallel robot control system constructed by adopting distributed structure, namely 'upper computer + lower computer' structure
As shown in FIG. 10, an ohm dragon CK3M multi-axis motion controller is used as a core control unit, an anti-idle high-performance track tracking control system of the sand blasting rust removal parallel robot moving platform is constructed, and the control system adopts a distributed structure of an upper computer control computer and a lower computer ohm dragon CK3M multi-axis motion controller.
5. And sending the calculated driving wheel control instruction to each motor driver to enable the sand blasting and rust removing parallel robot moving platform to move according to the expected track.
And (3) according to the control quantity of the driving wheels of the mobile platform calculated in the steps (28), (31) and (32), the control quantity is sent to a motor driver of the mobile platform of the sand blasting rust removing parallel robot through a control system by programming an upper computer so as to drive a mechanism to move according to a desired track.
Claims (2)
1. The anti-idle high-performance track tracking control method for the sand blasting and rust removing parallel robot moving platform is characterized by comprising the following steps of:
1) According to the sand blasting process requirements of the sand blasting and derusting parallel robot, and by fully considering the running stability of the mobile platform, designing a grating sand blasting path and an S curve acceleration and deceleration as an expected track of the mobile platform; defining an expected slip rate according to a steel grit slip characteristic curve;
2) According to the physical characteristics of the steel grit, a bekker pressure-bearing model of the driving wheel is built, the 'weakening amount' of the slip rate to the driving force in the model is calculated according to the slip characteristic curve of the steel grit, and therefore a dynamic model of the sand blasting rust removal parallel robot is built, wherein the slip characteristic of the steel grit piled pavement and the resistance of the slip characteristic are considered;
3) Based on the model in the step 2), a method for controlling anti-idle high-performance track tracking of a moving platform of a sand blasting rust removing parallel robot is designed, wherein in the method, an actual acceleration value of a vehicle body is measured by a vehicle-mounted accelerometer, a wheel rotating speed value is measured by an encoder, and a slip rate error lambda is calculated by the two measured values e Judging whether the mobile platform idles or not, and adopting different control methods according to the condition of the mobile platform idles so as to realize high-performance track tracking motion control of the mobile platform; no idling of moving platform, lambda e When the system is=0, the system adopts a steel grit resistance input compensation tracking error smooth sliding mode track tracking control method; complete idle running, lambda e When the sliding ratio is=1, the system determines the optimal sliding ratio according to the steel grit sliding characteristic curve, and performs sliding ratio error control; in the event of incomplete idle running, 0<λ e When the weight coefficient is less than 1, the system adopts the variable fuzzy weight coefficient to carry out the steel grit resistance input compensation tracking error smooth sliding mode track tracking control and the composite of the slip rate error controlControlling;
4) Adopting an upper computer and lower computer structure to construct a sand blasting rust removing parallel robot control system;
5) The calculated driving wheel control instruction is sent to each motor driver, so that the moving platform of the sand blasting and rust removing parallel robot moves according to the expected track;
in the step 2), the slip ratio lambda is calculated to be larger than the optimal slip ratio lambda by the slip characteristic curve max When the "weakening amount" of the driving force is:
c in the formula 1 、C 2 、C 3 Is the slip characteristic parameter of the steel grit, F pmax Is the corresponding driving force under the optimal slip rate;
the driving resistance of the steel grit pavement is calculated by a driving wheel bekker pressure-bearing model and is as follows:
wherein r is the radius of the wheel, b is the width of the wheel, sigma m Maximum stress, θ is the wheel angle, θ m For the wheel angle corresponding to the maximum stress, θ 1 Is the maximum wheel angle;
thus, a dynamic model of the mobile platform is established by considering the sliding property and the resistance of the steel grit accumulation pavement:
in the method, in the process of the invention,
is a velocity vector and an acceleration vector under a world coordinate system of a mobile platform, and the units are m/s and m/s 2 ；τ x The unit is N, which is the weakening amount of the moment; τ is a moment input vector, and the unit is N; m, CThe mass matrix and the centrifugal force matrix are respectively adopted; b is an input transformation matrix; f (F) B The steel grit resistance is N;
in the step 3), when no idle running occurs on the mobile platform, λe=0, the system performs steel grit resistance input compensation tracking error smooth sliding mode track tracking control, and the design control law is:
wherein K is control gain, S is slip-form surface,
for the expected acceleration of the mobile platform in the world coordinate system, the unit is m/s 2 ,/>
The unit is m, which is the differentiation of the track tracking error;
when the movable platform runs completely idle, lambda e When=1, the system performs slip rate error control, and the design control law is:
wherein k is control gain, s is a sliding mode surface, m is wheel mass, and the unit is kg; v is the wheel speed in m/s, lambda i The slip ratio of the wheel is J, the rotational inertia of the wheel is represented by N.m, eta is an adhesion coefficient, g is a gravitational acceleration constant, and T B The influence of steel grit accumulation resistance on the moment of the wheel is shown;
when the movable platform runs incompletely, 0<λ e When the sliding rate is less than 1, the system adopts a steel grit resistance input compensation tracking error smooth sliding mode track tracking control method with variable fuzzy weight coefficient and compound control of the sliding rate error control, and a compound control law is designed as follows:
aT mi +(1-a)T ni (0＜a＜1) (6)
wherein a is a fuzzy weight coefficient.
2. The anti-idle high-performance track tracking control method for the sandblasting rust removing parallel robot moving platform according to claim 1, which is characterized by comprising the following steps of: the method also comprises the steps of taking the slip rate error and the derivative thereof as input, taking the composite control weight coefficient as output, and the fuzzy rule of the designed weight coefficient is as follows: when the slip ratio error is small, the fuzzy weight coefficient a is taken to be large, the system mainly performs smooth sliding mode track tracking control of tracking error, and the slip ratio error control is used as moment compensation; when the slip ratio error is medium, the value of the fuzzy weight coefficient a is medium, and the system equally performs smooth slip mode track tracking control and slip ratio error control of tracking error; when the slip rate error is large, the fuzzy weight coefficient a is small, the system mainly performs slip rate error control, and the smooth sliding mode track tracking control of the tracking error is used as moment compensation.
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