CN105955268B - A kind of UUV moving-target sliding mode tracking control methods considering Local obstacle avoidance - Google Patents
A kind of UUV moving-target sliding mode tracking control methods considering Local obstacle avoidance Download PDFInfo
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Abstract
The present invention is to provide a kind of UUV moving-target sliding mode tracking control methods considering Local obstacle avoidance.Real-time detection UUV, moving target and obstacle position information；Obtain moving target k moment state estimations；Establish the relative motion model of UUV and moving target and barrier；The size for being evaded radius of safety based on target following radius and barrier is independently switched according to the relative position of UUV and moving target and barrier between tracking strategy and collision prevention strategy；According to command speed and course and the UUV speed of a ship or plane and turn bow angular velocity measurement feedback, obtains tracing control deviation, resolve to obtain k moment UUV propeller thrust based on horizontal plane non-singular terminal sliding mode controller and rudder turns bow torque；Cycle executes above-mentioned steps, realizes the tracing control at moving target lower a moment.Sector planning strategy in complex environment is combined by the present invention with UUV kinetic models, ensures the tracking accuracy to moving target under the premise of UUV nevigation safeties.
Description
Technical field
The present invention relates to a kind of method for tracking target of underwater unmanned vehicle, specifically it is a kind of it is underwater nobody
The tracking of maneuvering target method of aircraft.
Background technology
With the increase of UUV missions task and application field, the Capability Requirement of UUV target followings is also greatly improved,
It is required that it can not only identify static target (such as rescue positioning and reach accident point, exploitation of mineral resources, pipeline location maintenance as early as possible),
It can be adaptively adjusted by predicting that dbjective state variation is made in order to avoid losing tracking object with Tracking Maneuvering Targets.
Currently, tracking of maneuvering target Study on Problems is concentrated mainly on the fields such as aerospace, generally refer to based on Kalman,
The Target state estimators such as particle filter；The moving-targets such as proportional navigation method, tail-chase method, fixed lead angle method, constant-bearing course guide
Method；The automatic obstacle avoiding methods such as Artificial Potential Field, fuzzy collision prevention method.Research for UUV underwater environments is not mature enough, for dynamic
It is less that the obstruction consideration being likely to occur during set objective track following is executed in state environment, even if there are movement rule in real time
It draws, also seldom UUV kinetic models and maneuvering performance is combined to be realized by motion control.Therefore, above-mentioned factor is introduced
In UUV target followings control, really reflects that its dynamic tracks avoidance ability, have for securely and reliably executing various job tasks
Significance.
Invention content
The purpose of the present invention is to provide one kind capable of realizing that UUV hinders motion target tracking while evading on its air route
Hinder the guiding strategy of object, stablize quickly, strong robustness the considerations of Local obstacle avoidance UUV moving-target sliding mode tracking control methods.
The object of the present invention is achieved like this：
Step 1：UUV passes through attitude transducer, position measuring system, the Forward-Looking Sonar of navigating, real-time detection UUV, movement mesh
It is marked with and obstacle position information；
Step 2：Moving target and barrier kinematics model are established, moving target k is obtained based on unscented kalman filter
Moment state estimation；
Step 3：The relative motion model for establishing UUV and moving target and barrier, for calculate the k moment track away from
From and the angle of sight；
Step 4：Based on target following radius D1Evade radius of safety D with barrier2Size, according to UUV with movement mesh
The relative position of mark and barrier, independently switches between tracking strategy and collision prevention strategy, changes UUV and controls sight, planning
UUVk time instructions speed and course；
Step 5：According to the command speed and course and the UUV speed of a ship or plane that are obtained in step 4 and turn bow angular velocity measurement feedback,
Tracing control deviation is obtained, resolves to obtain k moment UUV propeller thrust and side based on horizontal plane non-singular terminal sliding mode controller
Turn bow torque to rudder；
Step 6：Cycle executes step 1 to step 5, the tracing control at moving target lower a moment is realized, until task knot
Beam.
The present invention can also include：
1, the guide mode independently switched between tracking strategy and collision prevention strategy is embodied as：In global follow process
In, if there is ρoiv,k≤D2+(Rio+Rv), it is activated by collision prevention guidance law formula
Sight is switched to barrier and evades aspect, once confirm that UUV moves to safety zone and is carried out target following guidance law formulaTracking process is recovered immediately,
Wherein：ρoiv,kFor the distance between k moment UUV and i-th of barrier, UUV is reduced to radius Rv, RioIt is i-th
The radius of barrier, uvRef,kSpeed, r are guided for k moment UUVvRef,kFor the k moment UUV guiding turn bow angular speed,It navigates for maximum
Speed,For the minimum speed of a ship or plane, ψv,kFor k moment UUV course angle,Turn bow angular speed, n for UUV maximums0For tracking velocity gain,
n1Turn bow for tracking and controls gain, n2For collision prevention speed gain, n3Turn bow for collision prevention and controls gain, ρvg,kFor k moment UUV and mesh
The distance between mark, φvg,kFor the folder between k moment UUV and the angle of sight, that is, sight vector and inertial coodinate system E ξ axis of target
Angle, φoiv,kThe angle of sight, D between k moment UUV and i-th of barrier1For target following radius, D2Evade peace for barrier
Full radius,For saturation function and take the minimum value of Control of line of sight and saturation angular speed, Φ (α) that corner is transformed into area
Jian [-π,π].
2, UUV propeller thrusts described in step 5 and rudder turn bow torque and are embodied as：
Wherein：K moment UUV propeller thrust τu,k, k moment rudders turn bow torque τr,k, k moment UUV speed over ground
uv,k, k moment UUV guiding speed uvRef,k, k moment UUV are practical turns bow angular speed rv,k, the k moment UUV guiding turn bow angular speed
rvRef,k, k moment UUV lateral movement velocity vv,k；The non-singular terminal speed of a ship or plane controls sliding-mode surface s1Sliding-mode surface s is controlled with bow is turned2, sliding
Die face adjustable parameter β1> 0, β2> 0, p1、q1、p2、q2For positive odd number andSpeed of a ship or plane tracing control is inclined
Poor ue,k=uvRef,k-uv,k, bow is to angular speed control deviation re,k=rref,k-rv,k； d11=Xu+X|u|u|u|, d22=Yv+Y|v|v|v|, d33=Zw+Z|w|w|w|For kinetic simulation
Shape parameter；" ^ " indicates the estimated value of system model parameter, andI=1,2,3,5,6,
Indicate the Perturbation of model parameter, c1sat(s1/φ1)、c2sat(s2/φ2) be sliding mode controller discontinuous switching item, c1、
φ1、c2、φ2To change the adjustable parameter buffeted and perturb ability.
The present invention guides tactful control targe：Under the conditions of considering UUV constraint of saturation, the target in two-dimentional dynamic environment
Tracking and local avoidance problem.1. for position tracking, ifThen there is D1> 0 so that forHave2. for avoiding obstacles problem, if ρoiv(t0) > D2, then exist
D2> 0, make forThere is ρoiv(t) > (Rio+Rv) set up.
Wherein, q=[x y ψ]TIndicate position and course angle in inertial coodinate system, U=[u r]TIt indicates the speed of a ship or plane and turns bow angle
The kinematics dominant vector of speed composition, uses qv,k=[xv,k yv,k ψv,k]T、Uv,k=[uv,k rv,k]TIndicate the UUV shapes at k moment
State, qg,k=[xg,k yg,k ψg,k]T、Ug,k=[ug,k rg,k]TIndicate the dbjective state at k moment, qio,k=[xio,k yio,k
ψio,k]T、Uio,k=[uio,k rio,k]TIndicate i-th of barrier state of k moment.UUV is reduced to radius Rv, center is
(xv,k,yv,k) circle,The similar radius that obtains is RgTarget and radius be RioBarrier simplification representation.ρvg,kFor k when
Carve the distance between UUV and target, φvg,kFor the angle of sight (sight vector and the inertial coodinate system E ξ axis of k moment UUV and target
Between angle)；ρoiv,kFor the distance between k moment UUV and i-th of barrier, φoiv,kFor k moment UUV and i-th of obstacle
The angle of sight between object；D1For target following radius, D2Evade radius of safety for barrier.
For the constraint of saturation on UUV speed and course, if maximum speed isMaximum turns to change rateIn addition
To ensure that UUV hides under water, speed cannot decelerate to zero (can emerge), if the minimum speed of a ship or plane isThen have：The guiding strategy of formulation is specific as follows：
(1) target following guidance law is：
Wherein, n0For normal number speed gain, to ensure the flatness of tracking, make UUV when falling behind target farther out with
Apart from directly proportional speed tracing；n1Gain is controlled to turn bow, corner is limited in Qu Jian [ by Φ (α);-π,π)；It is full
And function, it takes Control of line of sight and is saturated the minimum value of angular speed.
(2) collision prevention guidance law is：
Wherein, 0 < n2≤ 1 rotating speed controls gain, n3Be designed as normal number turns bow control gain.
(3) sight switchover policy：During global follow, if there is ρoiv,k≤D2+(Rio+Rv) at the time of, just swash
Sight is switched to barrier and evades aspect by collision prevention guidance law living, once confirm UUV move to safety zone be carried out target with
Track guidance law immediately restores tracking process.
The present invention devises following non-singular terminal sliding mode speed control device and turns bow controller：
UUV propeller thrust control laws are：
UUV rudders turn bow Torque Control rule：
Wherein,d11=Xu+X|u|u|u|, d22=Yv+Y|v|v|v
|, d33=Zw+Z|w|w|w|For kinetic parameters；" ^ " indicates the estimated value of system model parameter, and I=1,2,3,5,6, indicate the Perturbation of model parameter, c1sat(s1/φ1)、c2sat(s2/φ2) it is sliding formwork
The discontinuous switching item of controller, by adjusting parameter c1, φ1, c2, φ2Controller robustness can be enhanced and improve sliding formwork buffeting
Phenomenon.
The speed of a ship or plane tracking error of UUV is ue,k=uvRef,k-uv,k, it is r to turn bow angular speed tracking errore,k=rref,k-rv,k,
The Non-Singular Terminal Sliding Mode face of design is respectively：
Wherein, β1> 0, β2> 0, p1, q1, p2, q2For positive odd number and
The present invention provides a kind of guidings that can realize UUV to motion target tracking while evading barrier on its air route
Strategy, and UUV kinetic models and motion control capabilities is combined to provide concrete methods of realizing.Beneficial effects of the present invention exist
In：
(1) using UUV and the distance between target and barrier as Dynamic Programming criterion, simplify dynamic environment target with
The analysis of track and local avoidance problem, it is contemplated that the simple and effective switchover policy that the motion control constraint of UUV is formulated realizes
Real-time smooth motion under UUV safeties and tracking accuracy require is planned.
(2) non-singular terminal sliding mode controller is devised, the system singular point that control is likely to occur in the process can be eliminated,
The stability contorting to instruction is realized in finite time, and is very suitable for underwater non-linear, and there are environmental disturbances and model to join
The complex working condition of number perturbation.The effective tracking process for considering UUV kinetic models is realized, quick, strong robustness is stablized.
Description of the drawings
Fig. 1 is the general frame of the present invention；
Fig. 2 is UUV target followings and passive avoidance Bi-objective control problem schematic diagram in plane；
Fig. 3 is that UUV target followings guide schematic diagram；
Fig. 4 is that UUV avoiding obstacles guide schematic diagram；
Fig. 5 is UUV pursuit movement target simulator cases track；
Fig. 6 a to Fig. 6 d are the control parameter figure of UUV pursuit movement target simulator cases；
Fig. 7 is that UUV pursuit movements target evades dynamic barrier emulation case track simultaneously；
Fig. 8 a to Fig. 8 d are the control parameter figure that UUV pursuit movements target evades that dynamic barrier emulates case simultaneously；
Fig. 9 is the flow chart of the present invention.
Specific implementation mode
The present invention will be further described below in conjunction with the accompanying drawings：
UUV needs to trail tracking specific objective when executing the tasks such as recycling docking, for underwater complex environment, with
The movement of track target unavoidably will appear random moving obstacle (ship, planktonic organism, underwater rubbish etc.) on air route, for this situation
The present invention provides a kind of simple and effective UUV dynamic environment tracking and controlling method.
Fig. 1 is the overall work block diagram of the present invention, is broadly divided into UUV models and detection system, Target state estimator, dynamic
Four parts of planning module and non-singular terminal sliding mode controller, target and Obstacle Position are obtained by UUV sonar contact systems,
UUV real time status informations are measured by a combination thereof navigation system, in conjunction with the specific steps of Fig. 9 description present invention.
Step 1：UUV passes through attitude transducer, position measuring system, the Forward-Looking Sonar etc. of navigating, real-time detection UUV, movement
Target and obstacle position information (analogous diagram of the invention is obtained by directly giving target and Robot Bar Movement Track)；
Step 2：According to target and the barrier characteristics of motion, its kinematics model is established, based on tracing point position by unwise
Kalman (UKF) filtering algorithm obtains its k moment state estimations；
If target dynamics model is Xk=FXk-1+GWk, state vectorF is system transfer matrix,
G is system noise transformation matrix, system mode noise Wk=[wx,k,wy,k]TFor zero-mean Gaussian noise, covariance Qk.Observation
Model is Zk=h (Xk)+Vk, wherein h is observation function, VkFor the measurement noise sequence of Gaussian distributed, covariance Rk, and
In the presence of
cov[Wk]=Qk,cov[Vk]=Rk
The simple flow of UKF algorithms is：
1. given system initial value (original state Estimation of Mean valueOriginal state estimate of variance P0)
2. calculating Sigma sampled points χiAnd its weights λi, the distribution function of approximation system state is carried out with minimum sample set
Wherein n is the dimension of state vector, and κ is scale parameter, and 2 are taken in the design.
3. prediction/time update carries out nonlinear transformation to Sigma sampled points and weighting is handled, it is equal to obtain state vector
Value, the one-step prediction value of state vector variance and output vectorPk|k-1、
It is filtered estimation using the state variable after transformation, to reduce evaluated error, simultaneously because the algorithm uses
Nonlinear dynamical equation or measurement equation, avoid linearized stability.
4. correction/measurement updaue
Wherein, YkFor k moment observations,PkRespectively k moment output vector and state vector variance,For its two
Person's covariance, MkFor UKF correcting gains,The as filtering estimated value of k moment states.
Step 3：It is opposite based on UUV and moving target and barrier according to filtered status information in step 2
Motion model calculates the tracking range and the angle of sight at k moment, and UUV target followings and passive avoidance are double in plane as shown in Figure 2
Target control problem；
When formulating guiding strategy, it is believed that UUV lateral velocities are a small coupling amounts, smaller on movement locus influence,
Kinematics model is reduced to the form such as formula (5) when design, and assumes that target and barrier meet the identical characteristics of motion：
Wherein q=[x y ψ]TIndicate position and course angle in inertial coodinate system, U=[u r]TIt indicates the speed of a ship or plane and turns bow angle
The kinematics dominant vector of speed composition.The k moment, for UUV with vectorial qv,k=[xv,k yv,k ψv,k]T、Uv,k=[uv,k
rv,k]TIt indicates, target is with qg,k=[xg,k yg,k ψg,k]T、Ug,k=[ug,k rg,k]TIt indicates, i-th of barrier be with qio,k
=[xio,k yio,k ψio,k]T、Uio,k=[uio,k rio,k]TTo indicate；UUV is reduced to radius R in the diagramv, center
For (xv,k,yv,k) circle, the similar radius that obtains is RgTarget and radius be RioBarrier simplification representation.
Bring UUV and the relative motion model of target into：
Wherein, ρvg,kFor the distance between k moment UUV and target, φvg,kFor the angle of sight (sight of k moment UUV and target
Angle between vector and inertial coodinate system E ξ axis).
Formula (6) takes differential form, simultaneous formula (5) to be derived by the tracking error form of UUV and target：
Similarly, the relative motion model of UUV and i-th of barrier is：
Wherein, ρoiv,kFor the distance between k moment UUV and i-th of barrier, φoiv,kHinder for k moment UUV and i-th
Hinder the angle of sight between object.
Step 4：Based on the k moment UUV being calculated in step 3 and target and the relative position of barrier, in conjunction with mesh
Mark tracking radius D1Evade radius of safety D with barrier2Requirement, formulate global follow and the autonomous switchover policy of Local obstacle avoidance, change
Become UUV and control sight, plans the command speed u at its k momentvRef,kWith command heading rvRef,k；
(1) target following guidance law：Design is in the case where maximum turns the limitation of bow angular speed, and the courses control UUV are as early as possible to tracking
Direction of visual lines rotates, and keeps monitoring with target velocity when UUV is in the close circle of target, is run away to when target maneuver and tracks circle
UUV is tracked using maximum speed when in addition, as shown in Figure 3.The mode of constant linear velocity is selected to advantageously reduce controlled quentity controlled variable as possible,
Increase the flexibility of speed of a ship or plane control to turn bow control, is specifically represented by：
Wherein, UUV has maximum speedMaximum turns to change rateConstraint of saturation, and to ensure that UUV is latent under water,
If the minimum speed of a ship or plane isI.e.n0Make to ensure the flatness of tracking for normal number speed gain
UUV fall behind target farther out when with to apart from directly proportional speed tracing；For saturation function, takes Control of line of sight and satisfy
With the minimum value of angular speed, function representation is：
n1Gain is controlled to turn bow, corner is limited in Qu Jian [ by Φ (α);- π, π), it is defined as：
(2) collision prevention guidance law：It is D when target enters radius2Barrier Danger Area within when, design in maximum turns bow angle
Under the limitation of speed, control UUV is diverted away from the direction of visual lines of barrier, avoidance as shown in Figure 4 with maximum line velocity as early as possible
Guiding strategy, function representation are：
Wherein, 0 < n2≤ 1 rotating speed controls gain, n3Be designed as normal number turns bow control gain.
(3) sight switchover policy：Based on the guiding of both the above situation, it can prove there is (n0,n1,D1) so that UUV pairs
The tracking error uniform convergence of target is in D1, there is (n2,n3,D2) so that carving at the beginningCondition
Under, system can ensure successfully avoiding obstacles.Obtaining target following in dynamic environment, passively the strategy of avoidance is simultaneously：Complete
During office's tracking, if there is ρoiv,k≤D2+(Rio+Rv) at the time of, it is activated by collision prevention guidance law, sight is switched to obstacle
Object is evaded, and immediately restores tracking process once confirming that UUV moves to safety zone.
Step 5：It also needs to be controlled in conjunction with actuating unit after formulating tracking strategy, therefore according to leading in step 4
Draw instruction and the UUV speed of a ship or plane and turn bow angular velocity measurement feedback, obtain tracing control deviation, design is dry for Parameter Perturbation and environment
The non-singular terminal sliding mode controller with very strong robustness is disturbed, resolving obtains k moment UUV propeller thrust τu,kAnd rudder
Turn bow torque τr,k；
There is following reduced form for horizontal plane UUV kinetic models：
The guidance law u that will be obtained in step 4vRef,kAnd rvRef,kAs k moment motion control expectation instructions, with UUV reality
Speed of a ship or plane course compares, and obtains tracing control deviation ue,k=uvRef,k-uv,k, re,k=rref,k-rv,k, slided based on non-singular terminal
Modulus principle separately designs speed and turns bow control sliding-mode surface：
Wherein, adjustable parameter β1> 0, β2> 0, p1, q1, p2, q2For positive odd number and
It is derived by horizontal plane UUV thrusts and turns bow Torque Control rule：
Wherein,d11=Xu+X|u|u|u|, d22=Yv+Y|v|v|v
|, d33=Zw+Z|w|w|w|For kinetic parameters；" ^ " indicates the estimated value of system model parameter, and I=1,2,3,5,6, indicate the Perturbation of model parameter, c1sat(s1/φ1)、c2sat(s2/φ2) it is sliding formwork
The discontinuous switching item of controller.
Construct Lyapunov functionsEqual positive definite, respectively derivation can prove
Negative definite, it can thus be appreciated that UUV tracing controls deviation can be stablized in finite time to nought state, i.e. speed over ground and reality
Turn bow angular speed track homing can instruct in finite time.
Step 6：It at the k+1 moment, gos to step one, executes step 1~step 5, obtain real-Time Tracking Control τu,k+1With
τr,k+1；As sampling carries out, the cycle above process is until receiving task END instruction.
Two Case Simulations of the present invention are provided, track and motion control Parameter Map are shown in attached drawing respectively.Fig. 5, Fig. 6 a extremely scheme
6d is maneuvering target tracking process, and whole process is relatively steady；Fig. 7, Fig. 8 a to Fig. 8 d show that tracking environmental is unknown, occur
The case where moving obstacle on-course interferes, still can fast and stable control to the movement instruction of mutation.
If Random moving obstacle equation of locus is
UUV radiuses Rv=3m, moving obstacle radius Ro=5m, target is close to radius of circle D1=10m, barrier risk area
Radius D2=25m, data acquisition intervals To=0.5s.It can be seen that sliding mode controller precision is high, fast miss is responded to control instruction
Difference is small, and UUV actual flight paths can overlap substantially with planned trajectory.In Fig. 7 cases, on the one hand this emulation mode can ensure pair
The tracking accuracy of moving-target, another aspect ρov(t)≤D2+(Ro+RvAvoidance obstacle is activated when)=33m until ρov(t) > D2+(Ro
+Rv), ρ during avoidance in short-termov(min)=26.8024m > Ro+Rv=8m has been always ensured that the nevigation safety of UUV.
Claims (3)
1. a kind of UUV moving-target sliding mode tracking control methods considering Local obstacle avoidance, it is characterized in that：
Step 1：UUV by navigate attitude transducer, position measuring system, Forward-Looking Sonar, real-time detection UUV, moving target with
And obstacle position information；
Step 2：Moving target and barrier kinematics model are established, the moving target k moment is obtained based on unscented kalman filter
State estimation；
Step 3：The relative motion model for establishing UUV and moving target and barrier, for calculate k moment tracking range and
The angle of sight；
Step 4：Based on target following radius D1Evade radius of safety D with barrier2Size, according to UUV and moving target and
The relative position of barrier independently switches between tracking strategy and collision prevention strategy, changes UUV and controls sight, when planning UUVk
Carve command speed and course；
Step 5：According to the command speed and course and the UUV speed of a ship or plane that are obtained in step 4 and turn bow angular velocity measurement feedback, obtains
Tracing control deviation resolves to obtain k moment UUV propeller thrust and rudder based on horizontal plane non-singular terminal sliding mode controller
Turn bow torque；
Step 6：Cycle executes step 1 to step 5, the tracing control at moving target lower a moment is realized, until task terminates.
2. a kind of UUV moving-target sliding mode tracking control methods considering Local obstacle avoidance according to claim 1, it is characterized in that
The guide mode independently switched between tracking strategy and collision prevention strategy is embodied as：During global follow, if there is
ρoiv,k≤D2+(Rio+Rv), it is activated by collision prevention guidance law formulaBy sight
It is switched to barrier and evades aspect, once confirm that UUV moves to safety zone and is carried out target following guidance law formulaTracking process is recovered immediately,
Wherein：ρoiv,kFor the distance between k moment UUV and i-th of barrier, RioFor the radius of i-th of barrier, UUV simplifies
For radius Rv, uvRef,kSpeed, r are guided for k moment UUVvRef,kFor the k moment UUV guiding turn bow angular speed,For maximum speed,
For the minimum speed of a ship or plane, ψv,kFor k moment UUV course angle,Turn bow angular speed, n for UUV maximums0For tracking velocity gain, n1For with
Track turns bow control gain, n2For collision prevention speed gain, n3Turn bow for collision prevention and controls gain, ρvg,kBetween k moment UUV and target
Distance, φvg,kAngle between k moment UUV and the angle of sight, that is, sight vector and inertial coodinate system E ξ axis of target,
φoiv,kThe angle of sight, D between k moment UUV and i-th of barrier1For target following radius, D2Evade safety for barrier
Radius,For saturation function and take the minimum value of Control of line of sight and saturation angular speed, Φ (α) that corner is transformed into section
[-π,π]。
3. a kind of UUV moving-target sliding mode tracking control methods considering Local obstacle avoidance according to claim 1 or 2, special
Sign is that UUV propeller thrusts described in step 5 and rudder turn bow torque and be embodied as：
Wherein：K moment UUV propeller thrust τu,k, k moment rudders turn bow torque τr,k, k moment UUV speed over ground uv,k, k when
Carve UUV guiding speed uvRef,k, k moment UUV are practical turns bow angular speed rv,k, the k moment UUV guiding turn bow angular speed rvRef,k, k when
Carve UUV lateral movement velocities vv,k；The non-singular terminal speed of a ship or plane controls sliding-mode surface s1Sliding-mode surface s is controlled with bow is turned2, ginseng that sliding-mode surface is adjustable
Number β1> 0, β2> 0, p1、q1、p2、q2For positive odd number andSpeed of a ship or plane tracing control deviation ue,k=
uvRef,k-uv,k, bow is to angular speed control deviation re,k=rref,k-rv,k；
d11=Xu+X|u|u|u|, d22=Yv+Y|v|v|v|, d33=Zw+Z|w|w|w|For kinetic parameters；" ^ " indicates system model ginseng
Several estimated values, andI=1,2,3,5,6, indicate the Perturbation of model parameter, c1sat
(s1/φ1)、c2sat(s2/φ2) be sliding mode controller discontinuous switching item, c1、φ1、c2、φ2To change energy of buffeting and perturb
The adjustable parameter of power.
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