CN104881044A - Adaptive tracking control method of multi-mobile-robot system under condition of attitude unknown - Google Patents

Abstract

The invention discloses an adaptive tracking control method of a multi-mobile-robot system under the condition of attitude unknown. The method includes the following steps of establishing a model for each mobile robot in the multi-mobile-robot system; establishing an error model (as shown in the description) with non-linear disturbance of a follower f and a navigator r, wherein in the multi-mobile-robot system, each mobile robot obtains the information of other mobile robots to carry out non-linear disturbance assessment to obtain the non-linear disturbance estimate value of the mobile robot; establishing an adaptive law (as shown in the description) of non-linear disturbance coefficients; establishing a second-order observer for the trigonometric function of the error angle of the follower and the navigator; and establishing an adaptive control law for the follower based on the observer through the combination of the observer and the adaptive law to perform tracking control of the follower and to make the follower realize the tracking control of the navigator.

Description

A kind of adaptive tracking control method of multiple-mobile-robot system of attitude the unknown

Technical field

The invention belongs to intelligent robot technology field, a kind of adaptive Gaussian filtering method for designing of multiple-mobile-robot system under being specifically related to attitude unknown condition.

Background technology

In recent years, the tracing control of multiple-mobile-robot system receives increasingly extensive concern with application, becomes a focal issue of complexity science research gradually.Wherein each mobile robot only utilizes local message to carry out alternately, and the advantage combining the means performance distributed resources such as communication realizes integrated planning, solves local conflicts, thus reaches overall re-set target.Mobile-robot system is a complicated intelligent system combined together by the various functions such as environment sensing, dynamic programming and decision-making, Behavior-Based control and execution.The achievement in research of many front subjects such as sensor technology, the information processing technology, electronic engineering technology, computer technology, Automated condtrol and artificial intelligence technology puts together by it, represent the most overachievement in electromechanical control field and electronic engineering field, one of field the most active in current numerous scientific and technical research field.Along with the development of intelligent robot performance, intelligent level improves constantly, the range of application of mobile robot has had great expansion, not only obtain applying comparatively widely in all conglomeraties such as industry, agricultural, medical and health industry, service sector, simultaneously also even have the occasion of life threat to obtain splendid application security protection, military project national defence and survey of deep space etc. are harmful.Therefore, mobile robot more and more receives the concern of current scholar.

In mobile-robot system, the multiple sensors that all robots utilize self to configure and actuator carry out perception environment and make suitable reaction to the change of environment, and whole mobile-robot system can be considered as a mobile sensor network and actor network to a certain extent; Meanwhile, whole mobile-robot system utilizes the communication facilities self be equipped with to carry out information sharing in control procedure, makes whole system become again a communication interconnected network to a certain extent.Due to the real system that mobile-robot system is under actual conditions, in reality, often environment is comparatively complicated simultaneously, emergency case is more, the situations such as easy appearance such as sensor fault, in order to improve the adaptive faculty of multi-agent system to environment, reduce multiple-mobile-robot system necessary quantity of information in control procedure and can reach the number of sensors reducing mobile robot and be equipped with, economize on resources with this and improve the adaptive faculty of multiple-mobile-robot system to complex environment.

Notice that emergency case is more in actual environment, there is the problem of nonlinear disturbance in the unknown and control inputs of the attitude for system, carry out estimating effectively to reduce the degree of dependence of system to status information to the attitude of unknown intelligent body by utilizing Observer Theory, there is the problem of nonlinear disturbance for Systematical control input simultaneously, adaptive control laws can be utilized to approach disturbance, system can be made to have more robustness, that system can adapt at complex environment better, also for the practical application of Large-scale Mobile robot system provides one solution effectively.

Under attitude unknown condition, the adaptive Gaussian filtering of multiple-mobile-robot system is all in the exploratory development stage at home and abroad, for the problem of attitude the unknown, a lot of achievement is all utilize sliding formwork to control the error of system is converged on sliding-mode surface gradually at present, but sliding formwork controls often easily to occur chattering phenomenon, simultaneously a lot of achievement for control system be also mainly ideal second-order integrator system, this just makes achievement cannot be suitable in the mobile-robot system of reality.

Summary of the invention

In view of this, the invention provides a kind of multiple-mobile-robot system adaptive tracking control method of attitude the unknown, the tracing control to multiple-mobile-robot system can be realized under attitude unknown condition, and the method is the self-adaptation control method based on observer, system can be made in the process developed to realize the tracing control of follower robot to pilotage people robot.

In order to achieve the above object, technical scheme of the present invention is: the method comprises the steps:

Step one: for each mobile robot in multiple-mobile-robot system, all carry out following modeling, first global coordinate system O-xy is set up: choosing any point O point in plane space is initial point, and the mutually orthogonal both direction choosing O point is respectively x-axis and y-axis; Then the local coordinate system C-x of current mobile robot is set up _ry _r: the AnchorPoint C point choosing current mobile robot is initial point, and the mutually orthogonal both direction choosing C point is respectively x _raxle and y _raxle; Wherein the coordinate of C point in global coordinate system O-xy is (x _c, y _c), local coordinate system is θ relative to the rotation angle of global coordinate system.

Step 2: in multiple-mobile-robot system, single mobile robot is divided into pilotage people and follower according to its track following, and wherein the coordinate of the AnchorPoint of pilotage people r in global coordinate system O-xy is (x _r, y _r), the local coordinate system of r is θ relative to the anglec of rotation of global coordinate system O-xy _r, the linear velocity of translation is v _r, the angular velocity of rotation is ω _r.

The coordinate of AnchorPoint in global coordinate system O-xy of follower f is (x _f, y _f), the local coordinate system of follower f is θ relative to the anglec of rotation of global coordinate system O-xy _f, the linear velocity of translation is v _f, the angular velocity of rotation is ω _f.

Then the error model of follower f and pilotage people r is:

$\left[\begin{array}{c}{\stackrel{.}{x}}_R\\ {\stackrel{.}{y}}_R\\ \stackrel{.}{\mathrm{\θ}}\end{array}\right]=\left[\begin{array}{c}\mathrm{\ω}{y}_e-v_f+v_r\cos {\mathrm{\θ}}_e\\ -\mathrm{\ω}{x}_e+v_r\sin {\mathrm{\θ}}_e\\ {\mathrm{\ω}}_r-{\mathrm{\ω}}_f-\mathrm{\σ}\end{array}\right]$

Wherein for follower f is along x _raxial speed, for follower f is along y _raxial speed, for the rotational angular velocity of follower f; Wherein x _efor the error in the direction of the x axis of f and r, y _efor the error in the y-axis direction of f and r, θ _efor the local coordinate system of f and r is relative to the error of the rotation angle of global coordinate system, with be respectively x _e, y _eand θ _ederivative.

Wherein σ is nonlinear disturbance, this nonlinear disturbance σ local smooth and finally can level off to one compact Ω _i∈ R, R are set of real numbers.

Step 3: in multiple-mobile-robot system, the information that each mobile apparatus obtains other mobile robots per capita carries out nonlinear disturbance assessment, obtains the estimated value of the nonlinear disturbance of this mobile robot wherein the estimated value of the disturbance factor W to this mobile robot, for forcing function, r ^v'for the theorem in Euclid space of v ' dimension, wherein function based on v '.

The adaptive law setting up nonlinear disturbance coefficient is:

Wherein c ₄and c ₅for auto-adaptive parameter, be derivative, φ=sin θ _e, ψ=cos θ _e, with be respectively the estimated value of φ and ψ.

Step 4: set up for θ _ethe second order observer of trigonometric function value, set up the derivative of second order observer state intermediate quantity f and g: then this second order observer is specially:

$\widehat{\mathrm{\φ}}=\hat{f}-c_4{v}_r{y}_e$

$\widehat{\mathrm{\ψ}}=\hat{g}-c_5{v}_r{x}_e$

with be respectively the estimated value of f and g; with be respectively the derivative of the estimated value of f and g; By this second order observer, obtain for v _rderivative.

Step 5: the control law of follower is set to:

v _f＝v _r+c ₂x _e-c ₃ω _ry _e

Wherein, c ₂, c ₃, c ₆be preset parameter, now the v of pilotage people r _rand ω _rfor the outside input continued, and c ₂> 0, c ₃>-1, c ₄< 0, c ₅< 0,1 > c ₆> 0, k > 0 is preset parameter, W _mrepresent the upper bound of excitation parameter W.

According to this control law, tracing control is carried out to follower.

Further, error analysis is carried out to the second order observer that step 5 is set up:

The error of this second order observer is respectively then the dynamic equation of this second order observer error is respectively:

Wherein with be respectively with derivative, when with when being approximately 0, this multiple-mobile-robot system keeps stable.

Beneficial effect:

The present invention is directed to the tracking control problem of multiple-mobile-robot system under attitude unknown condition, propose a kind of self-adaptation control method based on observer, the problem of figure state cannot be obtained from for follower in multiple-mobile-robot system, observer is designed to the trigonometric function of follower and pilotage people's error angle, the observation to follower and pilotage people's error angle is indirectly achieved with this, there is the problem of nonlinear disturbance for Systematical control input simultaneously, after modeling is carried out to this disturbance, devise adaptive control laws, finally by observer and the adaptive law a kind of self-adaptation control method based on observer designed in conjunction, successfully to achieve in multiple-mobile-robot system follower to the tracing control of pilotage people, enable the tracing control that follower realizes pilotage people.The control method that the present invention proposes goes for actual mobile-robot system, for the tracking control problem when emergency case such as sensor fault appear in mobile robot under complex environment provides a kind of effective solution, the method also can reduce the dependence of mobile robot to attitude sensor simultaneously, make mobile robot can with lower load, less energy consumption realizes control objectives.

Accompanying drawing explanation

Fig. 1-moveable robot movement model;

Fig. 2-multiple-mobile-robot system Trajectory Tracking Control model;

The original state of Fig. 3-MobileSim emulation experiment multiple-mobile-robot system;

The end-state of Fig. 4-MobileSim emulation experiment multiple-mobile-robot system.

Embodiment

To develop simultaneously embodiment below in conjunction with accompanying drawing, describe the present invention.

Under the present invention is directed to attitude unknown condition, multiple-mobile-robot system tracking control problem proposes a kind of self-adaptation control method based on observer, enables follower in multiple-mobile-robot system realize the tracing control to pilotage people.

Step one: single mobile robot's modeling

As shown in Figure 1, select a bit arbitrarily in plane space, this point is set to initial point O, sets up global coordinate system at this point and choose mutually orthogonal both direction as x-axis and y-axis.In order to local coordinate ties up to the mapping situation of global coordinate system, select robot AnchorPoint C point as the initial point of local coordinate axle, think that C point that is to say the center of gravity place of robot in normal conditions.In local coordinate system, use { x _r, y _rtwo axis that coordinates robot's local coordinate is fastened, this completes the definition of robot local coordinate system.Consider the global coordinate system at robot place, global coordinate system (x can be used in the position of C point, y) represent, simultaneously local coordinate system can be regarded as global coordinate system and have rotated θ and obtain, the linear velocity of supposition mobile robot translation is v (t) simultaneously, the angular velocity rotated is ω (t), so then can obtain the motion model that mobile robot fastens at world coordinates.

$\left[\begin{array}{c}{\stackrel{.}{x}}_R\\ {\stackrel{.}{y}}_R\\ \stackrel{.}{\mathrm{\&theta;}}\end{array}\right]=\left[\begin{array}{c}v\left(t\right)\cos \left(\mathrm{\&theta;}\right)\\ v\left(t\right)\sin \left(\mathrm{\&theta;}\right)\\ \mathrm{\&omega;}\left(t\right)\end{array}\right]=\left[\begin{array}{cc}\cos \left(\mathrm{\&theta;}\right)& 0\\ \sin \left(\mathrm{\&theta;}\right)& 0\\ 0& 1\end{array}\right]\left[\begin{array}{c}v\left(t\right)\\ \mathrm{\&omega;}\left(t\right)\end{array}\right]---\left(1\right)$

As can be seen from system model, the status information of model has 3, distributed x _r, y _r, θ, but controlled quentity controlled variable only has 2, be v (t), ω (t) respectively, this just makes system model be nonholonomic constraint model, there is being coupled of product form with controlled quentity controlled variable in quantity of state simultaneously, and this all drastically increases the difficulty of process mobile apparatus human model.

Step 2: multiple-mobile-robot system Trajectory Tracking Control modeling

What consider that this patent mainly studies is the track following problem of multiple-mobile-robot system, thus needs to study the state error between follower and pilotage people, therefore needs to make certain change to model.Assuming that pilotage people is all mobile apparatus human model, its status information (x _r, y _r, θ _r) represent, corresponding, control inputs (v _r, ω _r) represent, in order to pilotage people and follower be distinguished, the status information of follower and control inputs are then (x, y, θ) and (v, ω).The error coordinate of follower and pilotage people as shown in Figure 2.

According to the coordinate system in figure, the error model that just can obtain follower and pilotage people is

$\left[\begin{array}{c}{\stackrel{.}{x}}_e\\ {\stackrel{.}{y}}_e\\ {\stackrel{.}{\mathrm{\&theta;}}}_e\end{array}\right]=\left[\begin{array}{ccc}\cos \left(\mathrm{\&theta;}\right)& \sin \left(\mathrm{\&theta;}\right)& 0\\ -\sin \left(\mathrm{\&theta;}\right)& \cos \left(\mathrm{\&theta;}\right)& 0\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{x}_r-x\\ y_r-y\\ {\mathrm{\&theta;}}_r-\mathrm{\&theta;}\end{array}\right]---\left(2\right)$

(1) formula substituted into, can obtain formula (3), this formula is then the main research objects of these chapters and sections.

$\left[\begin{array}{c}{\stackrel{.}{x}}_e\\ {\stackrel{.}{y}}_e\\ {\stackrel{.}{\mathrm{\&theta;}}}_e\end{array}\right]=\left[\begin{array}{c}\mathrm{\&omega;}{y}_e-v+v_r\cos {\mathrm{\&theta;}}_e\\ -\mathrm{\&omega;}{x}_e+v_r\sin {\mathrm{\&theta;}}_e\\ {\mathrm{\&omega;}}_r-\mathrm{\&omega;}\end{array}\right]---\left(3\right)$

Step 3: nonlinear disturbance modeling

Formula (2) and (3) have given the citation form of moveable robot movement model and Trajectory Tracking Control, but two formulas belong to the model that control inputs under ideal conditions does not exist disturbance, because attitude angle controller exists nonlinear disturbance, in formula (3), mobile apparatus human model needs to be rewritten as

$\left[\begin{array}{c}{\stackrel{.}{x}}_e\\ {\stackrel{.}{y}}_e\\ {\stackrel{.}{\mathrm{\&theta;}}}_e\end{array}\right]=\left[\begin{array}{c}\mathrm{\&omega;}{y}_e-v+v_r\cos {\mathrm{\&theta;}}_e\\ -\mathrm{\&omega;}{x}_e+v_r\sin {\mathrm{\&theta;}}_e\\ {\mathrm{\&omega;}}_r-\mathrm{\&omega;}-\mathrm{\&sigma;}\end{array}\right]---\left(4\right)$

Assuming that this nonlinear disturbance local smooth and finally can level off to one compact Ω _i∈ R, then nonlinear disturbance σ can be defined as wherein v corresponding to each node i _ifunction, and W _ibe then a series of unknown parameter and bounded, namely | W _i| < W _m.V _ifunction can select multiple basic function, such as sign function, Gaussian function etc.Wen Zhong, be regarded as neural network trigger matrix and the while of being then neural network weight matrix be assumed that unknown quantity.

Step 4: the adaptive law for nonlinear disturbance designs

In order to compensate nonlinear disturbance, each intelligent body must carry out estimation compensation to this disturbance, and to this problem, main thinking the information of other intelligent bodies accessed by intelligent body i is carried out the control effects of evaluation control device, therefore, the estimated value of nonlinear disturbance is

Wherein the disturbance factor W to each intelligent body i _iestimated value.The adaptive law of nonlinear disturbance coefficient can be designed as:

Step 5: attitude Design of Observer

As can be seen from formula (4), directly to θ _ecarry out the computing estimating to need to carry out trigonometric function, after differentiate, computing is comparatively complicated, and the observer of this patent will directly to θ _etrigonometric function value observe, first introducing second order observer state intermediate quantity is:

f＝sinθ _e+c ₄v _ry _e

(7)

g＝cosθ _e+c ₅v _rx _e

Wherein f and g is intermediate quantity, does not have actual physical significance, c ₄, c ₅be respectively two preset parameters, differentiate carried out to formula (6) and formula (4) is substituted into and can obtain:

Suppose φ=sin θ _e, ψ=cos θ _e, then to θ _ethe estimated value of function of triangle can be write as the observer form design of this patent is as follows:

Step 6: attitude observer error analysis

Assuming that the error of observer is respectively the dynamic equation that can obtain observer error to its differentiate is respectively

$\stackrel{.}{\stackrel{~}{\mathrm{\&phi;}}}=\stackrel{.}{\mathrm{\&phi;}}-\stackrel{.}{\widehat{\mathrm{\&phi;}}}$

$\stackrel{.}{\stackrel{~}{\mathrm{\&psi;}}}=\stackrel{.}{\mathrm{\&psi;}}-\stackrel{.}{\widehat{\mathrm{\&psi;}}}$

Formula (7)-(9) are substituted into above formula can obtain

Positive and negatively between two to offset every in above formula, the observer error dynamics equation that can obtain abbreviation is:

To first formula, due to be respectively the product of unknown quantity and the sum of products of estimator, can not directly eliminate, pretend following mathematics manipulation

Above formula is substituted in the error dynamics equation of observer, then can obtain:

Step 7: the adaptive control laws based on observer designs

Assuming that there are 2 intelligent bodies in theorem in Euclid space, wherein 1 intelligent body is follower, another 1 intelligent body is pilotage people, the kinetics equation of intelligent body describes by formula (3), Trajectory Tracking Control model is described by formula (4), and the control law of follower is described by formula (11).When the control law of follower meets formula (12) and the linear velocity of pilotage people meets persistent excitation condition, system will realize locally asymptotic stability, and follower also can follow the tracks of pilotage people.

Wherein, ω _r, v _rbe respectively angular velocity and the linear velocity of pilotage people, c ₂, c ₃, c ₆be preset parameter.

For formula (12), due to the equal bounded of the number in bracket, k > 0 is preset parameter, can be carried out the scope of expansion system local stability large as far as possible like this by the size of adjustment k value, simultaneously when k value is enough large, wherein W _mrepresent the upper bound of excitation parameter W.

For 2 intelligent bodies existed in theorem in Euclid space, assuming that wherein 1 intelligent body is follower, another 1 intelligent body is pilotage people, the kinetics equation of intelligent body describes by formula (1), Trajectory Tracking Control model is described by formula (4), and the control law of follower is described by formula (11).When the control law of follower meets formula (12) and the linear velocity of pilotage people meets persistent excitation condition, system will realize local stability, and follower will the tracing control of experiment to pilotage people.

The present embodiment is the validity of authentication control method and feasibility by experiment:

Emulation experiment is mainly based on mobile robot's simulation test platform MobileSim, and the robot model in emulation is P3-DX type mobile robot.

Fig. 3 gives the initial position of mobile-robot system on MobileSim emulation platform,, in figure, No. 1 and No. 2 robots are respectively follower, and pilotage people robot then marks with leader, wherein the disturbance factor of No. 1 robot is less, and the disturbance factor of 2 good robots is larger.

Fig. 4 gives the end-state of mobile-robot system on MobileSim emulation platform, wherein the track of pilotage people is an arching trajectory, due to different from the relative distance of pilotage people, the track of each follower is not quite similar, but finally all achieves the tracing control to pilotage people.Although also the impact of different disturbances on control effects cannot be differentiated from this figure, but this figure has successfully tested proposed control algolithm can for the applicability of actual mobile-robot system, and the identical program of use is run and contrast and experiment by next step on the mobile robot of reality.

To sum up, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any amendment done, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (2)

1. the multiple-mobile-robot system adaptive tracking control method of attitude the unknown, it is characterized in that, the method comprises the steps:

Step one: for each mobile robot in multiple-mobile-robot system, all carry out following modeling, first global coordinate system O-xy is set up: choosing any point O point in plane space is initial point, and the mutually orthogonal both direction choosing O point is respectively x-axis and y-axis; Then the local coordinate system C-x of current mobile robot is set up _ry _r: the AnchorPoint C point choosing current mobile robot is initial point, and the mutually orthogonal both direction choosing C point is respectively x _raxle and y _raxle; Wherein the coordinate of C point in global coordinate system O-xy is (x _c, y _c), local coordinate system is θ relative to the rotation angle of global coordinate system;

Step 2: in multiple-mobile-robot system, single mobile robot is divided into pilotage people and follower according to its track following, and wherein the coordinate of the AnchorPoint of pilotage people r in global coordinate system O-xy is (x _r, y _r), the local coordinate system of r is θ relative to the anglec of rotation of global coordinate system O-xy _r, the linear velocity of translation is v _r, the angular velocity of rotation is ω _r;

The coordinate of AnchorPoint in global coordinate system O-xy of follower f is (x _f, y _f), the local coordinate system of follower f is θ relative to the anglec of rotation of global coordinate system O-xy _f, the linear velocity of translation is v _f, the angular velocity of rotation is ω _f;

Then the error model of follower f and pilotage people r is:

$\left[\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_R\\ {\stackrel{\&CenterDot;}{y}}_R\\ \stackrel{\&CenterDot;}{\mathrm{\&theta;}}\end{array}\right]=\left[\begin{array}{c}{\mathrm{\&omega;y}}_e-v_f+v_r{\cos \mathrm{\&theta;}}_e\\ {-\mathrm{\&omega;x}}_e+v_r\sin {\mathrm{\&theta;}}_e\\ {\mathrm{\&omega;}}_r-{\mathrm{\&omega;}}_f-\mathrm{\&sigma;}\end{array}\right]$

Wherein for follower f is along x _raxial speed, for follower f is along y _raxial speed, for the rotational angular velocity of follower f; Wherein x _efor the error in the direction of the x axis of f and r, y _efor the error in the y-axis direction of f and r, θ _efor the local coordinate system of f and r is relative to the error of the rotation angle of global coordinate system, with be respectively x _e, y _eand θ _ederivative;

Wherein σ is nonlinear disturbance, this nonlinear disturbance σ local smooth and finally can level off to one compact Ω _i∈ R, R are set of real numbers;

Step 3: in multiple-mobile-robot system, the information that each mobile apparatus obtains other mobile robots per capita carries out nonlinear disturbance assessment, obtains the estimated value of the nonlinear disturbance of this mobile robot wherein the estimated value of the disturbance factor W to this mobile robot, for forcing function, r ^v'for the theorem in Euclid space of v ' dimension, wherein function based on v ';

The adaptive law setting up nonlinear disturbance coefficient is:

Wherein c ₄and c ₅for auto-adaptive parameter, be derivative, φ=sin θ _e, ψ=cos θ _e, with be respectively the estimated value of φ and ψ;

Step 4: set up for θ _ethe second order observer of trigonometric function value, set up the derivative of second order observer state intermediate quantity f and g: then this second order observer is specially:

with be respectively the estimated value of f and g; with be respectively the derivative of the estimated value of f and g; By this second order observer, obtain for v _rderivative;

Step 5: the control law of follower is set to:

v _f＝v _r+c ₂x _e-c ₃ω _ry _e

Wherein, c ₂, c ₃, c ₆be preset parameter, now the v of pilotage people r _rand ω _rfor the outside input continued, and c ₂> 0, c ₃>-1, c ₄< 0, c ₅< 0,1 > c ₆> 0, k > 0 is preset parameter, W _mrepresent the upper bound of excitation parameter W;

According to this control law, tracing control is carried out to follower.

2. adaptive tracking control method as claimed in claim 1, is characterized in that, carry out error analysis to the second order observer that described step 5 is set up:

The error of this second order observer is respectively then the dynamic equation of this second order observer error is respectively:

Wherein with be respectively with derivative, when with when being approximately 0, this multiple-mobile-robot system keeps stable.