CN113031436B - Mobile robot model prediction track tracking control system and method based on event triggering - Google Patents
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Abstract
The invention provides a mobile robot model prediction track tracking control system and method based on event triggering, comprising the following steps: designing to obtain a model predictive controller; setting the current initial state of the mobile robot, generating a reference track, and obtaining a state predicted value of the mobile robot at the next moment; taking the obtained state predicted value at the next moment as a new current state of the mobile robot; setting an event triggering mechanism, and judging whether the new current state meets triggering conditions or not; repeating until the last track point on the discretized reference track is tracked; by designing the event triggering mechanism, the model predictive controller only acts at the occurrence time of the given event, so that compared with the traditional periodic sampling control, the event triggering mechanism only acts at the occurrence time of the given event, for example, the error exceeds a threshold value or reaches a specific time, the path following control is realized, and the calculated amount is greatly reduced.
Description
Technical Field
The invention belongs to the field of intelligence, and particularly relates to a mobile robot model prediction track tracking control system and method based on event triggering.
Background
The track tracking control method of the mobile robot has more research results in recent years, and the main track control algorithm in the current stage comprises synovial membrane control, model prediction control, robust control and the like, so that the model prediction control is widely applied in the field of mobile robot control by virtue of the advantages of the model prediction control in system constraint and multi-objective optimization problem processing.
Model predictive control requires solving a constraint optimization problem at each sampling time, so that a great demand exists for online calculation amount. Aiming at the problem, a robust predictive control algorithm based on event triggering is provided in the prior art, and it is emphasized that although the event triggering predictive control algorithm can process external disturbance through a terminal cost function, terminal constraint and a tightening set, the additional addition items can greatly increase the online calculation amount of an optimization problem, seriously affect the instantaneity of a controller, reduce the optimization performance of the controller, solve the optimization problem in time under the condition of limited hardware equipment performance, and control signals cannot be updated in time, so that the system performance is deteriorated and even unstable, and therefore, certain application and popularization difficulties exist.
Disclosure of Invention
The invention aims to provide a mobile robot model prediction track tracking control system and method based on event triggering, which solve the defect of reduced real-time performance of a controller caused by large calculated amount in the existing model prediction control.
In order to achieve the above purpose, the invention adopts the following technical scheme:
the invention provides a mobile robot model prediction track tracking control method based on event triggering, which comprises the following steps:
step 1, a linear discrete model of a mobile robot is established according to a nonlinear kinematic model of the mobile robot, a linear time-varying model is obtained according to the linear discrete model of the mobile robot, the linear time-varying model is used as a prediction model, and a model prediction controller is designed according to the prediction model;
step 2, setting the current initial state of the mobile robot, generating a reference track, discretizing the obtained reference track to obtain a discretized reference track, and selecting a first track point on the discretized reference track at the moment t=k;
step 3, combining the current initial state of the mobile robot, the first track point and a model predictive controller, and solving to obtain a control input increment sequence of the mobile robot in a control time domain;
step 4, updating the current initial state of the mobile robot set in the step 2 by using the first element in the obtained control input increment sequence to obtain a state predicted value of the mobile robot at the next moment;
step 5, taking the obtained state predicted value at the next moment as a new current state of the mobile robot;
step 6, setting an event triggering mechanism, and judging whether the new current state meets a triggering condition, wherein:
if yes, at the time t=k+1, the model prediction controller combines the new current position state and the next track point on the discretized reference track, solves to obtain a new control input increment sequence of the mobile robot in the control time domain, updates the current state of the mobile robot by using the first element in the new control input increment sequence to obtain a state predicted value of the mobile robot at the next time, and enters step 5;
if not, updating the state predicted value obtained in the step 4 by using the first element of the control input increment sequence obtained at the time t=k at the time t=k+1 to obtain a new state predicted value of the mobile robot at the next time, and entering the step 5;
and 7, repeating the step 5 and the step 6 until the last track point on the discretized reference track is tracked.
Preferably, in step 1, a model prediction controller is obtained according to a nonlinear kinematic model of a mobile robot, and the specific method is as follows:
obtaining a linearization discrete model of the mobile robot according to the nonlinear kinematic model of the mobile robot;
obtaining a linear time-varying model according to the obtained linear discrete model of the mobile robot; and taking the linear time-varying model as a prediction model, and designing to obtain a model prediction controller according to the prediction model.
Preferably, according to a nonlinear kinematic model of the mobile robot, a linearization discrete model of the mobile robot is obtained, and the specific method is as follows:
establishing a nonlinear kinematic model of the mobile robot, and carrying out linearization treatment on the nonlinear kinematic model by adopting a Taylor series expansion mode to obtain a linear error model; and discretizing the linear error model by adopting an Euler method to obtain a linearization discrete model of the mobile robot.
Preferably, in step 5, an event trigger mechanism is set, and the specific method is as follows:
at each sampling moment, when any state component pose coordinate of the mobile robot is larger than the state component pose coordinate of the threshold curve, setting the following triggering conditions:
in xi 1 ，ξ 2 And ζ3 represents the state component x, y,σ x ，σ y is->Representing the state components x, y,/-respectively>A corresponding threshold.
Preferably, the method for acquiring the threshold curve comprises the following steps:
in the track tracking process, the pose coordinates of the mobile robot at the same sampling moment are selected from N groups of historical data, and an average value is obtained, so that three variables are obtained;
setting the three variables as a threshold triggered by the event at the first sampling moment;
respectively obtaining three state component pose coordinate threshold curves of the mobile robot according to the obtained threshold values triggered by the events:
preferably, in step 5, an event trigger mechanism is set, and the specific method is as follows:
at each sampling moment, when any state component pose coordinate of the mobile robot is larger than the state component pose coordinate of the upper boundary of the threshold value band or smaller than the state component coordinate of the lower boundary of the threshold value band, setting the following triggering conditions:
in xi 1 ，ξ 2 ，ξ 3 Representing the state components x, y,σ x_u 、σ x_d 、σ y_u 、σ y_d 、/>and->Upper and lower threshold values of the abscissa and the ordinate and the rotation angle are respectively indicated.
Preferably, the threshold band acquisition method is as follows:
the relationship between the threshold curve and the maximum disturbance is utilized to form a threshold zone:
wherein,representing the upper bound of the disturbance.
The mobile robot model prediction track tracking control system based on event triggering can execute the control method and comprises a model construction module, a module parameter setting module, a data processing module and a data judging module, wherein:
the model construction module is used for building a linearization discrete model of the mobile robot according to a nonlinear kinematic model of the mobile robot, taking the linearization discrete model as a prediction model, and obtaining a model prediction controller according to the prediction model design;
the module parameter setting module is used for setting the current initial state of the mobile robot, generating a reference track, discretizing the obtained reference track to obtain a discretized reference track, and selecting a first track point on the discretized reference track at the moment t=k;
the data processing module is used for combining the current initial state of the mobile robot, the first track point and the model predictive controller, and solving to obtain a control input increment sequence of the mobile robot in a control time domain;
updating the set current initial state of the mobile robot by using the first element in the obtained control input increment sequence to obtain a state predicted value of the mobile robot at the next moment;
the data judging module is used for taking the obtained state predicted value at the next moment as a new current state of the mobile robot; setting an event triggering mechanism, and judging whether the new current state meets a triggering condition, wherein:
if so, at the time t=k+1, the model predictive controller combines the new current position state and the next track point on the discretized reference track to obtain a new control input increment sequence of the mobile robot in the control time domain;
if the state prediction value does not meet the requirement, at the time t=k+1, using the state prediction value obtained in the updating of the first element of the control input increment sequence obtained at the time t=k to obtain a new state prediction value of the mobile robot at the next time;
and repeating the operation until the last track point on the discretized reference track is tracked.
Compared with the prior art, the invention has the beneficial effects that:
according to the mobile robot model prediction track tracking control method based on event triggering, an event triggering mechanism is designed, so that a model prediction controller acts only at the occurrence time of a given event, namely, for a first triggering strategy, when any state component pose coordinate of a mobile robot is larger than any state component pose coordinate of a corresponding threshold curve, the mobile robot is regarded as meeting a triggering condition, the model prediction controller updates and solves a control sequence, otherwise, a first element of the control sequence is continuously applied until the triggering condition is met; for the second triggering strategy, when any state component pose coordinate of the mobile robot is larger than the state component pose coordinate of the upper boundary of the corresponding threshold zone or smaller than the state component pose coordinate of the lower boundary of the threshold zone, the control sequence is updated and solved by the model prediction controller, otherwise, the first element of the control sequence is continuously applied until the triggering condition is met; therefore, compared with the traditional periodic sampling control, the event triggering mechanism only acts at the moment when the given event occurs, such as that the error exceeds a threshold value or reaches a specific moment, so that the path following control is realized, and meanwhile, the calculated amount is greatly reduced.
Drawings
FIG. 1 is a schematic flow chart of the present invention;
FIG. 2 is an effect diagram of an embodiment tracking a straight line trajectory;
FIG. 3 is an effect diagram of an embodiment tracking a circular trajectory;
FIG. 4 is an on-line solution of an optimization problem for tracking a linear trajectory with two event-triggered strategies;
FIG. 5 is an on-line solution of the optimization problem for two event-triggered strategies tracking circular trajectories.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a mobile robot model prediction track tracking control method based on event triggering, which comprises the following steps:
s1: establishing a nonlinear kinematic model of the mobile robot, and carrying out linearization treatment on the nonlinear kinematic model by adopting a Taylor series expansion mode to obtain a linear error model; performing discretization processing on the linear error model by adopting an Euler method to obtain a linearization discrete model of the mobile robot;
s2: obtaining a linear time-varying model according to a linearization discrete model of the mobile robot, taking the linear time-varying model as a prediction model, and designing a model prediction controller according to the prediction model; the model predictive controller contains predictive equations, control optimization problems that satisfy objective functions and various constraints, and feedback mechanisms.
S3: generating a reference track, and discretizing the obtained reference track to obtain a discretized reference track; setting an initial state of the mobile robot; at the time t=k, selecting a first track point on the discretized reference track;
s4: combining the first track point, the initial state of the mobile robot and a model predictive controller, bringing a predictive equation into an objective function, solving a control optimization problem meeting the objective function and various constraints, and obtaining a control input increment sequence of the mobile robot in a control time domain
S5: the control input increment sequence obtained in the step S4 is processedThe first element->As a control input increment, updating the initial state of the mobile robot by using the control input increment to obtain a state predicted value xi (k+ 1|k) of the mobile robot at the next moment;
s6: taking the obtained state predicted value xi (k+ 1|k) as a new current state of the mobile robot;
s7: designing an event triggering mechanism, and judging whether the new current state meets triggering conditions, wherein:
if so, at the time t=k+1, the model predictive controller combines the new current state and the next track point on the discretized reference track, solves the control optimization problem meeting the objective function and various constraints to obtain a new control input increment sequence of the mobile robot in the control time domain, and updates the current state of the mobile robot by using the first element in the new control input increment sequence to obtain a state predictive value of the mobile robot at the next time, and enters S6;
if not, not updating the control input increment sequence at the time t=k+1, updating the state prediction value obtained in the step S5 along the first element of the control input increment sequence obtained at the previous time, and entering into the step S6;
s8: s6 to S7 are repeatedly performed until the last track point on the discretized reference track is tracked.
In the S1, a linearization discrete model of the mobile robot is established, and the specific method is as follows:
s101, establishing a nonlinear kinematic model of the mobile robot, specifically:
assuming that the system accords with incomplete constraint, the vehicle body does not slide laterally, the speed of the robot is generally low, the influence of lateral acceleration such as centrifugal acceleration and the like is small when the robot turns, and a kinematic model of the mobile robot is established as follows:
in the method, in the process of the invention,representing the state of the robot, where [ x y ]]Indicate position(s) (i.e.)>And v and ω are used for representing the centroid linear velocity and angular velocity of the mobile robot respectively for the pose angle of the mobile robot, namely the included angle between the positive direction of the x axis of the mobile robot body coordinate system and the positive direction of the x axis of the global coordinate system.
S102, expressing the kinematic model in a state vector form:
wherein, xi is a state vector; u is a control input; f (·) represents the mapping relationship.
S103, the state and the control quantity of the reference system at any moment meet the following relation:
s104, the formula (3) is carried out at an arbitrary reference point (xi) r ,u r ) The Taylor series expansion is performed, only the first-order term is reserved, the high-order term is ignored, and the following expression can be obtained:
s105, subtracting the formula (4) from the formula (3) to obtain a linearization error model of the mobile robot:
s106, performing discretization processing on the formula (5) by adopting an Euler method to obtain a linearization discrete model of the mobile robot:
wherein:
in S2, designing a predictive controller by using a linear time-varying model, wherein the specific method comprises the following steps:
s2021, design of a prediction equation:
considering the discretization model type (6) of the mobile robot, set up:
a new discrete state space expression is thus obtained:
in the middle ofIs a system matrix>Is a control matrix->Is an output matrix, m and n are the dimensions of the state quantity and the control quantity respectively. To simplify the expression settings:
the expression from which the predicted output in the predicted time domain can be derived is:
Y(t)＝Ψ t μ(k|t)+Θ t ΔU(t) (10)
wherein: :
in N p ，N c Respectively representing a prediction time domain and a control time domain.
S2022, control optimization problem:
the objective function of the predictive controller contains information such as system state quantity errors, control quantity changes and the like, and the optimal control problem established based on the objective function can ensure that the mobile robot can track the reference track rapidly and stably, and is as follows:
s.t.
u min (t+k)≤u(t+k)≤u max (t+k)
Δu min (t+k)≤Δu(t+k)≤Δu max (t+k)
y min (t+k)≤y(t+k)≤y max (t+k)
wherein Q and R are weight matrixes; n (N) P To predict the time domain; n (N) C To control the time domain; alpha is a weight system; epsilon is the relaxation factor.
Substituting equation (10) into the optimization function (11), and expressing the output deviation in the prediction time domain as:
wherein Y is ref ＝[η ref (t+1|t),...,η ref (t+N p |t)] T
Through corresponding matrix calculation, the optimization problem can be adjusted as follows:
J(ξ(t),u(t-1),ΔU(t))＝[ΔU(t) T ,ε] T H t [ΔU(t) T ,ε]+G t [ΔU(t) T ,ε]+P t (13)
wherein:P t ＝E(t) T QE(t)
the constrained optimization solving problem of model predictive control at each step is equivalent to solving the following quadratic programming problem:
ΔU min ≤ΔU(k)≤ΔU max ，
Y min -ε≤Ψ t μ(k|t)+Θ t ΔU(t)≤Y max -ε,
k＝t,...,t+N c -1，ε＞0
s2023, after completing the online solution of equation (14) at the sampling time in each control period, obtains a control input increment sequence in the control time domain:the first element in the control sequence is applied to the system as the actual control input increment, namely: />And refreshing the optimization problem by using the newly obtained state, and repeating the steps in a circulating way until the control process is completed.
In S6, the event trigger mechanism design includes the following steps:
s601, because various disturbance exists inevitably in the actual mobile robot system, the design of the event trigger mechanism needs to further consider the disturbance signal W epsilon W based on the formula (1) for useRepresents the upper perturbation bound, where W represents the tight set. The status signal considering the disturbance is expressed as follows:
s602, defining the next trigger time as t k+1 The method comprises the following steps:
the first trigger strategy design for triggering includes:
at each sampling instant, when any one of the state component pose coordinates of the mobile robot is greater than the state component pose coordinates of the threshold curve, the MPC controller performs a control action, based on which a sequence { t } is defined k |k∈N * Defining the moment for solving the optimization problem by the controller in the path following process of the mobile robotFor the next trigger time, the following trigger conditions are set:
in xi 1 ，ξ 2 ，ξ 3 Representing the state components x, y,σ x ，σ y is->Representing the values of the state components x, y,a corresponding threshold.
The method for selecting the threshold curve comprises the following steps: the pose coordinates of the mobile robot at the same sampling moment are selected from N groups of historical data, the pose coordinates are averaged to obtain three variables, the three variables are set as thresholds triggered by events at the first sampling moment, a known threshold for offline calculation exists at each sampling moment in the track tracking process, and finally three state component pose coordinate threshold curves of the mobile robot can be obtained respectively:
wherein,respectively representing pose information of the mobile robot in the ith group of sample data, wherein k is the kth sampling moment; sigma (sigma) x (k)、σ y (k)、/>And respectively representing the threshold values corresponding to the abscissa and the ordinate of the mobile robot and the rotation angle at the kth sampling moment.
The second trigger strategy design for triggering includes:
at each sampling instant, when any one of the state component pose coordinates of the mobile robot is greater than the state component pose coordinates of the upper bound of the threshold band or less than the state component coordinates of the lower bound of the threshold band, definingFor the next trigger time, the following trigger conditions are set:
in xi 1 ，ξ 2 ，ξ 3 Representing the state components x, y,σ x_u 、σ x_d 、σ y_u 、σ y_d 、/>and->Respectively represent the abscissa and the ordinate and the rotationUpper and lower boundary thresholds for corners.
The method for selecting the threshold value band comprises the following steps: the threshold zone may be constructed by using the relationship of the threshold curve and the maximum disturbance, with the control effect not being degraded:
in the example, for straight-line trajectory tracking, the prediction time domain and the control time domain are set to 5, the control period is 0.05s, and the straight line of y=10 is set as the reference path.
Error penalty term weight q= [1 0; 0.1; 0.0.5 ], r= [ 0.1; 0 0.1].
In the figure, TT is used to represent time triggering, that is, each sampling time is used to solve an optimization problem, ET1 and ET2 respectively represent that a first event triggering control strategy and a second event triggering control strategy are applied to a controller, and ρ=0.05 represents a bounded random disturbance upper bound.
In the example, for circular trajectory tracking, the prediction time domain and the control time domain are set to 20, the control period is 0.05s, and a circle with a radius of 5m is set as a reference path. Error penalty term weight q= [1 0; 0.1; 0.0.5 ] = [ 0.2; 0 0.2].
In the figure, TT is used to represent time triggering, that is, each sampling time is used to solve an optimization problem, ET1 and ET2 respectively represent that a first event triggering control strategy and a second event triggering control strategy are applied to a controller, and ρ=0.05 represents a bounded random disturbance upper bound.
As can be seen from fig. 4 and 5, on the premise of achieving the tracking effect, after the first and second event trigger control strategies are introduced, the calculated amount during the linear track tracking is reduced by 26.4% and 74%, and the calculated amount during the circular track tracking is reduced by 18.14% and 75.12%, respectively; meanwhile, the control signal at the previous moment is used because the triggering condition is not met, so that the consumption of extra communication resources is reduced.
The above embodiments are provided to illustrate the technical concept and features of the present invention and are intended to enable those skilled in the art to understand the content of the present invention and implement the same, and are not intended to limit the scope of the present invention. All equivalent changes or modifications made in accordance with the spirit of the present invention should be construed to be included in the scope of the present invention.
Claims (4)
1. The mobile robot model prediction track tracking control method based on event triggering is characterized by comprising the following steps of:
step 1, a linear discrete model of a mobile robot is established according to a nonlinear kinematic model of the mobile robot, a linear time-varying model is obtained according to the linear discrete model of the mobile robot, the linear time-varying model is used as a prediction model, and a model prediction controller is designed according to the prediction model;
step 2, setting an initial state of the mobile robot, generating a reference track, discretizing the obtained reference track to obtain a discretized reference track, and selecting a first track point on the discretized reference track at the time t=k;
step 3, combining the initial state of the mobile robot, the first track point and a model predictive controller, and solving to obtain a control input increment sequence of the mobile robot in a control time domain;
step 4, updating the initial state of the mobile robot set in the step 2 by using the first element in the obtained control input increment sequence to obtain a state predicted value of the mobile robot at the next moment;
step 5, taking the obtained state predicted value at the next moment as a new current state of the mobile robot;
step 6, setting an event triggering mechanism, and judging whether the new current state meets a triggering condition, wherein:
if yes, at the time t=k+1, the model prediction controller combines the new current position state and the next track point on the discretized reference track, solves to obtain a new control input increment sequence of the mobile robot in the control time domain, updates the current state of the mobile robot by using the first element in the new control input increment sequence to obtain a state predicted value of the mobile robot at the next time, and enters step 5;
if not, updating the state predicted value obtained in the step 4 by using the first element of the control input increment sequence obtained at the time t=k at the time t=k+1 to obtain a new state predicted value of the mobile robot at the next time, and entering the step 5;
step 7, repeating the step 5 and the step 6 until the last track point on the discretized reference track is tracked;
in step 6, an event trigger mechanism is set, and the specific method is as follows:
at each sampling moment, when any state component pose coordinate of the mobile robot is larger than the state component pose coordinate of the threshold curve, setting the following triggering conditions:
(17)
in the method, in the process of the invention,，/>，/>representing the state components of the system respectively->，/>，/>；/>，/>Is->Respectively represent status components->，，/>A corresponding threshold;
the method for acquiring the threshold value curve comprises the following steps:
during the track following process, fromThe pose coordinates of the mobile robot at the same sampling moment are selected from the group history data, and the average value is obtained to obtain three variables;
setting the three variables as a threshold triggered by the event at the first sampling moment;
respectively obtaining three state component pose coordinate threshold curves of the mobile robot according to the obtained threshold values triggered by the events:
；
or in the step 6, setting an event triggering mechanism, wherein the specific method is as follows:
at each sampling moment, when any state component pose coordinate of the mobile robot is larger than the state component pose coordinate of the upper boundary of the threshold value band or smaller than the state component coordinate of the lower boundary of the threshold value band, setting the following triggering conditions:
(19)
in the method, in the process of the invention,representing the state components of the system respectively->；/>、/>、/>、/>、/>Andupper and lower threshold values respectively representing the abscissa and the ordinate and the rotation angle;
the acquisition method of the threshold value band comprises the following steps:
the relationship between the threshold curve and the maximum disturbance is utilized to form a threshold zone:
wherein,representing the upper bound of the disturbance.
2. The method for controlling the model predictive trajectory tracking of a mobile robot based on event triggering according to claim 1, wherein in step 1, a model predictive controller is obtained according to a nonlinear kinematic model of the mobile robot, and the method specifically comprises:
obtaining a linearization discrete model of the mobile robot according to the nonlinear kinematic model of the mobile robot;
obtaining a linear time-varying model according to the obtained linear discrete model of the mobile robot; and taking the linear time-varying model as a prediction model, and designing to obtain a model prediction controller according to the prediction model.
3. The method for controlling the prediction track tracking of the mobile robot model based on event triggering according to claim 2, wherein the method is characterized in that a linearization discrete model of the mobile robot is obtained according to a nonlinear kinematic model of the mobile robot, and comprises the following specific steps:
establishing a nonlinear kinematic model of the mobile robot, and carrying out linearization treatment on the nonlinear kinematic model by adopting a Taylor series expansion mode to obtain a linear error model; and discretizing the linear error model by adopting an Euler method to obtain a linearization discrete model of the mobile robot.
4. A mobile robot model predictive trajectory tracking control system based on event triggering, characterized in that the system is capable of executing the control method of any one of claims 1-3, comprising a model construction module, a module parameter setting module, a data processing module and a data judging module, wherein:
the model construction module is used for building a linearization discrete model of the mobile robot according to a nonlinear kinematic model of the mobile robot, taking the linearization discrete model as a prediction model, and obtaining a model prediction controller according to the prediction model design;
the module parameter setting module is used for setting the current initial state of the mobile robot, generating a reference track, discretizing the obtained reference track to obtain a discretized reference track, and selecting a first track point on the discretized reference track at the moment t=k;
the data processing module is used for combining the current initial state of the mobile robot, the first track point and the model predictive controller, and solving to obtain a control input increment sequence of the mobile robot in a control time domain;
updating the set current initial state of the mobile robot by using the first element in the obtained control input increment sequence to obtain a state predicted value of the mobile robot at the next moment;
the data judging module is used for taking the obtained state predicted value at the next moment as a new current state of the mobile robot; setting an event triggering mechanism, and judging whether the new current state meets a triggering condition, wherein:
if so, at the time t=k+1, the model predictive controller combines the new current position state and the next track point on the discretized reference track to obtain a new control input increment sequence of the mobile robot in the control time domain;
if the state prediction value does not meet the preset value, at the time t=k+1, updating the obtained state prediction value by using the first element of the control input increment sequence obtained at the time t=k to obtain a new state prediction value of the mobile robot at the next time;
and repeating the operation until the last track point on the discretized reference track is tracked.
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