CN106292290B - A kind of calm rolling optimization control method of wheeled mobile robot point - Google Patents

A kind of calm rolling optimization control method of wheeled mobile robot point Download PDF

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CN106292290B
CN106292290B CN201610858245.7A CN201610858245A CN106292290B CN 106292290 B CN106292290 B CN 106292290B CN 201610858245 A CN201610858245 A CN 201610858245A CN 106292290 B CN106292290 B CN 106292290B
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mobile robot
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wheeled mobile
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point
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CN106292290A (en
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何德峰
郭晓慧
滕游
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Zhejiang Tgain Technology Co ltd
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Zhejiang University of Technology ZJUT
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

Abstract

A kind of calm rolling optimization control method of the point of wheeled mobile robot, kinetic model based on mobile robot under global coordinate system, utilize State Feedback Type model predictive control method, control constraints and state constraint are integrated in the design of a stability controller, by using variable replacement, final design goes out the smooth stabilization control law expression formula of Mobile Robot Control System, solve the problems, such as that mobile robot puts the stability problem of point stabilization as caused by the nonholonomic constraint of itself, the stability problem of point point stabilization caused by executing the acceleration that system certainly exists and constraint of velocity limitation displacement, and from external environment it is various uncertainty caused by point point stabilization stability problem, while guaranteeing to obtain good moveable robot movement track, more effectively improve movement Rapidity and accuracy.

Description

A kind of calm rolling optimization control method of wheeled mobile robot point
Technical field
The present invention relates to a kind of calm rolling optimization control methods of wheeled mobile robot point.
Background technique
With quickling increase for wheeled mobile robot application range, the real-time and quick response of motion planning and robot control Ability is also being continuously improved, and motion control method receives more and more attention.Wheeled mobile robot motion control Aim at the motion planning and point stabilization for solving the problems, such as mobile robot, wherein point stabilization is to pass through Feedback Control Laws Robot is asymptotic is moved to target point for driving, but wheeled mobile robot usually has nonholonomic constraint limitation, and there is no continuous Smooth control law energy Asymptotic Stabilizing mobile robot is asked so that wheeled mobile robot point stabilization becomes a challenge Topic.It is found by the retrieval of the document to existing wheeled mobile robot point-stabilized control method, wheeled mobile robot point town Locking control method mainly has: discontinuous point stabilization, time-varying point stabilization and mixing point stabilization, but these control methods are being taken turns During formula moveable robot movement Control System Design, all do not account for wheeled mobile robot executing agency it is physical about Beam and the limitation of robot moving section, and these control methods understand complexity, and the convergence rate of control effect is slow.Because In the practical control application of wheeled mobile robot, robot is required to meet the physical constraint of executing agency and movement speed and moves Dynamic section limitation, be exactly in wheeled mobile robot kinetic control system be required to meet system mode and control constraints, and Wheeled mobile robot is a typical nonholonomic constraint control system again, therefore, although wheeled mobile robot point is calm Control research achieves many achievements, but in recent ten years, related scholar and engineering specialist are challenging heavy for this Want problem still carried out it is a large amount of meticulously study and inquire into, with meet current wheeled mobile robot quick motion control for Effectively, an urgent demand of mobile robot high speed, high-precision motion control is easily realized.
Summary of the invention
In order to overcome, the understanding of existing wheeled mobile robot point-stabilized control method is complicated, realizes control that is difficult, calculating Amount processed is unsatisfactory for the deficiency of robot system constraint requirements, and the present invention provides a kind of control for understanding that intuitive, design is simple, calculating Amount meets the calm rolling optimization control method of wheeled mobile robot point of robot system constraint requirements.
The technical solution adopted by the present invention to solve the technical problems is:
A kind of calm rolling optimization control method of wheeled mobile robot point, the control method include the following steps:
1) three rank kinetic model of wheeled mobile robot motion process continuous time, is established, referring to formula (1):
Wherein, variable t indicates the time；x1(t) and x2(t) t moment wheeled mobile robot is illustrated respectively in rectangular co-ordinate The position coordinates of X-direction and Y-direction in system；x3(t) orientation in t moment wheeled mobile robot in rectangular coordinate system is indicated Angle；u1(t) and u2(t) linear velocity and angular speed of t moment wheeled mobile robot are illustrated respectively in；Consider modular form (1), it is fixed Status Bar vector x=[x of adopted wheeled mobile robot1 x2 x3]TWith control column vector u=[u1 u2]T, wherein symbol T table Show the transposition of vector；
2), consider modular form (1), define the expression function of dominant vector u, referring to formula (2):
Wherein, gijIt is unknown parameter, i=1,2, j=1,2,3；MatrixFormula (2) are substituted into mould Pattern (1) obtains formula (3):
3), with sampling period TsDiscrete time conversion is done to modular form (3), obtains wheeled mobile robot discrete time three Rank kinetic model, referring to formula (4):
And modular form (4) is abbreviated as formula (5):
X (k+1)=f (x (k), Gx (k)) (5)
Wherein, f (x (k), Gx (k))=[f1(x(k),Gx(k))f2(x(k),Gx(k))f3(x(k),Gx(k))]T, f1(x (k), Gx (k))=x1(k)+Ts[g11x1(k)+g12x2(k)+g13x3(k)]cosx3(k), f2(x (k), Gx (k))=x2(k)+Ts [g11x1(k)+g12x2(k)+g13x3(k)]sinx3(k), f3(x (k), Gx (k))=x3(k)+Ts[g21x1(k)+g22x2(k)+ g23x3(k)]；
4), consider modular form (5), establish the dynamic prediction model of wheeled mobile robot, referring to formula (6):
X (k+j+1 | k)=f (x (k+j | k), Gx (k+j | k)), j=0,1 ..., N-1 (6)
Wherein, x (k+j | k) indicates prediction of the Control of Wheeled Mobile Robots system in moment k to future time instance k+j state Vector；Positive integer N is predicted time window；The boundary constraint for considering the state and control amplitude of wheeled mobile robot, referring to Formula (7) and (8):
Wherein,xWithuThe lower bound of state and control is respectively indicated,WithRespectively indicate the upper bound of state and control；
5), consider formula (6), define a quadratic model object function, referring to formula (9):
Wherein, Q and R is the weighting matrix of positive definite, is respectively intended to punishment state variable and controls variable；When detecting current k The state x (k) at quarter defines an Optimal Control Problem, referring to formula (10):
Wherein, matrix G is decision variable；Symbol " s.t. " indicates constraint；Equation x (k | k)=x (k) is known as optimization problem Primary condition；Using numerical optimisation algorithms solving optimization problem (10), Optimal matrix value G is obtained*And optimal control codes, referring to formula (11):
Control amount (11) is acted on into wheeled mobile robot, after next sampling instant k+1 arrival, detects wheeled shifting The motion state x (k+1) of mobile robot, and with the primary condition of state update Optimal Control Problem (10), then optimization is counted Calculate the Optimal matrix value G at current time*And optimal control codes, in cycles, until wheeled mobile robot moves to target original Point is set to only.
Technical concept of the invention are as follows: require for wheeled mobile robot in nonholonomic constraint and state and control constraints Under the conditions of realize point a point stabilization problem, based on three rank kinetic models of wheeled mobile robot, pass through define machine People controls input function and three rank kinetic model of discrete time, the Optimal Control Problem of limited prediction time is established, in conjunction with rolling Dynamic optimal control principle, is calculated the optimal control input quantity of parameter at every sampling moment, realizes wheeled mobile robot Point point stabilization.The advantages of design method of the present invention is to understand that simple, versatile and control amount meets wheel type mobile machine Device people's restrict.
The main execution part of the present invention runs implementation on wheeled mobile robot motion control computer.This method application Process can be roughly divided into 3 stages:
1, it parameter setting: is imported in interface in parameter, input sample cycle Ts, state and control lower boundxWithu, state With the upper bound of controlWithPredicted time window N, weighting matrices Q and weighted matrix R are counted after input parameter confirmation by control Calculation machine, which will be arranged in data feeding computer storage unit RAM, to be saved；
2, offline debugging: clicking the Debug button in configuration interface, and control system enters the debugging of controller off-line simulation Stage adjusts weighting matrices Q and R in configuration interface, observes wheeled mobile robot state variable, that is, position and deflection Control effect thereby determines that one group of weighting matrix value that can well realize wheeled mobile robot point point stabilization；Weighting matrices Q With the value rule of R: Q is three rank positive definite diagonal matrix, and R is second order positive definite diagonal matrix；The adjustment rule of weighting matrices Q and R: The value for increasing matrix Q will shorten the adjustment time of wheeled mobile robot condition responsive, but increases and shorten wheeled mobile robot The overshoot and control amount of people's condition responsive, on the contrary, reducing the value of matrix Q for the condition responsive of gentle wheeled mobile robot Speed and control amount, but extend the adjustment time of wheeled mobile robot condition responsive；The value of increase matrix R will increase wheeled The adjustment time of mobile robot condition responsive, but shorten the overshoot and control amount of wheeled mobile robot condition responsive, phase Instead, the value for reducing matrix R will increase the condition responsive speed and control amount of wheeled mobile robot, but shorten wheel type mobile machine Therefore the adjustment time of device people's condition responsive when reality debugs weighting matrices Q and R, should weigh wheeled mobile robot state and ring The comprehensive performance between overshoot, adjustment time, damping effect and control amount answered；
3, on-line operation: clicking configuration interface " RUN " button, starting wheeled mobile robot motion control computer CPU reads sampling period Ts, state and control lower boundxWithu, state and control the upper boundWithPredicted time window N, add Weight matrix Q and R, and " wheeled mobile robot point point stabilization program " is executed, pass through on-line measurement wheeled mobile robot Position and azimuth, control enter the linear velocity and angular speed of wheeled mobile robot, realize wheeled mobile robot to target The point point stabilization of origin, when reaching in next sampling period, the physical location of on-line measurement wheeled mobile robot and side Parallactic angle repeats entire implementation procedure later, in cycles, realizes wheeled mobile robot to the point point stabilization of target point.
A full set of wheeled mobile robot point-stabilized control method can be at Control of Wheeled Mobile Robots system configuration interface Upper completion, this process can refer to the application of this specification examples provided hereinafter.It is calm with Conventional drum mobile robot point Control method is compared, and the maximum feature of the calm rolling optimization control method of the wheeled mobile robot point that the present invention provides is to control The nonholonomic constraint and state and control constraints of wheeled mobile robot are taken explicitly into account in device design process processed, and are pre-designed The function of Control of Wheeled Mobile Robots variable, to improve the safety of the calm movement of wheeled mobile robot point, quickly Property and stability.Implementation method illustrates practical effect of the invention by taking wheeled mobile robot origin point stabilization as an example in detail below Fruit, but application range of the invention is not limited with the wheeled mobile robot origin point stabilization in the present embodiment.
Beneficial effects of the present invention are mainly manifested in: 1, design is simple, is readily appreciated that, is versatile；2, in wheel type mobile Nonholonomic constraint and state and control constraints can be clearly handled in robot movement-control system's design process, and by preparatory The control variable function for designing wheeled mobile robot improves the safety, quickly of the calm movement of wheeled mobile robot point Property and stability.
Detailed description of the invention
Fig. 1 is schematic diagram of the wheeled mobile robot in X-Y plane path curves.
Fig. 2 is the schematic diagram of the change of line speed curve of wheeled mobile robot.
Fig. 3 is the schematic diagram of the angular speed change curve of wheeled mobile robot.
Specific embodiment
The invention will be further described below in conjunction with the accompanying drawings.
Referring to Fig.1~Fig. 3, a kind of calm rolling optimization control method of wheeled mobile robot point, the control method packet Include following steps:
1) three rank kinetic model of wheeled mobile robot motion process continuous time, is established, referring to formula (1):
Wherein, variable t indicates the time；x1(t) and x2(t) t moment wheeled mobile robot is illustrated respectively in rectangular co-ordinate The position coordinates of X-direction and Y-direction in system；x3(t) orientation in t moment wheeled mobile robot in rectangular coordinate system is indicated Angle；u1(t) and u2(t) linear velocity and angular speed of t moment wheeled mobile robot are illustrated respectively in；Consider modular form (1), it is fixed Status Bar vector x=[x of adopted wheeled mobile robot1 x2 x3]TWith control column vector u=[u1 u2]T, wherein symbol T table Show the transposition of vector；
2), consider modular form (1), define the expression function of dominant vector u, referring to formula (2):
Wherein, gijIt is unknown parameter, i=1,2, j=1,2,3；MatrixFormula (2) are substituted into mould Pattern (1) obtains formula (3):
3), using computer control principle, with sampling period TsDiscrete time conversion is done to modular form (3), is obtained wheeled Three rank kinetic model of mobile robot discrete time, referring to formula (4):
And modular form (4) is abbreviated as formula (5):
X (k+1)=f (x (k), Gx (k)) (5)
Wherein, f (x (k), Gx (k))=[f1(x(k),Gx(k)) f2(x(k),Gx(k)) f3(x(k),Gx(k))]T, f1 (x (k), Gx (k))=x1(k)+Ts[g11x1(k)+g12x2(k)+g13x3(k)]cosx3(k), f2(x (k), Gx (k))=x2(k)+ Ts[g11x1(k)+g12x2(k)+g13x3(k)]sinx3(k), f3(x (k), Gx (k))=x3(k)+Ts[g21x1(k)+g22x2(k)+ g23x3(k)]；
4), consider modular form (5), establish the dynamic prediction model of wheeled mobile robot, referring to formula (6):
X (k+j+1 | k)=f (x (k+j | k), Gx (k+j | k)), j=0,1 ..., N-1 (6)
Wherein, x (k+j | k) indicates prediction of the Control of Wheeled Mobile Robots system in moment k to future time instance k+j state Vector；Positive integer N is prediction time domain；The boundary constraint for considering the state and control amplitude of wheeled mobile robot, referring to formula (7) (8):
Wherein,xWithuThe lower bound of state and control is respectively indicated,WithRespectively indicate the upper bound of state and control；
5), consider formula (6), define a quadratic model object function, referring to formula (9):
Wherein, Q and R is the weighting matrix of positive definite, is respectively intended to punishment state variable and controls variable；When detecting current k The state x (k) at quarter defines an Optimal Control Problem, referring to formula (10):
Wherein, matrix G is decision variable；Symbol " s.t. " indicates constraint；Equation x (k | k)=x (k) is known as optimization problem Primary condition；Using numerical optimisation algorithms solving optimization problem (10), Optimal matrix value G is obtained*And optimal control codes, referring to formula (11):
Control amount (11) is acted on into wheeled mobile robot, after next sampling instant k+1 arrival, detects wheeled shifting The motion state x (k+1) of mobile robot, and with the primary condition of state update Optimal Control Problem (10), then optimization is counted Calculate the Optimal matrix value G at current time*And optimal control codes, in cycles, until wheeled mobile robot moves to target original Point is set to only.
This example is the calm process of wheeled mobile robot origin, and specific operation process is as follows:
1, in parameter setting interface, input sample cycle TsThe lower bound of=0.25s, statex=[- 10-10 0]TWith it is upper BoundaryThe lower bound of controlu=[- 0.47-3.77]TThe upper bound andPredicted time window N= 22, weighting matrices Q and R.
2, the Debug button is clicked on configuration interface and enter Debugging interface, start wheeled mobile robot motion control meter The CPU of calculation machine calls " the controller calculation procedure " that weaves in advance to solve controller, and specific calculating process is as follows: according to given Weighting matrices Q and R, solving optimization control problem (10), obtain one group of optimal solution G of parameter G*, define wheeled mobile robot People according to the value of Q and R and adjusts rule in an optimal controller (11) of k moment linear velocity and angular speed, more wheeled Position of mobile robot and azimuth response results and control amount calculated result, debugging Q and R are obtained
Debugging result is saved in computer storage unit RAM；
3, configuration interface " RUN " button is clicked, the CPU of starting Control of Wheeled Mobile Robots computer reads sampling week Phase Ts, state and control lower boundxWithu, state and control the upper boundWithPredicted time window N, weighting matrices Q and R, and It executes " wheeled mobile robot point point stabilization program ", by the position and azimuth of on-line measurement wheeled mobile robot, Control enters the linear velocity and angular speed of wheeled mobile robot, realizes that wheeled mobile robot calms to the point of target point and controls System, when reaching in next sampling period, the physical location of on-line measurement wheeled mobile robot and azimuth repeat whole later A implementation procedure realizes wheeled mobile robot to the point point stabilization of target point in cycles.
Described above is the wheeled mobile robot pair for the shown excellent performance of one embodiment that the present invention provides The point point stabilization effect of target point.It may be noted that above-described embodiment is used to illustrate the present invention, rather than to the present invention It is limited, within the spirit of the invention and the scope of protection of the claims, to any modification that the present invention makes, both falls within this The protection scope of invention.

Claims (1)

  1. The rolling optimization control method 1. a kind of wheeled mobile robot point is calmed, it is characterised in that: the control method includes such as Lower step:
    1) three rank kinetic model of wheeled mobile robot motion process continuous time, is established, referring to formula (1):
    Wherein, variable t indicates the time；x1(t) and x2(t) t moment wheeled mobile robot is illustrated respectively in rectangular coordinate system The position coordinates of X-direction and Y-direction；x3(t) azimuth in t moment wheeled mobile robot in rectangular coordinate system is indicated；u1 (t) and u2(t) linear velocity and angular speed of t moment wheeled mobile robot are illustrated respectively in；Consider modular form (1), definition wheel Status Bar vector x=[x of formula mobile robot1 x2 x3]TWith control column vector u=[u1 u2]T, wherein symbol T indicate to The transposition of amount；
    2), consider modular form (1), define the expression function of dominant vector u, referring to formula (2):
    Wherein, gijIt is unknown parameter, i=1,2, j=1,2,3；MatrixFormula (2) are substituted into modular form (1) formula (3) are obtained:
    3), with sampling period TsDiscrete time conversion is done to modular form (3), it is dynamic to obtain three rank of wheeled mobile robot discrete time Mechanical model, referring to formula (4):
    And modular form (4) is abbreviated as formula (5):
    X (k+1)=f (x (k), Gx (k)) (5)
    Wherein, f (x (k), Gx (k))=[f1(x(k),Gx(k)) f2(x(k),Gx(k)) f3(x(k),Gx(k))]T, f1(x (k), Gx (k))=x1(k)+Ts[g11x1(k)+g12x2(k)+g13x3(k)]cosx3(k), f2(x (k), Gx (k))=x2(k)+Ts [g11x1(k)+g12x2(k)+g13x3(k)]sinx3(k), f3(x (k), Gx (k))=x3(k)+Ts[g21x1(k)+g22x2(k)+ g23x3(k)]；
    4), consider modular form (5), establish the dynamic prediction model of wheeled mobile robot, referring to formula (6):
    X (k+j+1 | k)=f (x (k+j | k), Gx (k+j | k)), j=0,1 ..., N-1 (6)
    Wherein, x (k+j | k) indicates pre- direction finding of the Control of Wheeled Mobile Robots system in moment k to future time instance k+j state Amount；Positive integer N is predicted time window；The boundary constraint for considering the state and control amplitude of wheeled mobile robot, referring to formula (7) and (8):
    Wherein,xWithuThe lower bound of state and control is respectively indicated,WithRespectively indicate the upper bound of state and control；
    5), consider formula (6), define a quadratic model object function, referring to formula (9):
    Wherein, Q and R is the weighting matrix of positive definite, is respectively intended to indicate punishment state variable and control variable；When detecting current k The state x (k) at quarter defines an Optimal Control Problem, referring to formula (10):
    Wherein, matrix G is decision variable；Symbol " s.t. " indicates constraint；Equation x (k | k)=x (k) be known as optimization problem just Beginning condition；Using numerical optimisation algorithms solving optimization problem (10), Optimal matrix value G is obtained*And optimal control codes, referring to formula (11):
    Control amount (11) is acted on into wheeled mobile robot, after next sampling instant k+1 arrival, detects wheeled moving machine The motion state x (k+1) of device people, and with the primary condition of state update Optimal Control Problem (10), then optimization calculates and works as The Optimal matrix value G at preceding moment*And optimal control codes, in cycles, until wheeled mobile robot moves to target point position It is set to only.
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CN108839026B (en) * 2018-07-19 2021-04-06 浙江工业大学 Visual servo tracking prediction control method for mobile robot
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