CN104298113A - Self-adaptive fuzzy balance controller for two-wheeled robot - Google Patents
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Abstract
The invention relates to a self-adaptive fuzzy balance controller for a two-wheeled robot. A design method comprises the following steps that the two-wheeled robot is balanced on the ground, a main engine gyroscope is turned on, and an initial voltage is generated; a voltage excursion quantity, the inclination angle and the position difference and the speed difference of a left wheel and a right wheel are calculated and used as input variables of the self-adaptive fuzzy controller; output of the gyroscope is controlled to generate new voltage, and output of a motor is controlled to generate a new inclination angle; the position difference and the speed difference of the left wheel and the right wheel are recalculated, so that output of the motor is controlled to generate a new angular speed, and the angle is recalculated; control over speed coding on the gyroscope and the motor is continued through the self-adaptive fuzzy controller, and power output is equally conducted on the motor after addition; the steps are repeated, so that the system becomes stable. A traditional control method is poor in dynamic response and anti-jamming capability. The self-adaptive fuzzy balance controller not only can restrain external disturbance and adapt to the influences of environmental changes and parameters changes of the system, but also can effectively eliminate the influences of modeling errors and the like.
Description
Technical field
The present invention relates to the balance control field of coaxial two wheels robot, particularly a kind of coaxial two wheels robot adaptive fuzzy balance controller.
Technical background
Robot serves more and more important effect in modern society, and its product has been widely used all in the field such as industry, agricultural, medical science, military affairs, and the design of its controller is then one of gordian technique of manufacturing machine people.Robot system belongs to the nonlinear system of more complicated, and be easily subject to the impact of self and more extraneous uncertain factors, therefore the design of its controller just becomes a difficult problem.And double-wheel self-balancing robot structure is simple, be convenient to analyze, and be a kind of non-linear, multivariate, essence are unstable, the kinetic control system of strong coupling.Therefore, research double-wheel self-balancing robot to the Controller gain variations of whole robot field all tool be of great significance, be also simultaneously the ideal platform checking various control algolithm.At present, about the research and development typical case of coaxial two wheels robot balance method has: Chen Shaobin etc. propose a kind of optimal state feed-back control method that mobile robot trace is followed the tracks of for 2009, adopt Kalman filter to carry out state estimation to the system state equation with white Gaussian noise, propose a kind of optimal state feed-back control strategy based on Liapunov stability.Give the adaptive algorithm of compensated input signal interference.Section is learned and within superfine 2013, is proposed a kind of fuzzy evolution type POLE PLACEMENT USING (FEPP) control method. and adopt Lagrangian method to carry out the Dynamic Modeling of double-wheel self-balancing robot, by it is carried out Linearization with small deviations in equilibrium position, obtain system linearity nominal model.FEPP controller is devised to this 6 rank under-actuated systems, achieves dynamic stabilization and the travelling control of double-wheel self-balancing robot respectively.Mao Huan etc. propose a kind of reliability improved FOSM method for Double-wheel self-balancing robot in 2014, detection system inclination angle is in the vertical direction come by obliquity sensor, the pid algorithm after improving is adopted to implement to control, utilize PWM module to export and coordinate driving circuit, the motion of adjustment direct current generator, can make system reach mobile equilibrium.Li Zhi proposes a kind of double-wheel self-balancing robot LQR-FUZZY ALGORITHMS FOR CONTROL for superfine 2014, first the feedback matrix utilizing LQR method to generate is to construct fusion function, reduced the input dimension of system by fusion function, then by fuzzy controller, system is controlled.Emulation and experimental result show, adopt this kind of control strategy both can ensure robot stablizing, again can control to assigned address and angle.
Summarize the system of above patented technology or document introduction, coaxial two wheels robot self-balance method is broadly divided into traditional control method and intelligent control method: traditional control method mainly adopts PID method, feedback of status and Method of Pole Placement etc., the linear known system of main process; Because double-wheel self-balancing robot has strong nonlinearity, model out of true, control effects after therefore carrying out linearization to robot model, will be caused can not to reach optimum; And traditional control method dynamic response is undesirable, antijamming capability is poor.Based Intelligent Control mainly adopts fuzzy control, non-linear unknown system can be processed, do not require to set up system mathematic model, dynamic response, antijamming capability increase, but the control accuracy of fuzzy control method depends on the foundation of fuzzy rule base, raising number of fuzzy rules along with controlling extent accuracy is that progression increases, and the effect of control system is very large by the impact of expertise.
Summary of the invention
For the traditional control method such as PID, POLE PLACEMENT USING, dynamic response is undesirable, antijamming capability is poor, and control effects can not reach optimum; Fuzzy control too relies on expertise, and fuzzy rule is the problem that progression increases with control accuracy; The self-adaptation control method that the present invention adopts, be based upon on the basis of unknown system, by the parameter of the control law of varitrol in real time own, adapt to the impact of external environment change, the Parameters variation of system own, external interference etc., make whole system can by a certain performance index operation control in the best condition.It not only can suppress external interference, and the impact of the change that conforms, the Parameters variation of system own, to a certain extent, can also eliminate the impacts such as model errors effectively.Therefore, the present invention adopts self-adaptation control method design robot self-equilibrating controller, can improve self-equilibrating performance and the antijamming capability of robot.
The present invention just selects coaxial two wheels robot as controlled model, then the derivation of equation of state is carried out with the mechanical model of this coaxial two wheels robot, and the design of fuzzy controller is carried out according to the equation of state of coaxial two wheels robot, the present invention derives a self-adaptation law, this self-adaptation law mainly allows fuzzy controller proposed by the invention can be similar to a desirable controller, system can be reviewed respond and allow error convergence, to guarantee the stability of whole closed loop system.Each variate-value that this adaptive fuzzy controller will export according to coaxial two wheels robot, controls left and right servo motor and exports different power (speed) or rotation direction to revise car body position, and then reach the effect of vertical balanced control.
The invention has the beneficial effects as follows:
Adaptive fuzzy controller designed by the present invention can allow coaxial two wheels robot continue in an erect condition to keep balance, and its output responds and balance usefulness is all better than typical PID controller.
Accompanying drawing explanation
Fig. 1 is coaxial two wheels robot adaptive fuzzy balance controller process flow diagram of the present invention.
Fig. 2 is coaxial two wheels robot gyroscope angle of inclination definition figure of the present invention.
Fig. 3 is coaxial two wheels robot balance method schematic diagram of the present invention.
Fig. 4 is adaptive fuzzy balance control system Organization Chart of the present invention.
Fig. 5 is the former piece portion ownership function of adaptive fuzzy controller of the present invention.
Fig. 6 is the coaxial two wheels robot angle of inclination comparison diagram of application self-adapting fuzzy controller of the present invention and PID controller.
Embodiment
Below in conjunction with accompanying drawing, coaxial two wheels robot adaptive fuzzy balance controller of the present invention is elaborated further.
Fig. 1 is coaxial two wheels robot balance control flow chart, and coaxial two wheels robot is equilibrated at ground.When coaxial two wheels robot beat, open main frame gyroscope, an initial voltage can be produced at the beginning after gyroscope drift, the mode that this parameter first calculates through Gyro scale is fixedly gone out side-play amount, then the problem that angle of inclination solves angular error is simultaneously calculated, then alternate position spike and the velocity contrast of left and right wheels is calculated, then derivation self-adaptation law, design adaptive fuzzy controller, and control gyroscope and motor with adaptive fuzzy controller, the power stage of motor is controlled through adding the General Logistics Department.After motor action, export the angular velocity producing and make new advances via computing, then recalculate angle, then control gyroscope and motor rotary speed coding being done to adaptive fuzzy controller is continued, add the General Logistics Department equally to export motor power, so go round and begin again, this system just can be allowed to tend towards stability.
Coaxial two wheels robot balance control flow concrete steps are as follows:
Step one: coaxial two wheels robot is equilibrated at ground
Step 2, open main frame gyroscope read initial voltage
When coaxial two wheels robot beat, open main frame gyroscope, an initial voltage can be produced after gyroscope drift at the beginning
Step 3, calculating voltage side-play amount calculate angle of inclination
As shown in (1) formula, get the level of gyroscope output voltage values mean value in the hope of gyroscope its output voltage when static at that time, wherein
,
,
,
for getting arbitrarily a certain gyroscope output voltage values,
,
for a certain its mean value of gyroscope output voltage values;
As shown in (2) formula, try to achieve its average side-play amount after tried to achieve level is deducted 2.5V, wherein
for actual output voltage side-play amount.Afterwards, each gyroscope signal is come in later, and deducting side-play amount is used as compensation.
，
(1)
(2)
Step 4, the velocity contrast calculating left and right wheels and alternate position spike
G inside Fig. 2
1for the central shaft of NXT, be also central shaft selected in gyroscope, Oa and Ob is respectively the central point (center of circle) of the right and left circular wheel, and O1 is the central point of the straight line that Oa and Ob even rises simultaneously, is also G simultaneously
1the center of gravity that central axis is located is then the situation of forward lean or layback in addition, G
2, G
3g
1axle center during skew,
for the angle leaning forward or swing back, S
1be two wheels strength forward, S
2be two wheels strength backward.Coaxial two wheels robot is in equilibrium at ground at the beginning, and wheel there is no rotation, does not also have angle of inclination, so by G
2, G
3be set to zero as (3) formula, S
1, S
2also be set to zero as (4) formula, after coaxial two wheels robot makes action, just can produce angle of inclination, wherein the computing method at pitch angle as shown in Equation (5)
(3)
(4)
(5)
If need work angle within ± 20 °, then the computing method at its pitch angle can be reduced to
(6)
This simplifies the error range calculated and is less than 2%.So can remove from and calculate arcsin function (sin
-1) trouble, and increase the speed of program computation.
As shown in Figure 3, requiring under the consistent and simple prerequisite of Controller gain variations mode of two wheel speeds, can be learnt by sport dynamics, mobile platform base be applied to robot the power force that spend to by two-wheeled and U, if the output taken turns adds the error of two-wheeled alternate position spike wherein, another takes turns the error cutting two-wheeled alternate position spike, so makes a concerted effort to be still original power, can not destroy the moment required for original balance method.Output strength again due to two-wheeled is different, can cause velocity contrast,
control the synchronous velocity contrast formula of two-wheeled as shown in (7) formula;
control the synchronous alternate position spike formula of two-wheeled as shown in (8) formula:
(7)
Wherein
: right wheel speed;
: revolver rotating speed
: two-wheeled go out power and
(8)
Wherein
: rightly take turns position;
: revolver position
The derivation of step 5, self-adaptation law and adaptive fuzzy controller design
First, the derive process of self-adaptation law of the present invention is as follows:
Generally, the desirable controller for coaxial two wheels robot can be expressed as:
（9）
Wherein
for unknown vector and
for unknown matrix,
for the output of controlled system,
for the output of controller,
for state vector.But due to
,
the unknown, desirable controller cannot realize;
Desirable controller (9) is expressed as:
（10）
We are by designed fuzzy controller
and the desirable controller of formula (10)
together substitute in the non-linear controlled system in multiple-input and multiple-output 2 rank of formula (9), in order to replace to fall original controller, can obtain
Can obtain after transposition
（11）
Suppose the fuzzy controller that existence one is best
, this fuzzy controller can be expressed as form:
（12）
Suppose
（13）
Wherein parameter
,
with
by we are supposed obtainable optimization control parameter, this parameter will make the best fuzzy controller supposing to exist
with desirable controller
between there is a minimum approximate error
.Therefore, we can ensure the stability of system.
Then, to design the process of adaptive fuzzy controller as follows in the present invention:
As Fig. 4, according to the self-adaptation law derived above, the present invention designs a fuzzy controller
in order to approximate ideal controller
, this fuzzy controller
can be expressed as
,
for the input of fuzzy controller, this input be according to output voltage (
), angle of inclination (
), the alternate position spike of left and right wheels (
), the synchronous velocity contrast of two-wheeled (
) etc. four variablees and expectation value (
,
,
,
) between error and error rate (
,
,
,
), acquired by, because coaxial two wheels robot belongs to the system of a multiple-input and multiple-output, this is difficult to design the fuzzy rule in fuzzy controller by causing us, therefore the present invention rule of thumb and the actual output response of coaxial two wheels robot, output errors all for coaxial two wheels robot is done an integration, and is defined as
, and the rate of change of sum of the deviations
then be defined as
, the input of fuzzy controller is described below:
Wherein
every output gain of coaxial two wheels robot, be the present invention rule of thumb and the actual output response institute of coaxial two wheels robot given,
for output voltage (
) gain,
for angle of inclination (
) gain,
for left and right wheels alternate position spike (
) gain,
for the synchronous velocity contrast of two-wheeled (
) gain;
be then the output of fuzzy controller, namely fuzzy controller according to input two-wheeled balance car error (
) and error change (
) the control signal revised, this control signal will the output of the left and right servo motor of impact, the output of fuzzy controller
be expressed as follows:
The fuzzy rule of the present invention ordered by adaptive fuzzy controller is as shown in table 1, wherein P representative just (Positive), N representative negative (Negative), Z represents zero (Zero), and in adaptive fuzzy controller, the rule of former piece portion ownership function as shown in Figure 5.
The fuzzy rule of table 1 adaptive fuzzy controller
Designed adaptive fuzzy controller and a typical PID controller are distinguished practical application on coaxial two wheels robot by the present invention, while coaxial two wheels robot performs balance control, the taking-up response results of two controllers and the balance usefulness of coaxial two wheels robot compare, and its comparative result is as follows:
Adaptive fuzzy controller and PID controller are revised according to every error of coaxial two wheels robot, after the control of adaptive fuzzy controller and PID controller, the body sway angle of coaxial two wheels robot more as shown in Figure 6, x-axis represents the time (ms), y-axis represents the inclined degree of coaxial two wheels robot vehicle body, the angle of inclination of the coaxial two wheels robot that red data controls for PID controller, the angle of inclination of the coaxial two wheels robot that blue data then controls for adaptive fuzzy controller.
As shown in Figure 6, the coaxial two wheels robot controlled by adaptive fuzzy controller, progressively enters steady state (SS) at the inclined degree of 4 seconds rear along with increasing progressively of time, and the body sway degree of coaxial two wheels robot all remains on
between; Review and control controlled coaxial two wheels robot by PID, when the 8th second, the 15th second and the 19th second, the body sway degree of coaxial two wheels robot has the sign exploded suddenly, therefore the present invention can learn, adaptive fuzzy controller proposed by the invention, for controlling coaxial two wheels robot balanced capacity in an erect condition, not only more typical PID controller is stable, and counterbalance effect is also better than typical PID controller.
Claims (4)
1. coaxial two wheels robot adaptive fuzzy balance controller, is characterized in that, comprises the following steps:
Step one: coaxial two wheels robot is equilibrated at ground (1-1);
Step 2, open main frame gyroscope read initial voltage (1-2): when coaxial two wheels robot beat, open main frame gyroscope, an initial voltage can be produced after gyroscope drift at the beginning;
Step 3, calculating voltage side-play amount calculate angle of inclination (1-3): the mode that this parameter first calculates through Gyro scale is fixedly gone out voltage deviation, then calculates the problem that angle of inclination solves angular error simultaneously;
Step 4, the velocity contrast calculating left and right wheels and alternate position spike (1-4);
The derivation of step 5, self-adaptation law and adaptive fuzzy controller design (1-5);
Step 6, control motor and gyrostatic output (1-6): control gyroscope and motor with adaptive fuzzy controller, control the power stage of motor through adding the General Logistics Department;
Step 7: produce new angular velocity (1-7): after motor action, the angular velocity producing and make new advances is exported via computing, recalculate angle again, then control gyroscope and motor rotary speed coding being done to adaptive fuzzy controller is continued, add the General Logistics Department equally to export motor power, so go round and begin again, this system just can be allowed to tend towards stability.
2. method according to claim 1: the mode that described step 3, calculating voltage side-play amount calculate angle of inclination is:
As shown in (1) formula, get the level of gyroscope output voltage values mean value in the hope of gyroscope its output voltage when static at that time, wherein
,
,
,
for getting arbitrarily a certain gyroscope output voltage values,
,
for a certain its mean value of gyroscope output voltage values;
As shown in (2) formula, try to achieve its average side-play amount after tried to achieve level is deducted 2.5V, wherein
for actual output voltage level; Afterwards, each gyroscope signal is come in later, and deducting side-play amount is used as compensation;
，
(1)
(2) 。
3. method according to claim 1: described step 4, the calculating velocity contrast of left and right wheels and the mode of alternate position spike are:
G
1for the central shaft of NXT, be also central shaft selected in gyroscope, Oa and Ob is respectively the central point (center of circle) of the right and left circular wheel, and O1 is the central point of the straight line that Oa and Ob even rises simultaneously, is also G simultaneously
1the center of gravity that central axis is located is then the situation of forward lean or layback in addition, G
2, G
3g
1axle center during skew,
for the angle leaning forward or swing back, S
1be two wheels strength forward, S
2be two wheels strength backward; Coaxial two wheels robot is in equilibrium at ground at the beginning, and wheel there is no rotation, does not also have angle of inclination, so by G
2, G
3be set to zero as (3) formula, S
1, S
2also be set to zero as (4) formula, after coaxial two wheels robot makes action, just can produce angle of inclination, wherein the computing method at pitch angle as shown in Equation (5)
(3)
(4)
(5)
If need work angle within ± 20 °, then the computing method at its pitch angle can be reduced to
(6)
This simplifies the error range calculated and is less than 2%; So can remove from and calculate arcsin function (sin
-1) trouble, and increase the speed of program computation;
Requiring under the consistent and simple prerequisite of Controller gain variations mode of two wheel speeds, can be learnt by sport dynamics, mobile platform base be applied to robot the power force that spend to by two-wheeled and U, if the output taken turns adds the error of two-wheeled alternate position spike wherein, another takes turns the error cutting two-wheeled alternate position spike, so make a concerted effort to be still original power, the moment required for original balance method can not be destroyed; Output strength again due to two-wheeled is different, can cause velocity contrast,
control the synchronous velocity contrast formula of two-wheeled as shown in (7) formula;
control the synchronous alternate position spike formula of two-wheeled as shown in (8) formula;
(7)
Wherein
: right wheel speed;
: revolver rotating speed
: two-wheeled go out power and
(8)
Wherein
: rightly take turns position;
: revolver position.
4. method according to claim 1: the mode of the derivation of described step 5, self-adaptation law and adaptive fuzzy controller design is:
First, the process of derivation self-adaptation law is as follows:
Generally, the desirable controller for coaxial two wheels robot can be expressed as:
（9）
Wherein
for unknown vector and
for unknown matrix,
for the output of controlled system,
for the output of controller,
for state vector; But due to
,
the unknown, desirable controller cannot realize;
Desirable controller (9) is expressed as:
（10）
We are by designed fuzzy controller
and the desirable controller of formula (10)
together substitute in the non-linear controlled system in multiple-input and multiple-output 2 rank of formula (9), in order to replace to fall original controller, can obtain
Can obtain after transposition
（11）
Suppose the fuzzy controller that existence one is best
, this fuzzy controller can be expressed as form:
（12）
Suppose
（13）
Wherein parameter
,
with
by we are supposed obtainable optimization control parameter, this parameter will make the best fuzzy controller supposing to exist
with desirable controller
between there is a minimum approximate error; Therefore, we can ensure the stability of system;
Then, the process designing adaptive fuzzy controller is as follows:
According to the self-adaptation law derived above, design a fuzzy controller
in order to approximate ideal controller
, this fuzzy controller
can be expressed as
,
for the input of fuzzy controller, this input be according to output voltage (
), angle of inclination (
), the alternate position spike of left and right wheels (
), the synchronous velocity contrast of two-wheeled (
) etc. four variablees and expectation value (
,
,
,
) between error and error rate (
,
,
,
), acquired by, because coaxial two wheels robot belongs to the system of a multiple-input and multiple-output, this is difficult to design the fuzzy rule in fuzzy controller by causing us, therefore rule of thumb and the actual output response of coaxial two wheels robot, output errors all for coaxial two wheels robot is done an integration, and is defined as
, and the rate of change of sum of the deviations
then be defined as
, the input of fuzzy controller is described below:
Wherein
every output gain of coaxial two wheels robot, be rule of thumb and the actual output response institute of coaxial two wheels robot given,
for output voltage (
) gain,
for angle of inclination (
) gain,
for left and right wheels alternate position spike (
) gain,
for the synchronous velocity contrast of two-wheeled (
) gain;
be then the output of fuzzy controller, namely fuzzy controller according to input two-wheeled balance car error (
) and error change (
) the control signal revised, this control signal will the output of the left and right servo motor of impact, the output of fuzzy controller
be expressed as follows:
。
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| CN105159294B (en) * | 2015-09-01 | 2019-01-18 | 深圳力子机器人有限公司 | For the design method of fork truck fuzzy logic motion controller |
| CN107643760A (en) * | 2017-08-24 | 2018-01-30 | 齐鲁工业大学 | A kind of coaxial two wheels robot balance controller based on LQR algorithms |
| CN109507871A (en) * | 2018-12-11 | 2019-03-22 | 广东工业大学 | Pid parameter setting method and product for the control of two-wheeled balance car car body balance |
| CN109507871B (en) * | 2018-12-11 | 2022-03-25 | 广东工业大学 | PID parameter setting method and product for two-wheel balance vehicle body balance control |
| CN109407689A (en) * | 2018-12-19 | 2019-03-01 | 四川大学 | Fuzzy control method, device and the balanced robot of balanced robot |
| CN110160527A (en) * | 2019-05-06 | 2019-08-23 | 安徽红蝠智能科技有限公司 | A kind of Mobile Robotics Navigation method and apparatus |
| CN110160527B (en) * | 2019-05-06 | 2020-08-28 | 安徽红蝠智能科技有限公司 | Mobile robot navigation method and device |
| CN110147042B (en) * | 2019-05-28 | 2020-06-16 | 金力 | Vertical AGV body control method based on fuzzy control and PID control |
| CN110147042A (en) * | 2019-05-28 | 2019-08-20 | 金力 | A kind of upright AGV car body control method based on fuzzy control combination PID control |
| CN111665838A (en) * | 2020-05-21 | 2020-09-15 | 浙江工业大学 | Attitude control method for self-balancing robot to resist continuous external force action |
| CN111665838B (en) * | 2020-05-21 | 2023-08-29 | 浙江工业大学 | Gesture control method for self-balancing robot to resist continuous external force action |
| CN112051842A (en) * | 2020-07-29 | 2020-12-08 | 浙江工业大学 | Obstacle crossing motion control method of two-wheeled self-balancing mobile robot |
| CN112947069A (en) * | 2021-01-28 | 2021-06-11 | 内蒙古大学 | Control method for moving two-wheeled robot |
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