CN108873893A - A kind of differential trolley position control method of two-wheel - Google Patents
A kind of differential trolley position control method of two-wheel Download PDFInfo
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- G—PHYSICS
- G05—CONTROLLING; REGULATING
- G05D—SYSTEMS FOR CONTROLLING OR REGULATING NON-ELECTRIC VARIABLES
- G05D1/00—Control of position, course or altitude of land, water, air, or space vehicles, e.g. automatic pilot
- G05D1/02—Control of position or course in two dimensions
- G05D1/021—Control of position or course in two dimensions specially adapted to land vehicles
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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
The invention discloses a kind of differential trolleies of two-wheel to position motion control method, includes the following steps：1) polar coordinate position of dandy horse is taken；2) double-loop feedbackc device is constructed, the inner ring of outer ring and reception apart from difference signal including receiving angle difference signal, the outer ring includes outer ring controller, and the inner ring is provided with inner loop control device, determines the response parameter of outer ring controller and inner loop control device；3) according to the response parameter of the outer ring controller and the inner loop control device, output signal is calculated；4) two path control signal is exported according to the inner loop control device and outer ring controller, motor speed and steering is controlled.Positioning system is suitable for any two-dimensional surface scene, it is only necessary to be supplied to one purpose coordinate of this set system, positioning operation can be completed.The fuzzy PID control method of twin nuclei is more preferable compared to conventional PID controllers time response, and overshoot inhibits more preferable, and control precision is more preferable.
Description
Technical field
The present invention relates to ground two-wheel differential mechanism people environment navigation control fields indoors, relate more specifically to a kind of double
Take turns differential trolley positioning motion control method.
Background technique
In the prior art, the differential trolley of two-wheel is carried out to be widely applied in robot field, and in motion planning and robot control
In the process, need to realize positioning and motion control in real time by positioning, the differential trolley of two-wheel is due to itself motion process ratio
It is more complex, although there are still not in real-time and accuracy for these methods at present there are some control localization methods
Foot, in the prior art, lacks a kind of differential trolley indoor positioning control method of two-wheel, can accurately and in real time realize
The coordinate of trolley is accurately positioned and motion control.
Therefore those skilled in the art are dedicated to developing a kind of differential trolley position control method of two-wheel, can be accurate
And the coordinate accurate positioning and motion control of trolley are realized in real time.
Summary of the invention
In view of the above drawbacks of the prior art, it is differential small that technical problem to be solved by the invention is to provide a kind of two-wheels
Vehicle indoor positioning control method can accurately and in real time realize the coordinate accurate positioning and motion control of trolley.
To achieve the above object, the present invention provides a kind of differential trolleies of two-wheel to position motion control method, including following
Step：
1) polar coordinate position of dandy horse is taken；
2) double-loop feedbackc device is constructed, the inner ring of outer ring and reception apart from difference signal including receiving angle difference signal,
The outer ring includes outer ring controller, and the inner ring is provided with inner loop control device, determines outer ring controller and inner loop control device
Response parameter；
3) according to the response parameter of the outer ring controller and the inner loop control device, output signal is calculated；
4) two path control signal is exported according to the inner loop control device and outer ring controller, to motor speed and turns to progress
Control movement.
Preferably, in the step 2), the outer ring controller is set as angle ring fuzzy controller；The inner ring
Controller is set as rang ring fuzzy controller；
Angle ring fuzzy controller and the rang ring fuzzy controller are established according to the following formula：
Wherein, kpFor proportionality coefficient；
kiFor integral coefficient；
kdFor differential coefficient；
X (t) is input quantity；
U (t) is output quantity.
In the step 4), after motor movement, step 2) is repeated to 4), until moving of car reaches purpose coordinate.
Preferably, in the step 2), include the following steps：
21) the polar data difference for calculating purpose coordinate and being currently located；
22) according to fuzzy inference rule and subordinating degree function and coordinate difference, determine that angle ring fuzzy controller is joined
Several and rang ring fuzzy controller parameter.
Preferably, in the step 21), include the following steps：
211) the range difference Δ d of input and course angular difference Δ θ are indicated with the input error signal e controlled, by error e with
Error rate ec is as input to the controller；
212) for margin of error e and error rate ec, according to pre-set quantizing range carry out seven grades of quantizations NB,
NM,NS,ZO,PS,PM.PB}.The fuzzy reasoning table that E, EC result generated after quantization can be set according to table 1, searches and generates relatively
The fuzzy control parameter Δ k answeredp、Δki、Δkd。
213) three independent output Δ k are calculated using mamdani fuzzy logic inference algorithmp、Δki、Δkd；
214) according to the fuzzy ranges domain for outputting and inputting variable, seven variables i.e. fuzzy subset is defined：{NB,NM,
NS,ZO,PS,PM,PB}；Output Δ k is established according to following tablep、Δki、ΔkdFuzzy control rule table：
215) according to the fuzzy if-then rules table of step 214), output Δ k is obtainedp、Δki、ΔkdFuzzy output amount, press
According to following equation computing controller in k-th sampling time point, pid parameter：
kp(k)=kp0+Δkp(k), ki(k)=ki0+Δki(k), kd(k)=kd0+Δkd(k)
Wherein, kpIt (k) is the proportionality coefficient of k-th of sampling time point；
kp0For the proportionality coefficient of initial time；
kiIt (k) is the integral coefficient of k-th of sampling time point；
ki0For the integral coefficient of initial time；
kdIt (k) is the differential coefficient of k-th of sampling time point；
kd0For the differential coefficient of initial time.
Preferably, in the step 4), the control signal of bicyclic fuzzy controller output is needed according to the following steps to it
It is transported to driving unit after being parsed, then completes difference speed regulation：
41) the control signal T of the outer ring outputθ(t), sign judgement is carried out to it, sign represents electricity rotating forward
Or reversion；
42) driving motor rotation is adjusted after carrying out quantization level to the size of the signal；
43) to the control signal T of inner ring outputd(t), quantization ambiguity solution is carried out；
44) to Td(t) quantization level is equally carried out, different speed regulation gears is taken according to the result after quantization.
The beneficial effects of the invention are as follows：(1) positioning system is practically applicable to any two-dimensional surface scene, it is only necessary to be supplied to this set
One purpose coordinate of system, can be completed positioning operation.(2) if giving a series of purpose coordinate, the set system is equipped
Robot can then complete to seek diameter behavior, if to the path that recorder people passes through, a two-dimensional surface can be generated
Figure.(3) fuzzy PID control method of twin nuclei is more preferable compared to conventional PID controllers time response, and overshoot inhibits more preferable, control
Precision processed is more preferable.(4) since direct current generator is waited during exercise, rated speed and with idling speed between there are non-linear relations.?
What is taken in the present invention is a kind of method that control signal ambiguity parses and is quantified as several gears.This method is indifferent to control
The specific revolving speed of motor processed, so as to avoid being difficult to overcome unintentional nonlinearity in electric machine speed regulation control, for most of direct current
The robot chassis of frequency conversion drive mode all has good adaptability.
Detailed description of the invention
Fig. 1 is method execution flow chart of the invention.
Fig. 2 is system construction drawing of the invention.
Fig. 3 is bicyclic fuzzy-adaptation PID control flow chart of the invention.
Fig. 4 is bicyclic fuzzy structure chart of the invention.
Fig. 5 is E, EC, Δ k in the present inventionp、Δki、ΔkdMembership function figure.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples：
As shown in Figure 1, a kind of differential trolley of two-wheel positions motion control method, include the following steps：
1) polar coordinate position of dandy horse is taken；
2) double-loop feedbackc device is constructed, the inner ring of outer ring and reception apart from difference signal including receiving angle difference signal,
The outer ring includes outer ring controller, and the inner ring is provided with inner loop control device, determines outer ring controller and inner loop control device
Response parameter；
3) according to the response parameter of the outer ring controller and the inner loop control device, output signal is calculated；
4) two path control signal is exported according to the inner loop control device and outer ring controller, to motor speed and turns to progress
Control movement.
Further, in the step 2), the outer ring controller is set as angle ring fuzzy controller；In described
Ring controller is set as rang ring fuzzy controller；
Angle ring fuzzy controller and the rang ring fuzzy controller are established according to the following formula：
Wherein, kpFor proportionality coefficient；
kiFor integral coefficient；
kdFor differential coefficient；
X (t) is input quantity；
U (t) is output quantity.
In the step 4), after motor movement, step 2) is repeated to 4), until moving of car reaches purpose coordinate.
In practical application, most systems have the characteristics such as non-linear, time-varying, delay, it is difficult to establish accurately mathematical modulo
Type.Therefore, it is difficult to realize effectively control with the relative theory of classic control and modern control theory.Traditional PID controller is rung
The function is answered to be：Proportionality coefficient kp, integral coefficient ki, differential coefficient kdIt is constant, no
Has automatic adjusument.
And fuzzy-adaptation PID control is then to organically combine two kinds of control theories, that is, overcome PID control be easy to produce it is super
The not high disadvantage of reconciliation fuzzy control stable state accuracy, and the stronger reliability of PID control and the stronger Shandong of fuzzy control can be gathered
The advantages of stick.Improve control precision, response speed, the reliability and stability of control system.
Such as attached drawing 4, it is fuzzy controller structure chart of the invention, the signal of input is range difference Δ d and course angle
Poor Δ θ indicates that r (t) indicates controller input signal with the input error signal e of control.Error e and error rate ec make
For the input of controller, fuzzy control rule will carry out online modification to pid parameter, and determine output valve U by PID regulator
(t), realized by controlled device parsing and be calculated as Y (t) amount of exercise, can satisfy the e and ec of different moments to pid parameter from
Adjusting requires.
Further, in the step 2), include the following steps：
21) the polar data difference for calculating purpose coordinate and being currently located；
22) according to fuzzy inference rule and subordinating degree function and coordinate difference, determine that angle ring fuzzy controller is joined
Several and rang ring fuzzy controller parameter.
Further, in the step 21), include the following steps：
211) the range difference Δ d of input and course angular difference Δ θ are indicated with the input error signal e controlled, by error e with
Error rate ec is as input to the controller；
212) for margin of error e and error rate ec, according to pre-set quantizing range carry out seven grades of quantizations NB,
NM,NS,ZO,PS,PM.PB}.The fuzzy reasoning table that E, EC result generated after quantization can be set according to table 1, searches and generates relatively
The fuzzy control parameter Δ k answeredp、Δki、Δkd。
In the present embodiment, angle controller and distance controller two paths of data are handled respectively, are set according to the differential trolley of two-wheel
Quantized result E is divided into seven grades, and with following symbol firstly, quantifying the margin of error e of angle controller by the mobility of meter
It number is indicated：{NB,NM,NS,ZO,PS,PM,PB}；Wherein, NB grades of data value range is set as [- 45, -25]；NM grades
Data value range be set as [- 25, -15]；NS grades of data value range is set as [- 3, -15]；ZO grades of data value
Range is set as [- 3,3]；PS grades of data value range is set as [3,15]；PM grades of data value range be set as [15,
25]；PB grades of data value range is set as [25,45].
Meanwhile the error rate ec of angle controller is quantified, wherein the value range of ec be set as [- 90,
90], quantized result EC is divided into seven grades, and is indicated with following symbol：{NB,NM,NS,ZO,PS,PM,PB}；Wherein, NB
The data value range of shelves is set as [- 90, -50]；Wherein, NM grades of data value range is set as [- 50, -30]；NS grades
Data value range is set as [- 30, -6]；ZO grades of data value range is set as [- 6,6]；PS grades of data value range
It is set as [6,30]；PM grades of data value range is set as [30,50]；PB grades of data value range is set as [50,90].
Likewise, the margin of error e of distance controller is quantified, wherein the range of e is set as [- 100,100]；It will
Quantized result E is divided into seven grades, and is indicated with following symbol：{NB,NM,NS,ZO,PS,PM,PB}；Wherein, NB grades of data
Value range is set as [- 100, -50]；NM grades of data value range is set as [- 50, -20]；NS grades of data value range
It is set as [- 20, -5]；ZO grades of data value range is set as [- 5,5]；PS grades of data value range is set as [5,20]；
PM grades of data value range is set as [20,50]；PB grades of data value range is set as [50,100].
Meanwhile the error rate ec of distance controller is quantified, wherein the value range of ec be set as [- 200,
200], quantized result EC is divided into seven grades, and is indicated with following symbol：{NB,NM,NS,ZO,PS,PM,PB}；Wherein, NB
The data value range of shelves is set as [- 200, -100]；NM grades of data value range is set as [- 100, -40]；NS grades of number
[- 40, -10] are set as according to value range；ZO grades of data value range is set as [- 10,10]；PS grades of data value range
It is set as [10,40]；PM grades of data value range is set as [40,100]；PB grades of data value range be set as [100,
200]。
In other embodiments, the quantizing range of error and error rate can be according to the mobility of the trolley of design
Difference carries out difference setting, to reach identical technical effect.It can be carried out according to system situation as the gear of quantization
Different steppings, such as 7 grades divide equally, to realize identical technical effect.
213) three independent output Δ k are calculated using mamdani fuzzy logic inference algorithmp、Δki、Δkd；
214) according to the fuzzy ranges domain for outputting and inputting variable, seven variables i.e. fuzzy subset is defined：{NB,NM,
NS,ZO,PS,PM,PB}；Output Δ k is established according to following tablep、Δki、ΔkdFuzzy control rule table：
Table 1 exports Δ kp、Δki、ΔkdAmount fuzzy control rule table
215) according to the fuzzy if-then rules table of step 214), output Δ k is obtainedp、Δki、ΔkdFuzzy output amount, press
According to following equation computing controller in k-th sampling time point, pid parameter：
kp(k)=kp0+Δkp(k), ki(k)=ki0+Δki(k), kd(k)=kd0+Δkd(k)
Wherein, kpIt (k) is the proportionality coefficient of k-th of sampling time point；
kp0For the proportionality coefficient of initial time；
kiIt (k) is the integral coefficient of k-th of sampling time point；
ki0For the integral coefficient of initial time；
kdIt (k) is the differential coefficient of k-th of sampling time point；
kd0For the differential coefficient of initial time.
To the margin of erroreAnd error rateecUsing E, EC as the input of fuzzy controller after progress quantification treatment, using
Three independent output Δ k are obtained after mamdani fuzzy logic inference algorithmp、Δki、Δkd.Wherein output and input variable
Fuzzy ranges domain defines seven variables i.e. fuzzy subset：{NB,NM,NS,ZO,PS,PM,PB}.Input E and EC and output Δ
kp、Δki、ΔkdBe subordinate to letter referring to attached drawing 5.In the present embodiment, seven are defined according to moving of car situation and actual conditions
Variable in other embodiments, can be defined according to different situations and be searched.
The core of design of fuzzy control is to establish fuzzy reasoning table, output variable Δ kp、Δki、ΔkdFuzzy control rule
Then shown in table such as step 214).
Ambiguity solution quantization, by totally 49 fuzzy control rule combinations of the description in table 1, we have obtained output Δ
kp、Δki、ΔkdFuzzy output amount, the present embodiment is to realize fuzzy judgment using weighted mean method.
In the present embodiment, according to the feedback in moving of car situation and experiment, output Δ k is carried out according to the following tablep、
Δki、ΔkdJudgement is searched.
Table 2 exports Δ kp、Δki、ΔkdFuzzy judgment look-up table
The thought of fuzzy controller is the Δ k exported by automatic adjusumentp、Δki、Δkd, to pid parameter kp、ki、
kdReal-time adaptive correction is carried out, the deviation inhibited between the controlled quatity of system and expection in real time is finally reached, reaches adaptive
Purpose should be controlled.The fuzzy controller is in k-th sampling time point, pid parameter kp(k)=kp0+Δkp(k), ki(k)
=ki0+Δki(k), kd(k)=kd0+Δkd(k)。
Further, in the step 4), the control signal of bicyclic fuzzy controller output is needed according to the following steps pair
It is transported to driving unit after being parsed, then complete difference speed regulation：
41) the control signal T of the outer ring outputθ(t), sign judgement is carried out to it, sign represents electricity rotating forward
Or reversion；
42) driving motor rotation is adjusted after carrying out quantization level to the size of the signal；
43) to the control signal T of inner ring outputd(t), quantization ambiguity solution is carried out；
44) to Td(t) quantization level is equally carried out, different speed regulation gears is taken according to the result after quantization.
In the present embodiment, 10 gears can be quantified as, the speed that each shelves represent two motors is only poor Big generation
The table difference of two wheel speeds, that is, steering angle size.The control signal T of rang ring outputd(t), it also needs to its amount
Dissolve blurring process, Td(t) same to carry out 5 grades of quantizations, different speed regulation gears is taken according to the result after quantization.
It, can also according to circumstances, by T in other embodimentsθ(t)、Td(t) different grades of quantization is carried out, to adapt to difference
The motor and working order of model.
As shown in figure 3, according to range difference and course angular difference (Δ d, Δ θ).The method for constructing bicyclic fuzzy-adaptation PID control.
Motion positions are just so operated conversion to control two-way difference feedback signal.When (Δ d, Δ θ) respectively tends to 0, positioning
Just complete.
System structure diagram of the invention as shown in Fig. 2.The number of the two-way encoder after difference motor is acquired first
According to, it then resolves to obtain coordinate position locating for current trolley (x (t), y (t)) by the kinematics model of dandy horse,
External world's input needs to position the purpose coordinate (x reached0,y0), calculate with the distance between changing coordinates (x (t), y (t)) difference and
Course angular difference (Δ d, Δ θ).
The bicyclic fuzzy control localization method of the differential trolley of two-wheel that the technical program provides, external world's input, which needs to position, to be reached
Purpose coordinate (x0,y0), calculate the distance between changing coordinates (x (t), y (t)) difference and course angular difference (Δ d, Δ θ).Structure
Double-loop feedbackc device is made, this two-way feedback signal is as input.Angle difference signal is input to outer ring, is input to apart from difference signal
Inner ring.Controller in this two-way feedback loop uses fuzzy controller.Traditional PID controller receptance function is：The difference of fuzzy controller is proportionality coefficient kp, integral coefficient ki、
Differential coefficient kdWhen adaptive transformation.Fuzzy inference rule and value subordinating degree function, the angle of controller input are established in advance
Spend poor Δ θ, range difference Δ d and its change rateIt will corresponding one group of ratio, integral, differential coefficient.
Compared to traditional PID controller, faster, over control is smaller for fuzzy controller convergence rate.
The bicyclic fuzzy control localization method of the differential trolley of the two-wheel, the control signal exported by bicyclic fuzzy controller need
Ambiguity solution operation is carried out to it.The control signal T of angle ring outputθ(t), sign judgement, sign meeting are carried out to it
It instructs two-wheel differential driving module to provide correct direction information, 10 grades of quantizations secondly is carried out to the size of control signal.Quantization
Output result afterwards can instruct two-wheel differential driving module to provide correct steering angle.The control signal T of rang ring outputd
(t), it also needs to quantify it ambiguity solution process, Td(t) same to carry out 10 grades of quantizations, the output after quantization can instruct two-wheel poor
Point drive module provides suitable movement velocity.
The bicyclic fuzzy control localization method of the differential trolley of this two-wheel, in two-wheel differential driving module.Motor uses two
Direct current generator, driving method are PWM wave allotment control.Speed-regulating signal is divided into 10 gears, the PWM wave being stepped up with 10 gear frequencies
Driving motor.Instruction after motor drive module receives the ambiguity solution of controller return, motor can differential driving two-way
Motor completes motor imagination.
The preferred embodiment of the present invention has been described in detail above.It should be appreciated that those skilled in the art without
It needs creative work according to the present invention can conceive and makes many modifications and variations.Therefore, all technologies in the art
Personnel are available by logical analysis, reasoning, or a limited experiment on the basis of existing technology under this invention's idea
Technical solution, all should be within the scope of protection determined by the claims.
Claims (5)
1. a kind of differential trolley of two-wheel positions motion control method, it is characterized in that：Include the following steps：
1) polar coordinate position of dandy horse is obtained；
2) double-loop feedbackc device is constructed, the inner ring of outer ring and reception apart from difference signal including receiving angle difference signal is described
Outer ring includes outer ring controller, and the inner ring is provided with inner loop control device, determines the response of outer ring controller and inner loop control device
Parameter；
3) according to the response parameter of the outer ring controller and the inner loop control device, output signal is calculated；
4) two path control signal is exported according to the inner loop control device and outer ring controller, motor speed and steering is controlled
It is mobile.
2. the differential trolley of two-wheel as described in claim 1 positions motion control method, it is characterized in that：In the step 2), institute
It states outer ring controller and is set as angle ring fuzzy controller；The inner loop control device is set as rang ring fuzzy-adaptation PID control
Device；
Angle ring fuzzy controller and the rang ring fuzzy controller are established according to the following formula：
Wherein, kpFor proportionality coefficient；
kiFor integral coefficient；
kdFor differential coefficient；
X (t) is input quantity；
U (t) is output quantity.
In the step 4), after motor movement, step 2) is repeated to 4), until moving of car reaches purpose coordinate.
3. the differential trolley of two-wheel as claimed in claim 2 positions motion control method, it is characterized in that：
In the step 2), include the following steps：
21) the polar data difference for calculating purpose coordinate and being currently located；
22) according to fuzzy inference rule and subordinating degree function and coordinate difference, determine angle ring fuzzy controller parameter and
Rang ring fuzzy controller parameter.
4. the differential trolley of two-wheel as claimed in claim 3 positions motion control method, it is characterized in that：In the step 21), packet
Include following steps：
211) the range difference Δ d of input and course angular difference Δ θ are indicated with the input error signal e controlled, by error e and error
Change rate ec is as input to the controller；
212) to margin of error e and error rate ec according to pre-set quantizing range carry out seven grades quantization NB, NM, NS,
ZO,PS,PM.PB}；The fuzzy reasoning table that E, EC result generated after quantization can be set according to fuzzy control rule table, searches life
At corresponding fuzzy control parameter Δ kp、Δki、Δkd。
213) three independent output Δ k are calculated using mamdani fuzzy logic inference algorithmp、Δki、Δkd；
214) according to the fuzzy ranges domain for outputting and inputting variable, seven variables i.e. fuzzy subset is defined：{NB,NM,NS,ZO,
PS,PM,PB}；Output Δ k is established according to following tablep、Δki、ΔkdFuzzy control rule table：
215) according to the fuzzy if-then rules table of step 214), output Δ k is obtainedp、Δki、ΔkdFuzzy output amount, under
Pid parameter of the column formula computing controller in k-th of sampling time point：
kp(k)=kp0+Δkp(k), ki(k)=ki0+Δki(k), kd(k)=kd0+Δkd(k)
Wherein, kpIt (k) is the proportionality coefficient of k-th of sampling time point；
kp0For the proportionality coefficient of initial time；
kiIt (k) is the integral coefficient of k-th of sampling time point；
ki0For the integral coefficient of initial time；
kdIt (k) is the differential coefficient of k-th of sampling time point；
kd0For the differential coefficient of initial time.
5. the differential trolley of two-wheel as claimed in claim 2 positions motion control method, it is characterized in that：It is double in the step 4)
The control signal of ring moulds fuzzy controllers output, needs to be transported to driving unit after parsing it according to the following steps, then
Complete difference speed regulation：
41) the control signal T of the outer ring outputθ(t), sign judgement is carried out to it, sign represents electricity and rotates forward or anti-
Turn；
42) driving motor rotation is adjusted after carrying out quantization level to the size of the signal；
43) to the control signal T of inner ring outputd(t), quantization ambiguity solution is carried out；
44) to Td(t) quantization level is equally carried out, different speed regulation gears is taken according to the result after quantization.
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Cited By (3)
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| CN110716561A (en) * | 2019-11-26 | 2020-01-21 | 轻客智能科技（江苏）有限公司 | Sweeper forward-looking pose control method and system for trajectory tracking |
| CN110960401A (en) * | 2019-11-18 | 2020-04-07 | 南京伟思医疗科技股份有限公司 | Rehabilitation weight-reduction walking training vehicle for realizing linear following through distance detection and control method |
| CN115031088A (en) * | 2022-06-27 | 2022-09-09 | 合肥工业大学 | Speed and acceleration control method of pipeline detector |
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