CN110083059A - A kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode - Google Patents
A kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode Download PDFInfo
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Abstract
The invention discloses a kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode, point stabilization process is divided into the following steps: (1) kinematics model of nonholonomic mobile robot in the planes is portrayed using rectangular coordinate system;(2) nonholonomic mobile robot kinematics model is converted into chained form system model under rectangular coordinate system, using multi tate input sample method by chained form system discretization, and one sensor is installed in nonholonomic mobile robot vehicle body, for constantly transmitting the position coordinates of nonholonomic mobile robot in the planes;(3) constantly collected position data is transferred in sliding mode control algorithm module sensor, so that nonholonomic mobile robot is finally calmed in finite time.A kind of pure geometric operation of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode of the invention, time discretization, control are stablized, lower to hardware device requirement, practical, are easy to be commercialized.
Description
Technical field
The present invention relates to nonholonomic mobile robot movement control technology fields, and in particular to a kind of Discrete-time Sliding Mode it is non-complete
Whole robot stabilized control method.
Background technique
All trades and professions are almost permeated in the application of nonholonomic mobile robot at present.Nonholonomic mobile robot have estimate one's own ability light, carrying is big,
It drives and controls the advantages that relatively convenient, the speed of travel are fast, work efficiency is high, to show one's talent from all kinds of robots.
Solving the problems, such as that finite time is calmed using nonholonomic mobile robot is a challenging task, is led in control
Domain causes more and more concerns.The calm complexity for having its own of finite time, the Stabilization of nonholonomic mobile robot are answered
With very extensive, such as the handover control of vehicle parking task, task.Substantially have for the control algolithm of nonholonomic mobile robot at present
Two kinds: (1) self adaptive control, (2) robust control;But the calculating of these algorithms is complicated, computationally intensive, wants to the real-time of system
Ask high, this will increase algorithm cost of implementation, be unfavorable for practical application.
Therefore, the above problem is not solved, needs to propose that a kind of calculation amount is small, real-time is good, at low cost, utilizes practical application
Nonholonomic mobile robot finite time point stabilization algorithm.
Summary of the invention
The purpose of the present invention is to solve the drawbacks described above in existing nonholonomic mobile robot control technology, provide it is a kind of from
The nonholonomic mobile robot stabilized control method of time sliding formwork is dissipated, the algorithm calculation amount is small, real-time is good, and cost of implementation is low, is convenient for
Practical application.
The invention is characterized in that following technical solution obtains:
A kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode, including the following steps:
(1), the kinematics model of nonholonomic mobile robot in the planes is portrayed using rectangular coordinate system;Nonholonomic mobile robot
Kinematics model obtained by formula (1):
In formula (1), [x, y]T∈R2Position coordinates of the nonholonomic mobile robot in plane XOY are represented, θ is before robot
Into directional velocity and X-axis forward direction angle, v indicates its advance space rate, and w indicates the angular speed of its rotation;
(2), nonholonomic mobile robot kinematics model is converted into chained form system model under rectangular coordinate system, utilizes multi-speed
Rate input sample method installs a sensor by chained form system discretization, and in nonholonomic mobile robot vehicle body, for constantly passing
The position coordinates of defeated nonholonomic mobile robot in the planes;
Formula (1) is converted to chained form system, the chained form system after conversion is provided by formula (2):
In formula (2), x1=x, x2=tan θ, x3=y, u1=v1Cos θ, u2=v2sec2θ;
By formula (2) Taylor expansion of chained form system at iteration chained form system, provided by formula (3):
U in formula (3)1(t) and u2(t) it is to keep constant numerical value in τ seconds:
For formula (4) to u2(t) multi-speed sample is used, is provided by formula (5):
Above-mentioned k is constant, and the Double Data Rate sampling model in formula (5), which is substituted into chained form system (3), can be obtained finally
Multi-speed sample equivalent model:
(3), the multi-speed sample equivalent model discrete time sliding formwork control indicated for the formula (6) in step (2)
Device processed;Discrete-time Sliding Mode face is provided by formula (7):
S={ x ∈ R3:x1(k)=x2(k)=x3}, (k)=0 (7)
R represents real number in formula (7), and Discrete-time Sliding Mode controller is provided by formula (8):
K in formula (8)*K τ is represented, Discrete-time Sliding Mode controller ensure that state x1(k), x2(k) and x3(k) having
Zero is converged in limited time.
The present invention has the following advantages that relative to existing control technology and effect:
Nonholonomic mobile robot control algolithm proposed by the present invention is based on rectangular co-ordinate and is obtained using geometry direct derivation, parameter
Simply, physical meaning is clear;Calculating in nonholonomic mobile robot control algolithm is to calculate to complete before point stabilization starts, and is calmed
Process is not necessarily to manual intervention, and calculation amount is small, real-time is good, and cost of implementation is low, is convenient for practical application.
Detailed description of the invention
Fig. 1 is nonholonomic mobile robot movement schematic diagram.
Specific embodiment
As shown in Figure 1, a kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode, including the following steps:
(1), the kinematics model of nonholonomic mobile robot in the planes is portrayed using rectangular coordinate system;Nonholonomic mobile robot
Kinematics model obtained by formula (1):
In formula (1), [x, y]T∈R2Position coordinates of the nonholonomic mobile robot in plane XOY are represented, θ is before robot
Into directional velocity and X-axis forward direction angle, v indicates its advance space rate, and w indicates the angular speed of its rotation;
(2), nonholonomic mobile robot kinematics model is converted into chained form system model under rectangular coordinate system, utilizes multi-speed
Rate input sample method installs a sensor by chained form system discretization, and in nonholonomic mobile robot vehicle body, for constantly passing
The position coordinates of defeated nonholonomic mobile robot in the planes;
Formula (1) is converted to chained form system, the chained form system after conversion is provided by formula (2):
In formula (2), x1=x, x2=tan θ, x3=y, u1=v1Cos θ, u2=v2sec2θ;
By formula (2) Taylor expansion of chained form system at iteration chained form system, provided by formula (3):
U in formula (3)1(t) and u2(t) it is to keep constant numerical value in τ seconds:
For formula (4) to u2(t) multi-speed sample is used, is provided by formula (5):
Above-mentioned k is constant, and the Double Data Rate sampling model in formula (5), which is substituted into chained form system (3), can be obtained finally
Multi-speed sample equivalent model:
(3), the multi-speed sample equivalent model discrete time sliding formwork control indicated for the formula (6) in step (2)
Device processed;Discrete-time Sliding Mode face is provided by formula (7):
S={ x ∈ R3:x1(k)=x2(k)=x3}, (k)=0 (7)
R represents real number in formula (7), and Discrete-time Sliding Mode controller is provided by formula (8):
K in formula (8)*K τ is represented, Discrete-time Sliding Mode controller ensure that state x1(k), x2(k) and x3(k) having
Zero is converged in limited time.Know that nonholonomic mobile robot can calm in finite time and keep in Fig. 1 according to chained form system
Bold line position and attitude.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (1)
1. a kind of nonholonomic mobile robot stabilized control method of Discrete-time Sliding Mode, it is characterised in that include the following steps:
(1), the kinematics model of nonholonomic mobile robot in the planes is portrayed using rectangular coordinate system;The fortune of nonholonomic mobile robot
Dynamic model of learning is obtained by formula (1):
In formula (1), [x, y]T∈R2Position coordinates of the nonholonomic mobile robot in plane XOY are represented, θ is what robot advanced
The angle of directional velocity and X-axis forward direction, v indicate its advance space rate, and w indicates the angular speed of its rotation;
(2), nonholonomic mobile robot kinematics model is converted into chained form system model under rectangular coordinate system, it is defeated using multi tate
Enter the method for sampling for chained form system discretization, and one sensor is installed in nonholonomic mobile robot vehicle body, it is non-for constantly transmitting
The position coordinates of complete machine people in the planes;
Formula (1) is converted to chained form system, the chained form system after conversion is provided by formula (2):
In formula (2), x1=x, x2=tan θ, x3=y, u1=v1Cos θ, u2=v2sec2θ;
By formula (2) Taylor expansion of chained form system at iteration chained form system, provided by formula (3):
U in formula (3)1(t) and u2(t) it is to keep constant numerical value in τ seconds:
For formula (4) to u2(t) multi-speed sample is used, is provided by formula (5):
Above-mentioned k is constant, the Double Data Rate sampling model in formula (5) is substituted into chained form system (3) can be obtained it is final more
Polydispersity index equivalent model:
(3), the multi-speed sample equivalent model discrete time sliding mode controller indicated for the formula (6) in step (2);
Discrete-time Sliding Mode face is provided by formula (7):
S={ x ∈ R3:x1(k)=x2(k)=x3}, (k)=0 (7)
R represents real number in formula (7), and Discrete-time Sliding Mode controller is provided by formula (8):
K in formula (8)*K τ is represented, Discrete-time Sliding Mode controller ensure that state x1(k), x2(k) and x3(k) when limited
It is interior to converge to zero.
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CN112769367A (en) * | 2021-01-07 | 2021-05-07 | 山东交通学院 | Permanent magnet linear motor data driving discrete iteration integral sliding mode control method and system |
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