CN111158242A - Convoy task cooperative control method and system based on obstacle environment and bounded input - Google Patents

Convoy task cooperative control method and system based on obstacle environment and bounded input Download PDF

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CN111158242A
CN111158242A CN202010053347.8A CN202010053347A CN111158242A CN 111158242 A CN111158242 A CN 111158242A CN 202010053347 A CN202010053347 A CN 202010053347A CN 111158242 A CN111158242 A CN 111158242A
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convoy
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宋锐
高嵩
郑玉坤
李贻斌
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Jinan Zhongfuture Industrial Development Co ltd
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Shandong University
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Abstract

The invention discloses a method and a system for collaborative control of a convoy task based on an obstacle environment and bounded input, wherein the method comprises the following steps: describing a physical model of the convoy task by adopting a multi-Euler-Lagrange system; an inner ring and outer ring control structure is adopted, the outer ring adopts a behavior control method based on a space, and expected speed and an expected motion track required by an inner ring physical model are generated; the inner ring is based on an improved proportional derivative sliding mode control method of the adaptive radial basis function neural network, so that each physical model can track expected speed and expected motion trail under the condition of interference and parameter uncertainty, and zero steady-state error and bounded input are realized. The controller provided by the invention has the advantages of simplicity, no model and capability of providing continuous control signals, and the adaptive radial basis function neural network adopted in the design of the controller has strong learning capability and robustness, thereby well compensating the interference and finally realizing zero steady-state error.

Description

Convoy task cooperative control method and system based on obstacle environment and bounded input
Technical Field
The invention relates to the technical field of cooperative control of a convoying task, in particular to a convoying task cooperative control method and system based on an obstacle environment and bounded input.
Background
The statements in this section merely provide background information related to the present disclosure and may not necessarily constitute prior art.
The issue of coordinated control of multi-euler lagrange systems has attracted widespread attention over the past few decades. Mobile robots, underwater vehicles, surface vessels, spacecraft, robotic arms, and the like all belong to the euler lagrangian system. Due to measurement noise, modeling errors, external disturbances and modeling simplifications and the often unmodeled dynamics in real systems, these can severely degrade system performance and cause control system instability. Furthermore, neglecting to deal with practical problems such as input saturation, obstacles and collisions can have catastrophic consequences. Therefore, research into these areas is of great importance and interest.
To date, some common applications associated with multi-Eulerian Lagrangian systems are distributed consensus, synchronization, including control, formation control, and trapping or convoying, respectively. An escort task is that a set of robots surround and track a moving object in an unknown environment. A specified distance is maintained between the robot and the target and the robot is evenly distributed around the target. The practical value of the convoy mission in the civilian and military fields has attracted the interest of many researchers. Many methods are used to accomplish this task, such as a round-robin tracking strategy, a behavior-based approach, a cluster space control approach, and so forth.
The behavior-based method belongs to a typical formation control method, has the advantages of flexibility, easy realization and update, but the main problem of the method is how to mathematically formalize the method. Compared with other behavior methods, the behavior based on empty space (NSB) control has the obvious feature of clearly expressing the mathematical expression. NSB control can be applied to p-dimensional space (wherein p is more than or equal to 2 and is a positive integer) to realize that a plurality of Euler Lagrange systems execute the convoy task and avoid obstacles. However, NSB control still has some unsolved problems, such as how to achieve more accurate nonlinear dynamic control under such behavior control architecture.
Sliding Mode Control (SMC) has robust performance to external disturbances and system uncertainty, and has been widely used in multi-euler lagrange systems. However, it requires some a priori knowledge of the system parameters, which is difficult to obtain in many practical applications. The Proportional Derivative (PD) control method is linear and modeless, easy to implement, and can be used to replace the equivalent control portion of SMC. The prior art describes how to use PD controllers in conjunction with SMCs and the control methods of linear robot systems based on PD controllers and SMCs. In the above method, the selection of the controller parameters requires knowledge of the upper bound of uncertainty, which is difficult to achieve in some cases.
In recent years, more and more learning-based methods have been used to identify models and enhance the robustness of traditional control methods. Neural Networks (NN) can be used as a tool to model nonlinear functions due to their good approximation capability. The prior art introduces a Radial Basis Function Network (RBFN) to approximate the non-linear dynamics of a SCARA-type robot arm. RBFNNS can be used to estimate the unknown required control quantity so that zero steady state error tracking can be achieved. The prior art discloses a hierarchical control strategy that combines the advantages of integrated sliding mode control (IntSMC) and the advantages of arbitrary function approximation of RBFNNS, which can guarantee a faster convergence of state variables to desired values in a short time and compensate for disturbances and uncertainties. However, the above method is mainly applied to a single controlled object, such as a mechanical arm or a quadrotor, and the above method is not applied to multiple controlled objects. In addition, none of the above methods takes into account the problem of input being bounded, which is contradictory to the fact that the actuator is capable of producing any torque, which is bounded and provided by the actuator in practice. Therefore, the prior art either requires a large torque generated by a large driving mechanism or cannot be put to practical use at all.
Disclosure of Invention
In order to solve the problems, the invention provides a collaborative control method and a collaborative control system for a convoy task based on an obstacle environment and bounded input, wherein the convoy task and an obstacle avoidance task are considered, NSB control is adopted in the design of an outer ring, and a generated speed vector is used as a reference value of the inner ring. In the inner ring, an IRPD-SMC technology based on an arctan function and an adaptive RBFNNS is provided, so that the robot is ensured to follow a reference track and zero steady-state error is realized.
In some embodiments, the following technical scheme is adopted:
the convoy task cooperative control method based on the obstacle environment and bounded input comprises the following steps:
describing a physical model of the convoy task by adopting a multi-Euler-Lagrange system;
an inner ring and outer ring control structure is adopted, the outer ring adopts a behavior control method based on a space, and expected speed and an expected motion track required by an inner ring physical model are generated; the inner ring is based on an improved proportional derivative sliding mode control (IRPD-SMC) method of an adaptive radial basis function neural network, so that each physical model can track expected speed and expected motion trail under the condition of interference and parameter uncertainty, and zero steady-state error and bounded input are realized.
The inner ring is based on the improved proportional derivative sliding mode control method of the adaptive radial basis function neural network, and the control law is as follows:
Figure BDA0002371978710000021
wherein k isαiIs a position error dependent gain for canceling position errors; k is a radical ofβiIs a differential related gain used for predicting the overall response trend and preventing the system from acting too violently; λ is the approximate proportional gain; k is a radical ofiIs the robust term gain, κ is a constant;
Figure BDA0002371978710000022
is the reference torque ρiEstimated value of eiIs a position tracking error,
Figure BDA0002371978710000023
Is the velocity tracking error, siIs a slip form surface.
In other embodiments, the following technical solutions are adopted:
a convoy mission cooperative control system based on obstacle environment and bounded input comprises: the controller adopts an inner ring and outer ring control structure, the outer ring adopts a behavior control method based on a space, and expected speed and an expected motion track required by an inner ring physical model are generated; the inner ring is based on an improved proportional derivative sliding mode control method of the adaptive radial basis function neural network, so that each physical model can track expected speed and expected motion trail under the condition of interference and parameter uncertainty, and zero steady-state error and bounded input are realized.
In other embodiments, the following technical solutions are adopted:
a terminal device comprising a processor and a computer-readable storage medium, the processor being configured to implement instructions; the computer readable storage medium stores a plurality of instructions adapted to be loaded by a processor and to perform the above-described obstacle environment and bounded input based convoy mission cooperative control method.
In other embodiments, the following technical solutions are adopted:
a computer-readable storage medium having stored therein a plurality of instructions adapted to be loaded by a processor of a terminal device and to execute the aforementioned obstacle environment and bounded input-based convoy mission cooperative control method.
Compared with the prior art, the invention has the beneficial effects that:
under the condition that model uncertainty, interference and obstacles exist, the coordination control problem of the multi-Euler Lagrange system under the bounded input escort task is researched; a robust hierarchical control structure consisting of NSB and IRPD-SMC is designed; in order to avoid obstacles and complete a convoying task, NSB control is adopted in the outer ring design, and the speed and the track required by the inner ring are generated; IRPD-SMC is proposed in inner loop design to track the desired trajectory and speed. Thus, the controller compensates for unknown disturbances and parameter uncertainty well, ensures bounded control inputs, and achieves fast convergence, robustness, and zero steady-state error. Finally, all robots in p-dimensional space can achieve uniform distribution around the target and robust delivery of the target at a specified distance while avoiding obstacles (where p ≧ 2 is a positive integer).
In practice, the actuators are limited in their ability and in many cases they may not be able to produce the desired torque large enough to cause a reduction in the performance of the control system. Therefore, the practical problem of bounded control input is considered, the input is ensured to be of limited amplitude, the performance of the control system can be ensured to be stable, and the control system can be really applied in practice.
The adaptive radial basis function neural network adopted in the design of the controller has strong learning capability and robustness, interference is well compensated, and zero steady-state error is finally realized.
The controller proposed by the present invention is simple, model-free and capable of providing a continuous control signal, making it easy to implement in practice.
Drawings
FIG. 1 is a block diagram of coordinated control of an escort task based on an obstacle environment and bounded input according to a first embodiment of the present invention;
FIG. 2 is a schematic diagram of hyperbolic tangent function and arctangent function according to an embodiment of the present invention;
FIG. 3 is a graph of 5.5 × arctan (0.2 × x) and arctan (0.2 × x) as a function of an embodiment of the present invention;
FIG. 4 is a diagram illustrating the trajectory of the target and the robot when the IRPD-SMC is adopted in case 1 according to the first embodiment of the present invention;
FIGS. 5(a) - (d) are control results when IRPD-SMC is used in case 1 according to a first embodiment of the present invention;
FIGS. 6(a) - (d) are control results when PD-SMC is used in case 1 according to a first embodiment of the present invention;
FIGS. 7(a) - (d) are control results of the case 1 in which APD-SMC is used according to the first embodiment of the present invention;
FIGS. 8(a) - (d) are control results when ASMC is used in case 1 in accordance with one embodiment of the present invention;
FIG. 9 is a control input in case 1 where IRPD-SMC is used according to a first embodiment of the present invention;
FIG. 10 is a diagram illustrating the trajectory of a robot and a target in case 2 using IRPD-SMC according to a first embodiment of the present invention;
FIGS. 11(a) - (d) are control results when IRPD-SMC is used in case 2 according to a first embodiment of the present invention;
FIGS. 12(a) - (d) are control results of the case 2 in the first embodiment of the present invention when APD-SMC is used;
FIGS. 13(a) - (d) are control results when ASMC is used in case 2 in the first embodiment of the present invention;
FIG. 14 is a diagram of the trajectory of the robot and the target in case 3 using IRPD-SMC according to a first embodiment of the present invention;
fig. 15 shows the distance between the robot and the obstacle when IRPD-SMC is used in case 3 according to a first embodiment of the present invention;
FIGS. 16(a) - (d) are control results when IRPD-SMC is used in case 3 according to a first embodiment of the present invention;
FIGS. 17(a) - (d) are control results of the case 3 in which APD-SMC is used according to the first embodiment of the present invention;
fig. 18(a) - (d) are control results when ASMC is used in case 3 in the first embodiment of the present invention.
Detailed Description
It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the disclosure. Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments according to the present application. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
Example one
In one or more embodiments, disclosed is a convoy mission cooperative control method based on an obstacle environment and bounded input, referring to fig. 1, including:
describing a physical model of the convoy task by adopting a multi-Euler-Lagrange system;
an inner ring and outer ring control structure is adopted, the outer ring adopts a behavior control method based on a space, and expected speed and an expected motion track required by an inner ring physical model are generated; the inner ring is based on an improved proportional derivative sliding mode control method of the adaptive radial basis function neural network, so that each physical model can track expected speed and expected motion trail under the condition of interference and parameter uncertainty, and zero steady-state error and bounded input are realized.
In order to avoid obstacles and form convoy formation, the embodiment adopts the behavior based on empty space (NSB) control in the design of the outer ring controller, and generates the speed required by the inner ring. In the design of an inner ring, a proportional derivative sliding mode control (IRPD-SMC) method based on an improved adaptive Radial Basis Function Neural Network (RBFNNs) has the following robustness under the condition of interference and parameter uncertainty, and realizes zero steady-state error and bounded input. Finally, all robots in p-dimensional space can achieve uniform distribution around the target and robust delivery of the target at a specified distance while avoiding obstacles (where p ≧ 2 is a positive integer).
The stability and convergence of the system are strictly proved by using the Lyapunov stability theory, and the effectiveness of the proposed control strategy is verified by comparing with PD-SMC, APD-SMC and ASMC simulation experiments in two-dimensional and three-dimensional space.
The method of the present embodiment will be described in detail below.
Consider a set of n mobile robots, whose dynamics can be described as an euler-lagrange system, expressed as:
Figure BDA0002371978710000051
wherein M isi(qi)∈Rp×pIs a positive definite inertia matrix, qi∈RpIs a vector of coordinates in a broad sense,
Figure BDA0002371978710000052
is the vector and centrifugal moment of Coriolis, gi(qi) Is the moment of gravity, τiIs the control input vector for robot i,
Figure BDA0002371978710000053
is an unknown disturbance.
The Euler-Lagrange system is assumed to have the following properties:
property 1 is bounded: for any one i, there is a normal number
Figure BDA0002371978710000054
m i,kCiAnd kgiSo that
Figure BDA0002371978710000055
And Ci(x,y)||≤kCiFor all vectors, | y | |
Figure BDA0002371978710000056
And gi(qi)||≤kgiThis is true.
Property 2 skew symmetry:
Figure BDA0002371978710000057
is diagonally symmetrical.
Property 3 dynamic parameter linearization: for all vectors
Figure BDA0002371978710000058
Figure BDA0002371978710000059
Is a regression vector, and ΘiIs a common parameter vector associated with the ith robot.
Properties 4: assumption of disturbance force
Figure BDA00023719787100000510
Is that the material is bounded by the surface,
Figure BDA00023719787100000511
ξ thereini>0。
1. Outer loop controller design
NSB control is used in the outer loop to combine three different tasks, define the final motion of the robot and generate the required speed. The proposed IRPD-SMC is used in the inner loop of the multi-euler lagrange system to compensate for unknown disturbances, parameter uncertainty and to guarantee bounded inputs etc. The whole control system diagram is shown in figure 1.
The convoying task with the obstacle avoidance requirement is decomposed into three different subtasks, namely obstacle avoidance subtasks, the subtasks that the robot is uniformly distributed around the target and the subtasks that the robot maintains on the surface of a sphere or a hyper-sphere with the target as the center, and the two next subtasks belong to the convoying task.
The expected speed of the convoy mission with the obstacle avoidance requirement is designed as
Figure BDA0002371978710000061
Wherein the content of the first and second substances,
Figure BDA0002371978710000062
representing the desired speed required by the obstacle avoidance subtask,
Figure BDA0002371978710000063
and
Figure BDA0002371978710000064
is the desired speed required for the convoy mission.
In the obstacle avoidance subtask, each robot is virtualized into a space
Figure BDA0002371978710000065
Is surrounded by
Figure BDA0002371978710000066
Represents the position of the current obstacle for the ith robot, and Bi,oRepresents fi,1d＝diRegion of where diIs the minimum allowable safe distance between the ith robot and the obstacle.
Figure BDA0002371978710000067
Figure BDA0002371978710000068
In the form of a jacobian matrix,
Figure BDA0002371978710000069
is the unit vector pointing to the nearest obstacle, αi,1>0 is a state dependent gain.
Figure BDA00023719787100000610
Figure BDA00023719787100000611
The obstacle avoidance task function and the task error function are respectively expressed as:
Figure BDA00023719787100000612
and
Figure BDA00023719787100000613
it is noted that the robot may be able to move the robot in a direction that is substantially perpendicular to the obstacle, if and only if the robot is sufficiently close to the obstacle,
Figure BDA00023719787100000614
when the obstacle avoidance task is not activated,
Figure BDA00023719787100000615
this task is built independently for each robot, rather than an accumulated task function.
In the subtasks where the robots are evenly distributed around the target, taking the planar case as an example, the ideal formation is a regular n-polygon and all the robots are eventually distributed at the vertices of the regular polygon.
The expected task function and the task function error are respectively as follows:
Figure BDA00023719787100000616
Figure BDA00023719787100000617
Figure BDA00023719787100000618
here, the first and second liquid crystal display panels are,
Figure BDA00023719787100000619
is the ideal distance between two adjacent robots.
kjIs an index that identifies the robot at the jth location along the circle, not necessarily the jth robot. The desired speed of the task is
Figure BDA0002371978710000071
The corresponding Jacobian matrix is
Figure BDA0002371978710000072
The pseudo inverse is
Figure BDA0002371978710000073
Figure BDA0002371978710000074
A constant positive definite matrix representing the gain.
In a subtask where the robot is maintained on a sphere or hypersphere surface centered on the target, the task function, the desired task function and the task function error are respectively:
Figure BDA0002371978710000075
Figure BDA0002371978710000076
Figure BDA0002371978710000077
the desired speed of this task is:
Figure BDA0002371978710000078
the corresponding jacobian matrix is:
Figure BDA0002371978710000079
the pseudo-inverse is:
Figure BDA00023719787100000710
Figure BDA00023719787100000711
and Λ2A constant positive definite matrix of gains is defined similarly.
Note 1.1. under three-dimensional space and p-dimensional (p >3) space, the problem of how to distribute points on spheres and hyperspheres is considered a Thomson problem. Many scholars have studied this problem and concluded that there is certainly a suitable distance.
Note 1.2. Once any robot is out of control and enters the virtual region BETA of another roboti,oThe robot will be considered an obstacle, which the rest of the robots must avoid. If two or more obstacles are considered simultaneously, the nearest obstacle will be processed first.
2. Inner loop controller design
In order to solve the problems of model uncertainty, external interference and the like and realize zero steady-state error tracking and bounded input, the IRPD-SMC is provided in an inner ring. The improved PD controller is used for stabilizing an equivalent part and providing a bounded input, the SMC part is used for compensating an external disturbance and a system uncertainty part, and the RBFNNS is used for estimating parameters unknown to the system.
(1)IRPD-SMC
Part of the control involves designing the controller and having each robot track the target trajectory
Figure BDA00023719787100000712
This trajectory may be formed byIn formula (2)
Figure BDA0002371978710000081
The result of the integration is that,
Figure BDA0002371978710000082
and similarly defined, they are bounded functions. Defining equivalent partial state quantities
Figure BDA0002371978710000083
Figure BDA0002371978710000084
Figure BDA0002371978710000085
Here, the first and second liquid crystal display panels are,
Figure BDA0002371978710000086
and
Figure BDA0002371978710000087
respectively, position tracking error and velocity tracking error.
γi＝diag(γi,1,γi,2...γi,p) Is a positive diagonal matrix defined as a sliding mode constant, and a sliding mode surface is defined as:
Figure BDA0002371978710000088
wherein the content of the first and second substances,
Figure BDA0002371978710000089
based on property 3, the reference moment is described as follows:
Figure BDA00023719787100000810
as can be seen,
Figure BDA00023719787100000811
unknown and difficult to determine because it contains perturbations and uncertain dynamics that are difficult to obtain. Therefore, RBFNNS is used to estimate the unknown and compensate for the interference.
Adaptive RBFNNS can be written as
Figure BDA00023719787100000812
Xi＝[xi,1,xi,2...xi,m]TIs an input to the computer system that is,
Figure BDA00023719787100000813
is a weight matrix, v is the number of neurons in the hidden layer,
Figure BDA00023719787100000814
is an activation function, one of which is commonly used:
Figure BDA00023719787100000815
ci,jis the center of the neuron, σi,jIs the width of the gaussian function.
The weight update rate is designed as follows:
Figure BDA00023719787100000816
μiis a positive fixed diagonal gain matrix.
There is an optimal RBFNNS to learn the reference moment ρiSo that
Figure BDA0002371978710000091
Figure BDA0002371978710000092
Is the optimal weight vector, εiIs provided withAnd (4) a bound nerve approximation error.
From the equations (6) and (9), it can be obtained
Figure BDA0002371978710000093
Wherein the content of the first and second substances,
Figure BDA0002371978710000094
the input of BBFNNS in the embodiment is selected as
Figure BDA0002371978710000095
By using estimated terms
Figure BDA0002371978710000096
The RPD-SMC control law is designed as follows:
Figure BDA0002371978710000097
in order to solve the problem of input bounding, the RPD-SMC control law needs to be improved. Currently, two typical saturation functions are available to ensure that the control input is bounded, a hyperbolic tangent function and an arctangent function, respectively. The curves of both functions are shown in fig. 2.
As shown in FIG. 2, the range of the arctangent function arctan (kx) is compared to the range (-1,1) of the hyperbolic tangent function tanh (kx)
Figure BDA0002371978710000098
Larger and for the same value of κ, (κ being a constant), the arc tan (κ x) function may approach saturation in a more gradual manner. The smaller the value of κ, the smaller the zero-crossing slope of the arc tan (κ x) function, the more nearly linearly the function approaches saturation. To better describe the direct proportional relationship between x and y, the arc tan (kx) function is typically multiplied by a certain amount of gain. As shown in fig. 3, by gain 5.5, y1Having an approximately proportional characteristic, i.e. y1＝5.5*arctan(0.2*x)。
Through the analysis, under the condition of fully considering actuator saturation, an arctangent function is designed to improve the PD part of the control law, so that an IRPD-SMC control law is proposed.
Figure BDA0002371978710000099
Wherein k isαiIs a position error dependent gain for canceling position errors; k is a radical ofβiIs a differential related gain used for predicting the overall response trend and preventing the system from acting too violently; λ is the approximate proportional gain; k is a radical ofiIs the robust term gain. All gains are positive.
Note 2.1 this embodiment does not consider the saturation behavior of the actuator, but instead presents a bounded input that can produce a finite magnitude. In practical applications, actuator saturation can be successfully prevented by appropriately adjusting the controller parameters.
Note 2.2 it can be seen that the proposed IRPD-SMC algorithm only correlates with the desired track signal
Figure BDA00023719787100000910
And error signal
Figure BDA00023719787100000911
It is related. Therefore, the proposed controller is model independent.
3. Stability analysis
From equation (4), one can obtain
Figure BDA0002371978710000101
Figure BDA0002371978710000102
From equations (1), (5) and (12), the following equations can be obtained:
Figure BDA0002371978710000103
theorem 3.1 consider the Eulerian Lagrangian system in equation (1), the IRPD-SMC control law designed by equation (11), and the weight update rate of equation (8). Provided that the control gain satisfies k, under the assumption that the properties 1-4 holdi>εi,maxRegardless of the interference and the uncertainty of the system, the following conclusions can be drawn.
1. If there is no conflict among the three tasks, the three tasks can be completed simultaneously, the whole system is globally and gradually stable, and the tracking error is
Figure BDA0002371978710000104
Converge to 0.
2. If the obstacle avoidance task is activated and conflicts with the convoy task, simultaneously setting the gain as
Figure BDA0002371978710000105
Wherein
Figure BDA0002371978710000106
Is based on robustness to noise. The obstacle avoidance task can be performed first, the system is globally asymptotically stable, and the tracking error is
Figure BDA0002371978710000107
Converge to 0.
And (3) proving that: lyapunov function V is selected as follows
V＝V1+V2
Figure BDA0002371978710000108
Figure BDA0002371978710000109
Wherein, η1，η2And η3Are positive design parameters, and
Figure BDA00023719787100001010
it is easy to conclude that V is a positive function. Base ofFrom equations (11) and (13), the following equations can be obtained:
Figure BDA00023719787100001011
will V1Differentiating time while substituting equations (4), (8) and (15) yields:
Figure BDA0002371978710000111
if k isi>εi,maxThat is to say
Figure BDA0002371978710000112
Is negatively determined and can be derived
Figure BDA0002371978710000113
It follows that the inner ring subsystem is globally asymptotically stable and the tracking error eiAnd
Figure BDA0002371978710000114
converge to 0.
Note 3.1. to eliminate chatter, introducing a hyperbolic tangent function, tanh (-), instead of a discontinuous sign (-), equation (11) can be modified:
Figure BDA0002371978710000115
wherein the content of the first and second substances,
Figure BDA0002371978710000116
will V2Differentiating the time to obtain:
Figure BDA0002371978710000117
two cases are discussed separately below: conflicting tasks and non-conflicting tasks;
suppose that between every two tasksWithout conflict, i.e.
Figure BDA0002371978710000118
Therefore, it is obtained from equation (18):
Figure BDA0002371978710000119
it can be concluded that if there is no conflict between each pair of tasks, the outer ring subsystem is globally asymptotically stable, and the tracking error eiAnd
Figure BDA00023719787100001110
converge to 0. If the obstacle avoidance task is activated and conflicts with the convoy task, V2This can be written as:
Figure BDA00023719787100001111
wherein the content of the first and second substances,
Figure BDA0002371978710000121
and P ═ Pij]I, j ═ 1,2,3, the submatrices of which are:
p11＝η1α1，
Figure BDA0002371978710000122
Figure BDA0002371978710000123
and
Figure BDA0002371978710000124
for arbitrary
Figure BDA0002371978710000125
Applying 2| ab ≦ a in equation (20)2+b2Obtaining:
Figure BDA0002371978710000126
wherein p isij,mAnd pij,mThe upper and lower limits of the induction sub-block of P are indicated, respectively.
Figure BDA0002371978710000127
Because | | J1||＝||J2||＝||J3||＝1，p22,m＝p 22,M0 and p33,m＝p33,M＝0，
Figure BDA0002371978710000128
And
Figure BDA0002371978710000129
will lose control, in which case V2Reset to
Figure BDA00023719787100001210
At the same time, the method can obtain,
Figure BDA00023719787100001211
it is also obtained that the outer ring subsystem is globally asymptotically stable.
In summary, the conclusion of theorem 3.1 holds true, meaning that the obstacle avoidance task has a higher priority and is executed first when it conflicts with the convoy task, second when no conflict exists, the convoy task is executed again, since NSB is a kinematics that works with a desired velocity rather than a desired position, a rational setting α is requiredi,1So that the velocity error dominates the position error.
By substituting equation (2) into equation (4) and considering that every two tasks conflict with each other, then
Figure BDA00023719787100001212
And
Figure BDA00023719787100001213
it can be removed. Thus, it is possible to provide
Figure BDA00023719787100001214
It is possible to obtain:
Figure BDA00023719787100001215
the inequality (22) is taken as an equation and the norm is taken on both sides, which can be obtained:
Figure BDA00023719787100001216
Figure BDA00023719787100001217
Figure BDA00023719787100001218
Figure BDA00023719787100001219
by selecting
Figure BDA00023719787100001220
Wherein
Figure BDA00023719787100001221
The design of (2) is based on robustness to noise, so that the function of the obstacle avoidance task can ensure that the robot is far away from the obstacle.
Note 3.2. if only two subtasks of the convoy task conflict, the robot only needs to complete the first two higher level tasks. No collision will occur, at this time
Figure BDA0002371978710000131
4. Simulation (Emulation)
In the embodiment, the comparison tests with APD-SMC, ASMC and PD-SMC show the superiority of the controller.
The kinetic equation for the robot is set as:
Figure BDA0002371978710000132
five robots are considered in the experiment of the two-dimensional space, six robots are adopted in the experiment of the three-dimensional space, and the system parameter is set to be M i1 and C i0. The outer loop parameters in two and three dimensions are shown in tables 1 and 2, respectively, and the controller parameters for ASMC, PD-SMC, APD-SMC and proposed IRPD-SMC were adjusted by trial and error, with the final selected parameter values shown in table 3.
TABLE 1
Two-dimensional spatial outer loop parameter values
Figure BDA0002371978710000133
TABLE 2
Three-dimensional space outer loop parameter value
Figure BDA0002371978710000134
TABLE 3
Control parameters of different controllers
Figure BDA0002371978710000135
Figure BDA0002371978710000141
Case 1. in two-dimensional space, the initial positions of the five robots are q, respectively1(0)＝[5,10]T,q2(0)＝[-5,5]T,q3(0)＝[-5,-5]T,q4(0)＝[5,-10]TAnd q is5(0)＝[5,0]T. The trajectory of the target is set to [3+0.1t,0 ═ c]TThe external disturbance parameter is
Figure BDA0002371978710000142
And
Figure BDA0002371978710000143
the values of the parameters for the outer and inner rings are shown in tables 1 and 3, respectively.
The trajectories of the five robots and the target in two-dimensional space are shown in fig. 4. Under the action of different controllers, the distance between the robot and the target, the distance between two adjacent robots, the position tracking error and the velocity tracking error are respectively shown in fig. 5(a) -8 (d). It can clearly be seen that there is a significant difference in the performance of these controllers when interference occurs. With the controller proposed herein, the control characteristics are significantly better than other controllers, as shown in fig. 5(a) - (d), fig. 5(a) is the distance between the robot and the target, fig. 5(b) is the distance between two adjacent robots, fig. 5(c) is the position tracking error, fig. 5(d) is the velocity tracking error, due to the learning ability and strong robustness of RBFNNS, the disturbances are well compensated and finally zero steady-state error is achieved.
In contrast, as shown in fig. 6(a) - (d), the PD-SMC controller cannot achieve zero steady-state error, and it can also be seen that the PD-SMC is limited in compensating for the interference. Sustained perturbation that is not changed when t-40S is introduced
Figure BDA0002371978710000144
At all times, the PD-SMC controller will always have tracking errors and all robots will never arrive on the reference trajectory anymore.
Finally, the control inputs of the IRPD-SMC are shown in fig. 9, and fig. 9 shows the control inputs of 5 robots when the IRPD-SMC is used, and it can be seen that the control inputs are small and do not exceed 4N. Likewise, by replacing the sign (-) function with the tanh (-) function, the tremor problem is solved and the control signal is continuous and physically realizable.
Case 2. to verify the noise immunity and robustness of the proposed controller, we performed the following simulation experiments and analyzed the results. In the two-dimensional space, the initial positions of the five robots and the set values of the outer and inner loop parameters are the same as in case 1. The target locus is [3+0.1t, sin0.1t%]TThe noise was considered and simulated by a gaussian function with a mean of 0 and a standard deviation of 0.2. The interference value is defined as
Figure BDA0002371978710000151
Where i is 1.
Fig. 10 shows the trajectories of five robots and targets when the IRPD-SMC technique is used in two dimensions for case 2. FIGS. 11(a) -13(d) show simulation experimental results for different controllers in the presence of interference and Gaussian noise. Compared to the controllers of fig. 12(a) -13(d), the proposed controller IRPD-SMC can effectively suppress noise and ensure position and velocity tracking errors of significantly less than 0.02m and 0.06m/s, respectively.
And 3, verifying the effectiveness of the proposed control law in the three-dimensional space under the condition that Gaussian noise and interference exist and the obstacle avoidance activity is in an activated state. In three-dimensional space, the initial positions of six robots are set to q1(0)＝[-10,1,0]T,q2(0)＝[-1,-10,0.3]T,q3(0)＝[10,0,1]T,q4(0)＝[0,0.5,10]T,q5(0)＝[0,10,0.3]TAnd q is6(0)＝[0,0,-10]T. The target locus is [0.1t,3+0.1t, sin0.1t%]TThe position of the obstacle is q0＝[15,3,-4.5]T. Interference value is set to
Figure BDA0002371978710000152
The parameters of the noise and the controller are set as in case 2, and the parameters of the outer loop controller are set as in table 2.
The simulation results of the proposed IRPD-SMC algorithm are shown in fig. 14-16 (d). Obviously, the proposed control strategy can make the robot change its own position to avoid obstacles and collisions when an obstacle avoidance task occurs. Further, as is clear from fig. 17(a) -18(d), APD-SMC and ASMC are less accurate in control than IRPD-SMC.
In summary, the simulation results verify that the control effect of the control method provided by the embodiment is obviously better than that of the PD-SMC, the APD-SMC, and the ASMC no matter whether the obstacle avoidance task is in the activated state or not. Due to the learning capability of RBFNNS and the strong robustness of SMC, IRPD-SMC has strong robustness to various interferences and noises. Furthermore, the IRPD-SMC may provide limited control inputs to prevent actuator saturation.
Example two
In one or more embodiments, a convoy mission coordinated control system based on an obstacle environment and bounded input is disclosed, comprising: the controller adopts an inner ring and outer ring control structure, the outer ring adopts a behavior control method based on a space, and expected speed and an expected motion track required by an inner ring physical model are generated; the inner ring is based on an improved proportional derivative sliding mode control method of the adaptive radial basis function neural network, so that each physical model can track expected speed and expected motion trail under the condition of interference and parameter uncertainty, and zero steady-state error and bounded input are realized.
The specific implementation method of the controller refers to the method disclosed in the first embodiment.
EXAMPLE III
In one or more embodiments, a terminal device is disclosed that includes a processor and a computer-readable storage medium, the processor to implement instructions; the computer readable storage medium is used for storing a plurality of instructions, and the instructions are suitable for being loaded by a processor and executing the convoy mission cooperative control method based on the obstacle environment and the bounded input in the first embodiment.
In another or more implementations, a computer-readable storage medium is disclosed, in which a plurality of instructions are stored, the instructions being adapted to be loaded by a processor of a terminal device and to perform the convoy mission cooperative control method based on an obstacle environment and bounded input in the first embodiment.
Although the embodiments of the present invention have been described with reference to the accompanying drawings, it is not intended to limit the scope of the present invention, and it should be understood by those skilled in the art that various modifications and variations can be made without inventive efforts by those skilled in the art based on the technical solution of the present invention.

Claims (10)

1. The convoy task cooperative control method based on the obstacle environment and bounded input is characterized by comprising the following steps of:
describing a physical model of the convoy task by adopting a multi-Euler-Lagrange system;
an inner ring and outer ring control structure is adopted, the outer ring adopts a behavior control method based on a space, and expected speed and an expected motion track required by an inner ring physical model are generated; the inner ring is based on an improved proportional derivative sliding mode control method of the adaptive radial basis function neural network, so that each physical model can track expected speed and expected motion trail under the condition of interference and parameter uncertainty, and zero steady-state error and bounded input are realized.
2. The collaborative control method for the convoy mission based on the obstacle environment and the bounded input according to claim 1, wherein the inner loop is based on a proportional derivative sliding mode control method of an improved adaptive radial basis function neural network, and the control law is as follows:
Figure FDA0002371978700000011
wherein k isαiIs a position error dependent gain for canceling position errors; k is a radical ofβiIs a differential related gain used for predicting the overall response trend and preventing the system from acting too violently; λ is the approximate proportional gain; k is a radical ofiIs the robust term gain, κ is a constant;
Figure FDA0002371978700000012
is the reference torque ρiEstimated value of eiIs a position tracking error,
Figure FDA0002371978700000013
Is the velocity tracking error, siIs a slip form surface.
3. The collaborative control method for an escort task based on an obstacle environment and bounded input according to claim 2, wherein the adaptive radial basis function neural network is specifically:
Figure FDA0002371978700000014
wherein the content of the first and second substances,
Figure FDA0002371978700000015
is the input signal of the neural network and,
Figure FDA0002371978700000016
is a weight matrix, v is the number of neurons in the hidden layer, Φi(Xi) Is an activation function;
the weight update rate is designed as follows:
Figure FDA0002371978700000017
wherein, muiIs a positive fixed diagonal gain matrix.
4. The coordinated convoy mission control method based on a barrier environment and bounded inputs according to claim 2, wherein, in order to eliminate tremor, a hyperbolic tangent function tanh () is introduced instead of a discontinuous sign () function, said control law being modified as:
Figure FDA0002371978700000018
wherein the content of the first and second substances,
Figure FDA0002371978700000019
5. the coordinated convoying task control method based on the obstacle environment and the bounded input according to claim 1, wherein the physical model comprises: any one of a multi-robot arm, a multi-mobile robot, a multi-underwater vehicle, a multi-surface ship, a multi-step robot, and a multi-spacecraft.
6. The collaborative control method for the convoy mission based on the obstacle environment and the bounded input according to claim 1, wherein the outer loop adopts a behavior control method based on the empty space to generate the expected speed and the expected movement track required by the physical model of the inner loop, and specifically comprises the following steps:
decomposing the navigation task with the obstacle avoidance requirement into an obstacle avoidance subtask and a navigation task; the convoy mission comprises the following steps: the subtasks of the robot distributed evenly around the target and the subtasks of the robot maintained on the surface of a sphere or a hyper-sphere centered on the target;
defining the priority of the subtasks;
the desired velocities of the individual tasks are projected into the empty space created by the Jacobian matrix of high priority tasks, building an integrated total desired velocity command to drive the physical model.
7. A convoy mission cooperative control system based on obstacle environment and bounded input is characterized by comprising: the controller adopts an inner ring and outer ring control structure, the outer ring adopts a behavior control method based on a space, and expected speed and an expected motion track required by an inner ring physical model are generated; the inner ring is based on an improved proportional derivative sliding mode control method of the adaptive radial basis function neural network, so that each physical model can track expected speed and expected motion trail under the condition of interference and parameter uncertainty, and zero steady-state error and bounded input are realized.
8. The convoy mission cooperative control system based on the obstacle environment and the bounded input according to claim 7, wherein the inner loop is based on a proportional derivative sliding mode control method of the improved adaptive radial basis function neural network, and the control law is as follows:
Figure FDA0002371978700000021
wherein k isαiIs a position error dependent gain for canceling position errors; k is a radical ofβiIs a differential related gain used for predicting the overall response trend and preventing the system from acting too violently; λ is the approximate proportional gain; k is a radical ofiIs the robust term gain, κ is a constant;
Figure FDA0002371978700000022
is the reference torque ρiEstimated value of eiIs a position tracking error,
Figure FDA0002371978700000023
Is the velocity tracking error, siIs a slip form surface.
9. A terminal device comprising a processor and a computer-readable storage medium, the processor being configured to implement instructions; a computer readable storage medium storing a plurality of instructions adapted to be loaded by a processor and to perform the method for collaborative control of an escort mission based on an obstacle environment and bounded input according to any of claims 1-6.
10. A computer-readable storage medium having stored thereon a plurality of instructions adapted to be loaded by a processor of a terminal device and to execute the method for collaborative control of escort mission based on obstacle environment and bounded input according to any one of claims 1 to 6.
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