CN112286056B - Consistency control method for multi-neutral buoyancy robot - Google Patents
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Abstract
The invention discloses a consistency control method for a multi-neutral buoyancy robot, provides a parameter adjusting method according to a linear matrix inequality, and belongs to the field of robot control; firstly, establishing a neutral buoyancy robot system model under an inertial coordinate system, and establishing an input item and an output item of the system; then establishing a multi-neutral buoyancy robot information interaction model into a directed topology model, and giving important assumptions of the interaction model; on the basis of the two, a distributed reduced order disturbance observer is designed to estimate a consistency error state and unknown disturbance in real time, and a parameter adjusting method of the disturbance observer is provided; finally, a feedback controller is designed according to the distributed reduced-order forced disturbance observer, and consistency and strong robustness of the multi-neutral buoyancy robot system are guaranteed. The invention combines the characteristics of the neutral buoyancy robot model, and the designed control strategy has good control performance and is suitable for engineering application.
Description
Technical Field
The invention belongs to the field of robot control, and particularly relates to a consistency control method for a multi-neutral buoyancy robot.
Background
Due to deepening of space research and improvement of space application capability, research on microgravity environment simulation experiments for ground verification is receiving more and more extensive attention at home and abroad. In the research of microgravity environment simulation experiments, the application of a neutral buoyancy system to the simulation experiments in the microgravity environment is one of the important methods. In addition, as space operation tasks are complex and changeable, a single large-scale spacecraft cannot well complete the tasks, and therefore the problem that multiple neutral buoyancy robots simulate multiple spacecrafts to complete the operation tasks is urgently needed to be solved. The neutral buoyancy robot is a typical Lagrangian system, the coupling exists in the internal state, and the viscous resistance in water is large, so when a plurality of neutral buoyancy robots are designed to work cooperatively, the influence on the system caused by external disturbance and internal uncertainty must be considered. Meanwhile, the conditions of sudden failure of the sensor and the like can cause the wild value of the sensor, further cause system oscillation and even cause system instability, so that the designed distributed attitude control algorithm still can well realize the consistency control of the multi-neutral buoyancy robot under the condition that various uncertainties exist.
The robustness performance of the consistency control strategy for the multi-neutral buoyancy robot is poor at present, but the control accuracy has very important significance for improving the robustness performance of the system for the neutral buoyancy robot with strong coupling, strong nonlinearity and space external disturbance; meanwhile, the influence of the sensor outlier on the system is well considered by aiming at the consistency control strategy of the multi-neutral buoyancy robot at present, and in order to process the sensor outlier problem and improve the robustness of the system, a control method based on a distributed reduced-order forced disturbance observer is adopted.
For a traditional disturbance observer, the disturbance observer is usually designed for a single system, and in addition, the influence of a sensor field value on a multi-robot system is rarely considered, so that the disturbance observer has a limitation in engineering application.
Disclosure of Invention
The invention aims to provide a consistency control method for a multi-neutral buoyancy robot, which aims to solve the problems.
In order to achieve the purpose, the invention adopts the following technical scheme:
a consistency control method for a multi-neutral buoyancy robot comprises the following steps:
step 1, establishing a neutral buoyancy robot attitude kinematics and dynamics model under an inertial coordinate system;
step 2, establishing a multi-neutral buoyancy robot information interaction model;
step 3, constructing a distributed reduced order forced disturbance observer, providing a distributed reduced order forced disturbance observer and a saturation upper bound function parameter adjusting method, and adjusting parameters of the disturbance observer by solving a linear matrix inequality;
step 4, designing a distributed controller based on the reduced-order forced disturbance observer, providing a parameter adjustment method of the distributed controller, and adjusting the parameters of the controller by solving a linear matrix inequality;
and 5, finishing a control strategy of consistency of the multi-neutral buoyancy robot.
Further, step 1 specifically includes:
the underwater six-degree-of-freedom robot dynamics and kinematics model comprises the following steps:
wherein M is RB Representing the body inertia matrix, C RB Representing the Kerio force matrix of the body, M AM Representing the water flow medium inertia matrix, C, associated with the body AM Representing the body-related Corio force matrix of the aqueous flow medium, D r (v r (t)) v (t) is the viscous drag and g (η (t)) is the negative buoyancy; tau. c (t) represents a control torque; j (η (t)) represents a Jacobian matrix; eta (t), v (t) and v r (t)＝v(t)-v c (t) respectively representing the position and velocity of the body in a body coordinate system and the generalized velocity of the fluid in the body coordinate system, v c (t) is the speed of the water flow in the body coordinate system;
suppose that:
1. water velocity v in body coordinate system c Being slowly time-varying, i.e. v c (t)≈0；
2.v c The velocity v of the underwater robot is small, and is approximately C (v (t)) v (t) ≈ C (v (t) r (t))v r (t)；
Equation (1) is simplified to the form:
wherein M = M RB +M AM ，C＝C RB +C AM
Finally, the equation of motion under the inertial system is obtained:
in the formula (I), the compound is shown in the specification,
M * ＝J -T (η(t))MJ -1 (η(t))
D * (v(t),η(t))＝J -T (η(t))D(v(t))J -1 (η(t))
g * (η(t))＝J -T (η(t))g(η(t))
wherein D * (v(t),η(t))v(t),g * And (η (t)) is an unknown term.
Further, step 2 specifically includes:
consider first that there are N +1 neutrally buoyant robots, consider i =0 as the leader robot, consider i =1, 2.. The.n as the follower robot; wherein leader system state η is assumed 0 ,
Is bounded; neutral buoyancy robot information interaction model established as directed topology
Wherein
Representing a set of respective neutral buoyancy robots;
represents the set of all transmissions; the adjacency matrix of the follower is defined as
Wherein, when the l posture information of the follower neutral buoyancy robot is directly transmitted to the neutral buoyancy robot i, a il > 0, otherwise, a il =0, and is adjacent to the matrix diagonal element a ii ＝0；N i Representing the set of all the received neighbor neutral buoyancy robots of the neutral buoyancy robot i; defining the Laplace matrix as L = [ ] il ]∈R N×N Wherein, when i = l,
when i ≠ L, L il ＝-a il (ii) a When the neutral buoyancy robot i can directly receive the posture information of the leader, b i > 0, otherwise, b i =0; definition matrix
It is assumed that each follower neutrally buoyant robot can receive information directly or indirectly from the leader neutrally buoyant robot.
Further, step 3 specifically includes:
firstly, defining the consistency error of the local neighbor of the ith follower neutral buoyancy robot as
Wherein, the first and the second end of the pipe are connected with each other,
is leader following consistency error;
considering the neutral buoyancy robot attitude kinematics and a second-order equation of a kinetic equation, constructing a reduced-order forced disturbance observer for estimating the system uncertainty and the environment external disturbance:
wherein beta is i2 ,β i3 For observer gain, ρ is a positive constant, z i2 And z i3 Is a reduced order observer state estimation, γ i ＝diag{σ i1 ,…,σ i6 }，
σ ij Is the dynamic upper bound of the saturation function, obtained by the differential equation
Wherein the content of the first and second substances,
and j =1,2,3,4,5,6;
the parameters of the disturbance observer are adjusted by solving the following linear matrix inequality, so that the disturbance observer achieves a good estimation effect;
in the formula (I), the compound is shown in the specification,
denotes the kronecker product, I N Is an N-dimensional identity matrix, P i ＝S i -1 ,R i Is a positive definite symmetric matrix, J is a diagonal matrix and satisfies J = T -1 LT, wherein T -1 Is a non-singular matrix, m i Is that the positive definite constant satisfies M i -1 ＜m i I 6 ，c i Positive definite constant satisfies
Further, step 4 specifically includes:
the following states are defined first:
according to the transformed system state, the following distributed controllers are designed:
in the formula, k i1 ,k i2 Is the gain of the controller and is,
it is unknown disturbance information observed by the disturbance observer that is used to compensate the uncertainty inside the system and the varying external disturbance in real time,
the distributed controller parameter adjusting method is given below, and the controller parameters are adjusted by solving the following linear matrix inequality, so that the multi-neutral buoyancy robot system obtains a good control effect;
wherein the content of the first and second substances,
is a positive definite symmetric matrix, B i And D i Is defined asLower part
B i ＝[0,I 6 ] T ,
Wherein λ is i Is the ith eigenvalue of matrix J.
Further, step 5 specifically includes:
finally obtaining the control torque tau i And (t) carrying out control in a neutral buoyancy robot system model (4) under an inertial coordinate system, respectively designing a distributed reduced order forced disturbance observer and a controller for the neutral buoyancy robot according to a control strategy, and controlling the neutral buoyancy robot so as to enable the multiple neutral buoyancy robots to achieve consistency.
Compared with the prior art, the invention has the following technical effects:
the invention provides a consistency control method of a multi-neutral buoyancy robot based on a distributed reduced-order forced disturbance observer, which comprises the steps of designing the distributed reduced-order forced disturbance observer aiming at a neutral buoyancy robot by establishing a neutral buoyancy robot system model under an inertial coordinate system, and providing parameters of the disturbance observer by solving a linear matrix inequality; the distributed controller is designed to control the neutral buoyancy robot, real-time compensation is carried out on uncertainty of the system, robustness of a control algorithm is strong, higher control accuracy and higher response speed can be obtained, and engineering implementation is facilitated.
The invention provides a distributed reduced order forced disturbance observer, obtains parameters of the distributed reduced order forced observer by solving a linear matrix inequality, simultaneously considers the condition that a sensor has a wild value, improves the robustness of a system and is convenient for engineering realization;
on the basis of a distributed reduced-order forced disturbance observer, a multi-robot consistency controller is designed, and when a consistency result is obtained, real-time compensation is performed on internal uncertainty and external disturbance of a system, so that more excellent control performance is obtained;
based on a distributed control strategy, the information interaction of the multi-neutral-buoyancy robot under the directed topology is realized, the information transmission is reduced, and the application scene of the multi-neutral-buoyancy robot is greatly expanded.
Drawings
FIG. 1 is a flow chart of the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings:
referring to fig. 1, a consistency control method for a multi-neutral-buoyancy robot includes:
the first step is as follows: establishing neutral buoyancy robot attitude kinematics and dynamics model under inertial coordinate system
Consider the underwater six-degree-of-freedom robot dynamics and kinematics models of equations (1) - (2).
Wherein M is RB Representing the body inertia matrix, C RB Representing the Kerio force matrix of the body, M AM Representing the inertia matrix of the water flow medium, C, associated with the body AM Representing the body-related Corio force matrix of the aqueous flow medium, D r (v r (t)) v (t) is the viscous drag and g (η (t)) is the negative buoyancy; tau is c (t) represents a control torque; j (η (t)) represents a Jacobian matrix; eta (t), v (t) and v r (t)＝v(t)-v c (t) respectively representing the position and velocity of the body in a body coordinate system and the generalized velocity of the fluid in the body coordinate system, v c And (t) is the speed of the water flow under the body coordinate system.
For ease of design, the following assumptions are generally made:
1. water velocity v in body coordinate system c Being slowly time-varying, i.e. v c (t)≈0；
2.v c The velocity v relative to the underwater robot is small, and is approximately C (v (t)) v (t) ≈ C (v (t) r (t))v r (t)。
Equation (1) is simplified to the form:
wherein M = M RB +M AM ，C(v(t))＝C RB +C AM
Finally, the motion equation under the inertial system is obtained:
in the formula (I), the compound is shown in the specification,
M * ＝J -T (η(t))MJ -1 (η(t))
D * (v(t),η(t))＝J -T (η(t))D(v(t))J -1 (η(t))
g * (η(t))＝J -T (η(t))g(η(t))
wherein D * (v(t),η(t))v(t),g * And (η (t)) is an unknown term.
The relevant parameters are defined as follows:
r B ＝[x B ,y B ,z B ] T ＝[0,0,0] T ，r G ＝[x G ,y G ,z G ] T ＝[0,0,0.05] T ，m＝125，
wherein x is B ，y B And z B Is the floating center coordinate, x G ，y G And z G Representing coordinates of the centroid, m representing mass, I 0 Is a matrix of moments of inertia, v 1 ＝[μ υ ω] T And v 2 ＝[p q r] T Is the translational and angular velocity components of the velocity v (t), C AM And C RB Respectively, the coriolis matrix and the coriolis matrix that the motion of the fluid being discharged has.
The second step is that: establishing multi-neutral buoyancy robot information interaction model
First we consider N +1 neutrally buoyant robots, we consider i =0 as the leader robot and i =1,2. Wherein, for design convenience, we assume leader System State η 0 ,
Is bounded. The information interaction model of the neutral buoyancy robot can be established into a directed topology
Wherein
Representing a collection of respective neutral buoyancy robots.
Representing the set of all transmissions. The neighbor matrix of the follower is defined as
Wherein, when the posture information of the follower neutral buoyancy robot is directly transmitted to the neutral buoyancy robot i, a il > 0, otherwise, a il =0, and is adjacent to the matrix diagonal element a ii ＝0。N i Represents the set of all the received neighbor neutral buoyancy robots of the neutral buoyancy robot i. We define the Laplace matrix as L = [ ] il ]∈R N×N Wherein, when i = l,
when i ≠ L, L il ＝-a il . When the neutral buoyancy robot i can directly receive the posture information of the leader, b i > 0, otherwise, b i =0. We define a matrix
Here, we assume that each follower neutrally buoyant robot can receive information of the leader neutrally buoyant robot, either directly or indirectly.
In this example, consider 4 neutrally buoyant robots, one of which is the leader neutrally buoyant robot, and the remaining 3 which are the follower neutrally buoyant robots. The relevant topological parameters are given below
The third step: construction of distributed reduced-order forced disturbance observer
Firstly, defining the consistency error of the local neighbor of the ith follower neutral buoyancy robot as
Wherein, the first and the second end of the pipe are connected with each other,
is the leader following consistency error.
Considering the attitude kinematics and the second order equation of the dynamic equation of the neutral buoyancy robot, a reduced order forced disturbance observer is constructed for estimating the system uncertainty and the environmental external disturbance:
wherein, beta i2 ,β i3 For observer gain, ρ is a positive constant, z i2 And z i3 Is a reduced order observer state estimation, γ i ＝diag{σ i1 ,…,σ i6 }，
σ ij Is the dynamic upper bound of the saturation function, obtained by the differential equation
Wherein the content of the first and second substances,
and j =1,2,3,4,5,6.
The parameters of the disturbance observer can be adjusted by solving the following linear matrix inequality, so that the disturbance observer achieves a good estimation effect.
In the formula (I), the compound is shown in the specification,
denotes the kronecker product, I N Is an N-dimensional identity matrix, P i ＝S i -1 ,R i Is a positive definite symmetric matrix, J is a diagonal matrix and satisfies J = T -1 LT, wherein T -1 Is a non-singular matrix, m i Is that the positive definite constant satisfies M i -1 ＜m i I 6 ，c i Positive definite constant satisfies
In this example, ρ =1.5,m i ＝187.5,c i ＝125，β i2 ,β i3 The values of (A) are as follows:
β i2 ＝diag{500 500 1500 500 1500 1500},
β i3 ＝diag{100 100 200 100 200 200},
the fourth step: design distributed controller based on reduced order compulsory observer
Based on a reduced order observer, we design the following distributed controller.
The following states are defined first:
according to the transformed system state, the following distributed controllers are designed:
in the formula, k i1 ,k i2 Is the gain of the controller and is,
it is unknown disturbance information observed by the disturbance observer that is used to compensate for uncertainty and varying external disturbance inside the system in real time,
the distributed controller parameter adjusting method is given below, and the controller parameters can be adjusted by solving the following linear matrix inequality, so that the multi-neutral-buoyancy-force robot system can obtain a good control effect.
Wherein, the first and the second end of the pipe are connected with each other,
is a positive definite symmetric matrix, B i And D i Is defined as follows
B i ＝[0,I 6 ] T ,
Wherein λ is i Is the ith eigenvalue of the matrix J.
In this example, the values of the adjustable parameters are:
k i1 ＝15,k i2 ＝15,λ i ＝1。
the fifth step: control strategy for achieving consistency of multi-neutral buoyancy robot
Finally obtaining the control torque tau i (t) bringing into an inertial coordinate systemAnd controlling the neutral buoyancy robot system model (4), respectively designing a distributed reduced-order forced disturbance observer and a controller for the neutral buoyancy robot according to a control strategy, and controlling the neutral buoyancy robot to ensure that the multiple neutral buoyancy robots reach consistency.
This invention is not described in detail and is within the ordinary knowledge of a person skilled in the art.
Claims (2)
1. A consistency control method for a multi-neutral buoyancy robot is characterized by comprising the following steps:
step 1, establishing a neutral buoyancy robot attitude kinematics and dynamics model under an inertial coordinate system;
step 2, establishing a multi-neutral buoyancy robot information interaction model;
step 3, constructing a distributed reduced order forced disturbance observer, providing a distributed reduced order forced disturbance observer and a saturation upper bound function parameter adjusting method, and adjusting parameters of the disturbance observer by solving a linear matrix inequality;
step 4, designing a distributed controller based on the reduced order forced disturbance observer, providing a parameter adjustment method of the distributed controller, and adjusting the parameters of the controller by solving a linear matrix inequality;
step 5, completing a control strategy of consistency of the multi-neutral buoyancy robot;
the step 1 specifically comprises:
the underwater six-degree-of-freedom robot dynamics and kinematics model comprises the following steps:
wherein, M RB Representing the body inertia matrix, C RB Representing the Kerio force matrix of the body, M AM Display and machineBody-related water flow medium inertia matrix, C AM Representing the body-related Corio force matrix of the aqueous flow medium, D r (v r (t))v r (t) is viscous drag, g (η (t)) is negative buoyancy; tau. c (t) represents a control torque; j (η (t)) represents a Jacobian matrix; eta (t), v (t) and v r (t)＝v(t)-v c (t) respectively representing the position and velocity of the body in a body coordinate system and the generalized velocity of the fluid in the body coordinate system, v c (t) is the speed of the water flow under the body coordinate system;
suppose that:
1. water velocity v in body coordinate system c Being slowly time-varying, i.e. v c (t)≈0；
2.v c The velocity v relative to the underwater robot is small, and is approximately C (v (t)) v (t) ≈ C (v (t) r (t)) v r (t)；
Equation (1) is simplified to the form:
wherein M = M RB +M AM ，C＝C RB +C AM
Finally, the motion equation under the inertial system is obtained:
in the formula (I), the compound is shown in the specification,
M * ＝J -T (η(t))MJ -1 (η(t))
D * (v(t)，η(t))＝J -T (η(t))D(v(t))J -1 (η(t))
g * (η(t))＝J -T (η(t))g(η(t))
wherein D * (v(t)，η(t))v(t)，g * (η (t)) is unknown;
the step 2 specifically comprises the following steps:
first consider that there are N +1 neutral buoyancy robots, consider i =0 as the leader robot, and i =1, 2. Wherein leader system state η is assumed 0 ，
Is bounded; neutral buoyancy robot information interaction model established as directed topology
Wherein
Representing a set of respective neutral buoyancy robots;
represents the set of all transmissions; the neighbor matrix of the follower is defined as
Wherein, when the l posture information of the follower neutral buoyancy robot is directly transmitted to the neutral buoyancy robot i, a il > 0, otherwise, a il =0, and is adjoined by the matrix diagonal element a ii ＝0；N i Representing the set of all the received neighbor neutral buoyancy robots of the neutral buoyancy robot i; defining the Laplace matrix as L = [ L ] il ]∈R N×N Wherein, when i = l,
when i ≠ L, L il ＝-a il (ii) a When the neutral buoyancy robot i can directly receive the posture information of the leader, b i > 0, otherwise, b i =0; definition matrix
Assuming that each follower neutral buoyancy robot can directly or indirectly receive the information of the leader neutral buoyancy robot;
the step 3 specifically comprises the following steps:
firstly, defining the consistency error of the local neighbor of the ith follower neutral buoyancy robot as
Wherein the content of the first and second substances,
is leader following consistency error;
considering the attitude kinematics and the second order equation of the dynamic equation of the neutral buoyancy robot, a reduced order forced disturbance observer is constructed for estimating the system uncertainty and the environmental external disturbance:
wherein, beta i，2 ，β i，3 For observer gain, ρ is a positive constant, z i，2 And z i，3 Is the ith reduced order observer state estimate, γ i ＝diag{σ i1 ，…，σ i6 }，
σ ij J =1,2,3,4,5,6 is the dynamic upper bound of the saturation function;
σ ij obtained by the following differential equation
Wherein the content of the first and second substances,
and j =1,2,3,4,5,6;
the parameters of the disturbance observer are adjusted by solving the following linear matrix inequality, so that the disturbance observer achieves a good estimation effect;
in the formula (I), the compound is shown in the specification,
denotes the kronecker product, I N Is an N-dimensional identity matrix, P i ＝S i -1 ，R i Is a positive definite symmetric matrix, J is a diagonal matrix and satisfies J = T -1 LT, wherein T -1 Is a non-singular matrix, m i Is that the positive definite constant satisfies M i -1 ＜m i I 6 ，c i Positive definite constant satisfies
b i ＝diag{β i，2 ，β i，3 }，
The step 4 specifically comprises the following steps:
the following states are defined first:
according to the transformed system state, the following distributed controllers are designed:
in the formula, k i1 ，k i2 Is the gain of the controller(s),
it is unknown disturbance information observed by the disturbance observer that is used to compensate the uncertainty inside the system and the varying external disturbance in real time,
the distributed controller parameter adjusting method is given below, and the controller parameters are adjusted by solving the following linear matrix inequality, so that the multi-neutral buoyancy robot system obtains a good control effect;
wherein the content of the first and second substances,
is a positive definite symmetric matrix, B i And D i Is defined as follows
B i ＝[0，I 6 ] T ，
Wherein λ is i Is the ith eigenvalue of the matrix J.
2. The consistency control method of the multi-neutral-buoyancy robot according to claim 1, wherein the step 5 specifically comprises:
finally obtaining the control moment tau i (t) model of the neutrally buoyant robot system brought into the inertial coordinate system ( 4 ) The method comprises the steps of controlling, respectively designing a distributed reduced-order forced disturbance observer and a controller for the neutral buoyancy robot according to a control strategy, and controlling the neutral buoyancy robot, so that the multiple neutral buoyancy robots achieve consistency.
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