CN108445768B - Augmented self-adaptive fuzzy control method for operation space trajectory tracking of space robot - Google Patents

Augmented self-adaptive fuzzy control method for operation space trajectory tracking of space robot Download PDF

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CN108445768B
CN108445768B CN201810534470.4A CN201810534470A CN108445768B CN 108445768 B CN108445768 B CN 108445768B CN 201810534470 A CN201810534470 A CN 201810534470A CN 108445768 B CN108445768 B CN 108445768B
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fuzzy
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matrix
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CN108445768A (en
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陈志勇
李振汉
王奋勇
郑永铭
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Fuzhou University
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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
    • 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
    • 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
    • G05D1/0212—Control of position or course in two dimensions specially adapted to land vehicles with means for defining a desired trajectory

Abstract

The invention provides an augmented self-adaptive fuzzy control algorithm for tracking an operation space track of a floating-based space robot, which comprises the following specific steps of: step S1: establishing an under-actuated joint space system kinetic equation; step S2: deducing a corresponding operating space system kinetic equation by using the system motion relation; step S3: carrying out fuzzy approximation processing on each uncertain function item of the system by using a fuzzy approximation idea; step S4: adaptive modulation rhythm is introduced to adjust the fuzzy weight in real time, and an adaptive fuzzy controller is further designed to realize accurate tracking of the expected track of the system operation space. The control algorithm can be applied to an under-actuated model of the space robot with uncertain model parameters and external disturbance, and can realize accurate tracking of an operation space track; the calculation amount of the algorithm is reduced; the control moment of the mechanical arm joint and the control moment of the carrier attitude are independent, and the method is favorable for practical application.

Description

Augmented self-adaptive fuzzy control method for operation space trajectory tracking of space robot
Technical Field
The invention belongs to the field of robot intelligent control and numerical simulation, and particularly relates to an augmented self-adaptive fuzzy control method for space robot operation space trajectory tracking.
Background
With the rapid development of aerospace technology, space robots have become a main tool for space development and construction. Because the carrier base is not fixed, the dynamics modeling and nonlinear control problems of the space robot under the space weightlessness environment are far more complicated than those of the ground robot. In order to reduce the labor intensity of astronauts and improve the space operation efficiency, space robots are required to have certain autonomous and high-precision operation capability, so the design problem of a core control system of the space robots must be solved. In order to save control fuel consumption and prolong the whole service life of the system, the space robot carrier control system is always in a closed state, and the operation space task of the space robot carrier control system is mainly realized by a mechanical arm joint control system. However, due to the complexity of the structure, grabbing of unknown mass objects, fuel consumption and the like, the inertial parameters of the space robot system are often uncertain; the uncertainty of the parameters not only makes a space robot dynamic model not accurately obtained, but also makes a system motion Jacobian matrix reflecting the relation between the system operation space velocity and the joint space velocity have uncertainty. The result brings great difficulty to the design of the operation space trajectory tracking controller of the carrier pose uncontrolled space robot. In order to eliminate the influence of uncertainty of system parameters, various composite adaptive control and robust control methods are proposed, but the design of the control methods mostly depends on the characteristics of a dynamic model of the system (such as skew symmetry among correlation matrixes, an equation needing to meet the property of quasi-linearization and the like). Moreover, an extreme space environment with large temperature difference and strong radiation is easy to introduce unknown external disturbance influence to the space robot system, so that the space robot control system is required to not only eliminate the uncertainty of system parameters, but also have certain disturbance rejection capability. Therefore, how to design an effective control algorithm to meet the above-mentioned control requirements is a hot topic in the field of space robot control at present, and as one of the mainstream intelligent control algorithms, a fuzzy control algorithm independent of a controlled object model is a good choice.
Disclosure of Invention
The invention aims to provide an augmented self-adaptive fuzzy control algorithm to solve the control problem of space robot operation space trajectory tracking under the influence of uncertain system model parameters and external disturbance.
The invention adopts the following technical scheme: an augmented adaptive fuzzy control algorithm for tracking the track of an operation space of a floating-based space robot comprises the following specific steps: step S1: establishing an under-actuated joint space system kinetic equation; step S2: deducing a corresponding operating space system kinetic equation by using the system motion relation; step S3: carrying out fuzzy approximation processing on each uncertain function item of the system by using a fuzzy approximation idea; step S4: adaptive modulation rhythm is introduced to adjust the fuzzy weight in real time, and an adaptive fuzzy controller is further designed to realize accurate tracking of the expected track of the system operation space.
In an embodiment of the present invention, in step S1, an under-actuated joint space system kinetic equation is established by taking a planar floating base two-rod space robot as an example; the joint space system dynamic equation in the underactuated form is as follows:
Figure GDA0002765695820000021
wherein D (q) e R3×3A symmetric and positive definite inertia matrix of the system is obtained;
Figure GDA0002765695820000022
is a column vector containing the Coriolis force and the centrifugal force of the system; tau isc∈R3Bounded external perturbations for the system; q ═ α, θ1,θ2]TFor the attitude angle alpha of the system base and the joint angle theta of the two connecting rods1、θ2A column vector of components; tau epsilon to R2The control moment column vector of each joint of the mechanical arm.
In an embodiment of the present invention, the step S2 includes the following steps:
step S21: definition of X ═ Xp,yp]TFor the actual output of the operating space at the end of the system, Y ═ α, XT]TFor the expanded system to increase the control output, the joint space velocity
Figure GDA0002765695820000023
And increase the operating space velocity
Figure GDA0002765695820000024
The following relationships exist:
Figure GDA0002765695820000025
wherein the content of the first and second substances,
Figure GDA0002765695820000026
the generalized Jacobian matrix of the system after being augmented; matrix representation of the last two rows of J
Figure GDA0002765695820000027
And
Figure GDA0002765695820000028
the customary Jacobian matrix of cells, and Jij(i is 1, 2; j is 1,2,3) is a system inertia parameter and sine and cosine functions of each joint angle;
step S22: avoidance of the singular problem of dynamics of the system, Jv＝J-1(ii) present; considering the parameter uncertainty condition of the system; on the basis, an augmented Jacobian matrix estimation value is introduced
Figure GDA0002765695820000029
And converting the proposed joint space dynamics equation into an operation space dynamics equation form by utilizing the system kinematics relationship:
Figure GDA0002765695820000031
wherein the content of the first and second substances,
Figure GDA0002765695820000032
: step S23: defining state variables
Figure GDA0002765695820000033
And is
Figure GDA0002765695820000034
Converting the operating space dynamics equation into a state equation form:
Figure GDA0002765695820000035
wherein A ═ diag [ A ]1，A2，A3]，B＝diag[B1，B2，B3]，
Figure GDA0002765695820000036
Figure GDA0002765695820000037
Figure GDA0002765695820000038
In an embodiment of the present invention, in step S3:
step S31: the fuzzy control system is designed by adopting a single-value fuzzifier, a product inference engine and a central average defuzzifier, and the first fuzzy rule is
Figure GDA0002765695820000039
Wherein z is [ z ]1，z2，…，zn]∈RnY is the input quantity and output quantity of the fuzzy system, m is the fuzzy inference rule number,
Figure GDA00027656958200000310
and Y(l)Respectively corresponding fuzzy language word sets of system input quantity and output quantity;
step S32: the actual approximation output of the fuzzy control system is expressed as
y＝θTζ(z)
Wherein θ ═ y1，y2，…，ym]TAs a weight parameter column vector, ζ ═ ζ1(z)，ζ2(z)，...，ζm(z)]TThe regression column vector required to approximate y,
Figure GDA0002765695820000041
and is
Figure GDA0002765695820000042
Is a properly selected gaussian based membership function;
step S33: by utilizing the fuzzy control system, the sub-elements of the nonlinear term F and the diagonal elements of the nonlinear term H in the state equation are respectively approximated:
Figure GDA0002765695820000043
wherein the content of the first and second substances,
Figure GDA0002765695820000044
the optimal weight parameter column vector, Δ f, representing two fuzzy control systemsi、ΔhiiFor the corresponding fuzzy approximation error,
Figure GDA0002765695820000045
representing membership function column vectors corresponding to the two fuzzy control systems respectively; i is 1,2, 3;
the original state equation is then converted into
Figure GDA0002765695820000046
Wherein the content of the first and second substances,
Figure GDA0002765695820000047
Figure GDA0002765695820000048
in an embodiment of the present invention, the step S4 includes the following steps:
step S41: setting carrier attitude alpha and angular velocity
Figure GDA0002765695820000049
And angular acceleration
Figure GDA00027656958200000410
The expected trajectory of the system can be measured and increased
Figure GDA00027656958200000411
Xd＝[xpd，ypd]TA bounded end expected motion function that is second order derivable; defining propagation errors for a system
Figure GDA00027656958200000412
And e is aα＝[0，0]T，
Figure GDA0002765695820000051
Step S42: the following scheme for the augmented adaptive fuzzy control is designed:
Figure GDA0002765695820000052
wherein, thetaf、θhAre respectively the optimal weight
Figure GDA0002765695820000053
And
Figure GDA0002765695820000054
k is diag [ K ] as an estimate of1,K2,K3]∈R3×6Is a suitably selected error gain matrix and Ki∈R1×2I is 1,2, 3; the parameter σ is used to ensure that the first formula of the above equation is 0; substituting the designed control law into the state equation to derive an operation space error equation:
Figure GDA0002765695820000055
wherein A ispIs a-BK and ApIs HerviiThe matrix of the z-matrix is,
Figure GDA0002765695820000056
estimating an error for the weight;
step S43: under the condition of the assumption that the fuzzy system weight and the approximation error are bounded, the self-adaptive rhythm of the weight is introduced as follows:
Figure GDA0002765695820000057
wherein r isf、rhIs a properly selected adaptive adjustment factor; p is an equation
Figure GDA0002765695820000058
And P ═ diag [ P ]1,P2,P3]，Pi∈R2×2(i ═ 1,2,3) is a positive definite, symmetric matrix; q ═ diag [ Q ]1,Q2,Q3]，Qi∈R2×2(i ═ 1,2,3) is a positive definite, symmetric matrix selected as appropriate.
Compared with the prior art, the invention has the following beneficial effects: the invention provides an augmented self-adaptive fuzzy control algorithm for tracking an operation space track of a floating-based space robot. The control algorithm can be applied to an under-actuated model of the space robot with uncertain model parameters and external disturbance, and can realize accurate tracking of an operation space track; fuzzy approximation in the algorithm is only fit for diagonal elements of H, so that the calculation amount of the algorithm is reduced to a great extent; in addition, it is not difficult to find,
Figure GDA0002765695820000059
the 2 nd and 3 rd elements of the first row are zero, so that the joint control moment tau of the mechanical arm is independent from the carrier attitude control moment, and the carrier attitude angular acceleration is not actually required to be obtained by the joint control moment row tau
Figure GDA0002765695820000061
Information, which will be advantageous for practical applications.
Drawings
Fig. 1 is a model diagram of a floating-based space robot according to an embodiment of the present invention.
FIG. 2 is a block diagram of a fuzzy input q according to an embodiment of the present inventioniMembership functions of (a).
FIG. 3 is a block diagram of fuzzy input in an embodiment of the present invention
Figure GDA0002765695820000062
Membership functions of (a).
FIG. 4 is a diagram of operating space trajectory tracking with fuzzy adaptive law turned off in an embodiment of the present invention.
FIG. 5 is a diagram of tracking an operating space trajectory for turning on fuzzy adaptive law in an embodiment of the present invention.
FIG. 6 is a diagram illustrating changes in the trajectory of the base attitude for turning on the fuzzy adaptive law, in accordance with an embodiment of the present invention.
FIG. 7 is a diagram illustrating the overall structural dynamics of the system for turning on fuzzy adaptive law according to an embodiment of the present invention.
[ brief description of the drawings ]: { oxy } is the system inertial frame, { o }0x0y0{ O } is a follow-up coordinate system, set up on the baseixiyiAn arm lever following coordinate system established at the center of the joint i is formed in (i is 1 and 2); w0A robot arm carrier base in a floating state, Wi(i is 1,2) is the ith robot arm; ci(i is 0,1,2) is WiAnd at a position r in the inertial frame { oxy }i(i ═ 0,1, 2); the center of mass of the entire system model is rc(ii) a Floating foundation W0Has an attitude angle of alpha, each robot arm WiIs thetai(i＝1,2)
Detailed Description
The technical scheme of the invention is specifically explained below with reference to the accompanying drawings.
The technical scheme of the invention is as follows: an augmented adaptive fuzzy control algorithm for tracking the track of an operation space of a floating-based space robot comprises the following specific steps:
step S1: establishing an under-actuated joint space system kinetic equation;
step S2: deducing a corresponding operating space system kinetic equation by using the system motion relation;
step S3: carrying out fuzzy approximation processing on each uncertain function item of the system by using a fuzzy approximation idea;
step S4: adaptive modulation rhythm is introduced to adjust the fuzzy weight in real time, and an adaptive fuzzy controller is further designed to realize accurate tracking of the expected track of the system operation space.
In an embodiment of the present invention, taking a planar floating-base two-rod space robot as an example, in step S1, the under-actuated joint space system kinetic equation is:
Figure GDA0002765695820000063
wherein D (q) e R3×3A symmetric and positive definite inertia matrix of the system is obtained;
Figure GDA0002765695820000071
is a column vector containing the Coriolis force and the centrifugal force of the system; tau isc∈R3Bounded external perturbations for the system; q ═ α, θ1,θ2]TFor the attitude angle alpha of the system base and the joint angle theta of the two connecting rods1、θ2A column vector of components; tau epsilon to R2The control moment column vector of each joint of the mechanical arm.
In an embodiment of the present invention, in step S2:
definition of X ═ Xp,yp]TFor the actual output of the operating space at the end of the system, Y ═ α, XT]TFor the expanded system to increase the control output, the joint space velocity
Figure GDA0002765695820000072
And increase the operating space velocity
Figure GDA0002765695820000073
The following relationships exist:
Figure GDA0002765695820000074
wherein the content of the first and second substances,
Figure GDA0002765695820000075
the generalized Jacobian matrix of the system after being augmented; matrix representation of the last two rows of J
Figure GDA0002765695820000076
And
Figure GDA0002765695820000077
the customary Jacobian matrix of cells, and JijAnd (i is 1, 2; j is 1,2,3) is a system inertia parameter and sine and cosine functions of each joint angle.
Circumventing the singular problem of dynamics of the system (J)v＝J-1Present) and takes into account the system present parameter uncertainty condition. On the basis, an augmented Jacobian matrix estimation value is introduced
Figure GDA0002765695820000078
And converting the provided joint space kinetic equation into an operation space kinetic equation form by using the system kinematics relationship
Figure GDA0002765695820000079
Wherein the content of the first and second substances,
Figure GDA00027656958200000710
to facilitate the design of the fuzzy control algorithm of the system, state variables are defined
Figure GDA00027656958200000711
And is
Figure GDA00027656958200000712
Converting an operating space dynamics equation into a state equation form
Figure GDA0002765695820000081
Wherein A ═ diag [ A ]1，A2，A3]，B＝diag[B1，B2，B3]，
Figure GDA0002765695820000082
Figure GDA0002765695820000083
Figure GDA0002765695820000084
In an embodiment of the present invention, in step S3:
the fuzzy control system is designed by adopting a single-value fuzzifier, a product inference engine and a central average defuzzifier, and the first fuzzy rule is
Figure GDA0002765695820000085
Wherein z is [ z ]1，z2，…，zn]∈RnY is the input quantity and output quantity of the fuzzy system, m is the fuzzy inference rule number,
Figure GDA0002765695820000086
and Y(l)The fuzzy language word sets corresponding to the system input quantity and the system output quantity respectively.
The actual approximation output of the fuzzy control system can be expressed as
y＝θTζ(z)
Wherein θ ═ y1，y2，…，ym]TIs a weight valueParameter column vector, ζ ═ ζ1(z)，ζ2(z)，…，ζm(z)]TThe regression column vector required to approximate y,
Figure GDA0002765695820000087
and is
Figure GDA0002765695820000088
Is a suitably selected gaussian based membership function.
By using the fuzzy control system, the nonlinear terms F and H in the state equation are respectively approximated to the diagonal elements
Figure GDA0002765695820000091
Wherein the content of the first and second substances,
Figure GDA0002765695820000092
the optimal weight parameter column vector, Δ f, representing two fuzzy control systemsi、ΔhiiFor the corresponding fuzzy approximation error,
Figure GDA0002765695820000093
and representing the membership function column vectors corresponding to the two fuzzy control systems respectively.
The original state equation can then be converted into
Figure GDA0002765695820000094
Wherein the content of the first and second substances,
Figure GDA0002765695820000095
Figure GDA0002765695820000096
in an embodiment of the present invention, in step S4:
posture of setting carrierState α, angular velocity
Figure GDA0002765695820000097
And angular acceleration
Figure GDA0002765695820000098
The expected track of the system can be measured and expanded
Figure GDA0002765695820000099
Xd＝[xpd，ypd]TIs a bounded end expected motion function that is second order derivable. At the same time, the extension error of the system is defined
Figure GDA00027656958200000910
And eα＝[0,0]T,
Figure GDA00027656958200000911
The following scheme for the augmented adaptive fuzzy control is designed
Figure GDA00027656958200000912
Wherein, thetaf、θhAre respectively the optimal weight
Figure GDA00027656958200000913
And
Figure GDA00027656958200000914
k is diag [ K ] as an estimate of1,K2,K3]∈R3×6Is a suitably selected error gain matrix and Ki∈R1×2(i ═ 1,2,3), the parameter σ is used primarily to ensure that the first equation of the above is constant at 0 (i.e., the carrier attitude control torque is zero). Substituting the designed control law into the state equation to derive the operation space error equation
Figure GDA0002765695820000101
Wherein A ispIs a-BK and ApIs a matrix of a Hurwitz matrix,
Figure GDA0002765695820000102
the error is estimated for the weight.
Under the condition of assuming fuzzy system weight and bounded approximation error, the weight adaptive modulation is introduced as
Figure GDA0002765695820000103
Wherein r isf、rhIs a properly selected adaptive adjustment factor; p is an equation
Figure GDA0002765695820000104
And P ═ diag [ P ]1,P2,P3]，Pi∈R2×2(i ═ 1,2,3) is a positive definite, symmetric matrix; q ═ diag [ Q ]1,Q2,Q3]，Qi∈R2×2(i ═ 1,2,3) is a positive definite, symmetric matrix selected as appropriate.
Theorem 1: for a space robot system, the augmented adaptive fuzzy control scheme based on weight adaptive adjustment can effectively ensure that the tracking error of the system operation space is converged into a smaller neighborhood close to zero and is consistent and finally bounded.
And (3) proving that: choosing a positive definite function as follows
Figure GDA0002765695820000105
The derivation of V and the substitution of the system error equation and the weight adaptive law into it include
Figure GDA0002765695820000106
Due to eTOf PB' sThe 1 st element is 0, and,
Figure GDA0002765695820000107
is also 0, then
Figure GDA0002765695820000111
Wherein the content of the first and second substances,
Figure GDA0002765695820000112
is composed of
Figure GDA0002765695820000113
The first row and the first column of elements of (a) are 0.
Definition of
Figure GDA0002765695820000114
Simplification of
Figure GDA0002765695820000115
Figure GDA0002765695820000116
By choosing the appropriate Q, K, the following inequality holds
Q+2PB1K-PBBTP≥Rp
Wherein R ispFor positive definite matrix, further simplification
Figure GDA00027656958200001111
Figure GDA0002765695820000118
It can be seen that
Figure GDA0002765695820000119
When the temperature of the water is higher than the set temperature,
Figure GDA00027656958200001110
the system operating space tracking error will converge to a smaller neighborhood close to zero and consistently ends up bounded.
In an embodiment, as shown in fig. 1, a planar two-pole floating-based space robot model is provided. Wi(i ═ 0,1,2) corresponds to a mass and moment of inertia of mi、Ji(i ═ 0,1, 2); generalized coordinate q ═ α, θ1，θ2]TIs the attitude angle alpha of the base of the system and the joint angle theta of the two mechanical arms1、θ2A column vector of components; center of mass C of base0To o0Has a length of a, o0To o1The length is b; each arm has a length of li(i ═ 1,2), the center of gravity is at its geometric center of gravity. The specific values of the simulation are shown in the following table 1
TABLE 1 simulation of relevant parameters of a floating foundation space robot
Figure GDA0002765695820000121
Because of the uncertainty of the system parameters, the estimated Jacobian matrix is selected as
Figure GDA0002765695820000122
Setting of controller parameter rf＝35,rh＝0.8,Ki＝[12,11](i＝1,2,3),Q＝1000×I6×6The membership function of the input q of the fuzzy system is selected as
Figure GDA0002765695820000123
As shown in fig. 2. Input device
Figure GDA0002765695820000124
Is selected as
Figure GDA0002765695820000125
Figure GDA0002765695820000126
As shown in fig. 3.
In an embodiment, the number of fuzzy rules
Figure GDA0002765695820000127
Wherein n isbTo input the number, naIs the number of Gaussian basis functions in the membership functions. The specific fuzzy control rule is designed as follows
Figure GDA0002765695820000128
Figure GDA0002765695820000129
Figure GDA00027656958200001210
Figure GDA0002765695820000131
Figure GDA0002765695820000132
Figure GDA0002765695820000133
Fuzzy initial weight
Figure GDA0002765695820000134
Each element is 0,
Figure GDA0002765695820000135
Each element is taken to be 0.8, and the simulation time t is 20 s.
In an embodiment, the augmented adaptive fuzzy control law is
Figure GDA0002765695820000136
Wherein, thetaf、θhAre respectively the optimal weight
Figure GDA0002765695820000137
And
Figure GDA0002765695820000138
the error gain matrix K is diag K1,K2,K3]，Ki∈R1×2(i ═ 1,2,3), and σ is 0 in the first formula which ensures the above formula.
The fuzzy weight value is adaptive to rhythm as
Figure GDA0002765695820000139
Wherein r isf、rhFor positive adaptive law gain constants, the P matrix is the equation
Figure GDA00027656958200001310
Q ═ diag [ Q ], of1,Q2,Q3]For a given known positive definite symmetric matrix, Qi∈R2×2A positive definite symmetric matrix (i ═ 1,2, 3);
when the fuzzy adaptive law is closed, the operation space trajectory tracking diagram is shown in FIG. 4; when the weight adaptation law is turned on, the operation space trajectory tracking diagram is shown in fig. 5. It can be seen that: when the weight self-adaptation law is started, the expected track can be well tracked after 1/4 cycles (5s) are simulated, and the tracking effect is obviously improved. Fig. 6 shows the posture adjustment movement of the base due to the reaction force of the robot arm when the space robot performs the operation space tracking movement. In order to make the tracking motion of the system more intuitive, fig. 7 shows a dynamic change diagram when the whole space robot system performs the tracking motion of the operation space trajectory.
The above are preferred embodiments of the present invention, and all changes made according to the technical scheme of the present invention that produce functional effects do not exceed the scope of the technical scheme of the present invention belong to the protection scope of the present invention.

Claims (4)

1. An augmented self-adaptive fuzzy control algorithm for tracking the track of an operation space of a floating-based space robot is characterized in that: the method comprises the following specific steps:
step S1: establishing an under-actuated joint space system kinetic equation;
step S2: deducing a corresponding operating space system kinetic equation by using the system motion relation;
step S3: carrying out fuzzy approximation processing on each uncertain function item of the system by using a fuzzy approximation idea;
step S4: adaptive modulation rhythm is introduced to adjust the fuzzy weight in real time, and an adaptive fuzzy controller is further designed to realize accurate tracking of the expected track of the system operation space;
the step S2 includes the following steps:
step S21: definition of X ═ Xp,yp]TFor the actual output of the operating space at the end of the system, Y ═ α, XT]TControl output for expanded system augmentation, where xp、ypRespectively is the position coordinate of the tail end p of the mechanical arm along the x and y axes under the inertial coordinate system oxy, alpha is the attitude angle of the base, and then the space velocity of the joint
Figure FDA0002765695810000011
And increase the operating space velocity
Figure FDA0002765695810000012
The following relationships exist:
Figure FDA0002765695810000013
wherein the content of the first and second substances,
Figure FDA0002765695810000014
for the expanded lineA generalized jacobian matrix; matrix representation of the last two rows of J
Figure FDA0002765695810000015
And
Figure FDA0002765695810000016
the customary Jacobian matrix of cells, and Jij(i is 1, 2; j is 1,2,3) is a system inertia parameter and sine and cosine functions of each joint angle;
step S22: avoidance of the singular problem of dynamics of the system, Jv＝J-1(ii) present; considering the parameter uncertainty condition of the system; on the basis, an augmented Jacobian matrix estimation value is introduced
Figure FDA0002765695810000017
And converting the provided joint space system kinetic equation into an operation space system kinetic equation form by utilizing the system kinematics relationship:
Figure FDA0002765695810000018
wherein the content of the first and second substances,
Figure FDA0002765695810000019
wherein D (q) e R3×3Is a symmetric and positive definite inertia matrix of the system, which can be abbreviated as D;
Figure FDA0002765695810000021
is a column vector containing the Coriolis force and the centrifugal force of the system, which can be abbreviated as C; mp(q)、
Figure FDA0002765695810000022
Are abbreviated as M respectivelyp、Cp；
Figure FDA0002765695810000023
τc∈R3Represents the bounded externally perturbed column vector of the system, τ ∈ R2The control moment column vector of each joint of the mechanical arm is shown,
Figure FDA0002765695810000024
step S23: defining state variables
Figure FDA0002765695810000025
And is
Figure FDA0002765695810000026
Converting the operating space dynamics equation into a state equation form:
Figure FDA0002765695810000027
wherein A ═ diag [ A ]1,A2,A3],B＝diag[B1,B2,B3],
Figure FDA0002765695810000028
Figure FDA0002765695810000029
Figure FDA00027656958100000210
，
Figure FDA00027656958100000211
Denotes the ith component of the vector F, abbreviated as Fi；
hij(q) (i 1,2, 3; j 1,2,3) represents the ith row and jth column component of matrix H, abbreviated as Hij。
2. The augmented adaptive fuzzy control algorithm for floating-based space robot operating space trajectory tracking according to claim 1, characterized by: in the step S1, the robot is a plane floating base two-rod space robot, and an under-actuated joint space system kinetic equation is established; the joint space system dynamic equation in the underactuated form is as follows:
Figure FDA0002765695810000031
wherein D (q) e R3×3Is a symmetric and positive definite inertia matrix of the system, which can be abbreviated as D;
Figure FDA0002765695810000032
is a column vector containing the Coriolis force and the centrifugal force of the system, which can be abbreviated as C; tau isc∈R3Bounded external perturbations for the system; q ═ α, θ1,θ2]TFor the attitude angle alpha of the system base and the joint angle theta of the two connecting rods1、θ2A column vector of components; tau epsilon to R2The control moment column vector of each joint of the mechanical arm.
3. The augmented adaptive fuzzy control algorithm for floating-based space robot operating space trajectory tracking according to claim 1, characterized by: in the step S3:
step S31: the fuzzy control system is designed by adopting a single-value fuzzifier, a product inference engine and a central average defuzzifier, and the first fuzzy rule is
Figure FDA0002765695810000033
Wherein z is [ z ]1，z2，…，zn]∈RnY is the input quantity and output quantity of the fuzzy system, m is the fuzzy inference rule number,
Figure FDA0002765695810000034
and Y(l)Respectively corresponding fuzzy language word sets of system input quantity and output quantity;
step S32: the actual approximation output of the fuzzy control system is expressed as
y＝θTζ(z)
Wherein θ ═ y1，y2，…，ym]TAs a weight parameter column vector, ζ ═ ζ1(z),ζ2(z),…,ζm(z)]TThe regression column vector required to approximate y,
Figure FDA0002765695810000035
and is
Figure FDA0002765695810000036
Is a properly selected gaussian based membership function;
step S33: respectively approximating equations by using the fuzzy control system
Figure FDA0002765695810000037
The sub-elements of the medium vector F
Figure FDA0002765695810000041
And diagonal elements H of matrix Hii(q)(i＝1,2,3)：
Figure FDA0002765695810000042
Wherein q ═ α, θ1,θ2]TRepresenting the attitude angle alpha of the base and the joint angle theta of the two links1、θ2The column vector of the component is composed of,
Figure FDA0002765695810000043
representing two fuzzy controlsThe optimal weight parameter column vector of the system,
Figure FDA0002765695810000044
Δhii(q) is the corresponding fuzzy approximation error, abbreviated as Δ fiAnd Δ hii；
Figure FDA0002765695810000045
Figure FDA00027656958100000415
Representing the respective corresponding membership function column vectors of the two fuzzy control systems, which are respectively abbreviated as zetai、
Figure FDA00027656958100000416
i＝1，2，3；
The original state equation is then converted into
Figure FDA0002765695810000046
Wherein the content of the first and second substances,
Figure FDA0002765695810000047
Figure FDA00027656958100000414
Figure FDA0002765695810000048
4. the augmented adaptive fuzzy control algorithm for floating-based space robot operating space trajectory tracking according to claim 1, characterized by: the step S4 includes the following steps:
step S41: setting the attitude angle alpha and angular velocity of the base
Figure FDA0002765695810000049
And angular acceleration
Figure FDA00027656958100000410
The expected increasing track of the system under the measurable and operating space is
Figure FDA00027656958100000411
Xd＝[xpd,ypd]TA bounded end expected motion function that is second order derivable; defining an extension error of a system under an operating space
Figure FDA00027656958100000412
And eα＝[0,0]T,
Figure FDA00027656958100000413
xp、ypRespectively is the position coordinate of the tail end p of the mechanical arm along the x and y axes under the inertial coordinate system oxy, xpd、ypdRespectively representing the expected position coordinates of the tail end p of the mechanical arm along the x axis and the y axis under the inertial coordinate system oxy;
step S42: the following scheme for the augmented adaptive fuzzy control is designed:
Figure FDA0002765695810000051
wherein τ ∈ R2Control moment column vectors of all joints of the mechanical arm;
Figure FDA0002765695810000052
to represent
Figure FDA0002765695810000053
The transpose of (a) is performed,
Figure FDA0002765695810000054
is an estimated value of J, and is,
Figure FDA0002765695810000055
the generalized Jacobian matrix of the system after being augmented;
Figure FDA00027656958100000513
the membership function column vector corresponding to the fuzzy control system used for approximating each sub-element of the vector F; zeta is a membership function column vector corresponding to a fuzzy control system for approximating each diagonal element of the matrix H;
θf、θhare respectively the optimal weight
Figure FDA0002765695810000056
And
Figure FDA0002765695810000057
k is diag [ K ] as an estimate of1,K2,K3]∈R3×6Is a suitably selected error gain matrix and Ki∈R1×2I is 1,2, 3; the parameter σ is used to ensure that the first formula of the above equation is 0; substituting the designed control law into an equation
Figure FDA0002765695810000058
And (3) deriving an operation space error equation:
Figure FDA0002765695810000059
wherein B ═ diag [ B ═ B1,B2,B3]，
Figure FDA00027656958100000510
h1j(j 2,3) denotes the sub-element in row 1 and column j of the matrix H, H2j(j ═ 1,3) represents the subelements in row 2 and column j of matrix H; h is3j(j ═ 1,2) denotes row 3 of the matrix HA sub-element of the j-th column; Δ hiiRepresenting an approximation error generated by approximating diagonal elements of the ith row and the ith column of the matrix by using a fuzzy system;
Figure FDA00027656958100000511
Δfi(i ═ 1,2,3) is the approximation error resulting from approximating the ith subelement of vector F using a fuzzy system; a. thepIs a-BK and ApIs a Helwitz matrix, A ═ diag [ A ═ A1,A2,A3]，
Figure FDA00027656958100000512
Figure FDA0002765695810000061
Estimating an error for the weight;
step S43: under the condition of the assumption that the fuzzy system weight and the approximation error are bounded, the self-adaptive rhythm of the weight is introduced as follows:
Figure FDA0002765695810000062
wherein r isf、rhIs a properly selected adaptive adjustment factor; p is an equation
Figure FDA0002765695810000063
And P ═ diag [ P ]1,P2,P3]，Pi∈R2×2(i ═ 1,2,3) is a positive definite, symmetric matrix; q ═ diag [ Q ]1,Q2,Q3]，Qi∈R2×2(i ═ 1,2,3) is a positive definite, symmetric matrix selected as appropriate.
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