CN103624784A - Self-adaptation control method for space multi-arm complicated-connection complex - Google Patents

Abstract

The invention discloses a self-adaptation control method for a space multi-arm complicated-connection complex. The self-adaptation control method for the space multi-arm complicated-connection complex is high in precision, good in adaptability and independent from specific parameter values of the complex, on-line identification does not need to be carried out on parameters in an ontrack mode, only measurable output is needed, and a controller has good robustness on uncertainty of the parameters. According to the self-adaptation control method for the space multi-arm complicated-connection complex, a simple self-adaptation control method is popularized to controlled objects which have high relative orders and non-approximate strict positive realness. When the self-adaptation control method is used for solving the problem of closed-chain control of mechanical arms, mechanical arm system closed-chain motion constraint conditions are introduced into trajectory planning, ideal trajectories, meeting the motion constraint conditions, of the mechanical arms are given through the trajectory planning, and therefore the problem of closed-chain control of the mechanical arms is simplified into the problem that tracking of mechanical arm systems meets the requirement for tracking of the ideal trajectories of kinematics constraint.

Description

The complicated association's self-adaptation control method that connects of a kind of space multi-arm

Technical field

The present invention relates to the complicated association's self-adaptation control method that connects of a kind of space multi-arm, relate in particular to the complicated association's high-accuracy self-adaptation control method that connects of a kind of space multi-arm, belong to Spacecraft Attitude Control field.

Background technology

In the manipulator motion stage, no matter to catch or exhausting section, the motion of system is typical multi-body system, and wherein the motion of arbitrary body all can have influence on the motion state of other each body in system, and its sports coupling relation is very complicated; Especially when the collaborative target acquisition of multi-arm, form after closed chain, there is Dynamics Coupling relation in the motion of each body not only, and system also exists direct kinematic constraint.Conventionally, in operating process, control target for keeping platform stable, and make each mechanical arm follow the tracks of desired motion track simultaneously.In whole system motion, exist Dynamics Coupling even directly kinematic constraint in the situation that, seek many bodies control method for coordinating to reach the matter of utmost importance that above-mentioned control target is system controller design; The main target of its design is: in the controller design of a certain movable body or kinematic system, seek suitable technological means, reduce the impact of other movable bodies in system as far as possible, make all movable bodies of controlling that need in system all can follow the tracks of its desired motion track with degree of precision, thereby reach many bodies, coordinate the object of controlling; On this basis, the parameter uncertainty of the outer interference of the design of controller reply and system has stronger adaptivity or robustness.

According to two phase controller mentality of designing ，Jiang association's pose stabilization controls and mechanical arm Trajectory Tracking Control above, separate CONTROLLER DESIGN, being coupled as between the two processed distracter each other.Operation task mainly comprises acquisition phase, mass property parameter identification stage and mechanical arm system recovery stage.The complicated association that connects of multi-arm is because structure is very complicated, and mechanical arm system exists flexible problem, makes its system model very complicated.System is in the different operational phases, and because system configuration exists very large variation, its dynamic property exists very large difference, thereby its controller design problem is also different.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, provide a kind of space multi-arm the complicated association's self-adaptation control method that connects, the method control accuracy is high.

Technical solution of the present invention is: the complicated association's self-adaptation control method that connects of a kind of space multi-arm, is characterized in that step is as follows:

(1) the multi-arm complicated Self Adaptive Control that connects association in space is resolved into the attitude control of association and the Trajectory Tracking Control of mechanical arm, the attitude of association is controlled and is adopted method shown in step (2) to complete, and the Trajectory Tracking Control of mechanical arm adopts method shown in step (3) to complete;

(2) according to the Attitude control model of room for manoeuvre control method ，Jiang association by the regress simple adaptive control attitude controller design of kinetics equation and kinematical equation, specific implementation process is as follows:

(2.1) first according to association attitude, control and require design reference kinetics equation and with reference to kinematical equation; Reference driving force is learned equation: $\begin{array}{c}{\stackrel{\·}{x}}_m=A_m{x}_m+B_m{u}_m\\ y_m=C_m{x}_m\end{array},$ State variable x wherein _m=y _m=ω _d,

i ₃be 3 rank unit matrix, ω _dfor expectation attitude angular velocity;

With reference to kinematical equation, be: $\left[\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_{d0}\\ {\stackrel{\&CenterDot;}{q}}_d\end{array}\right]=\frac{1}{2}\left[\begin{array}{c}-{q_d}^T\\ q_{d0}{\mathrm{<figure-callout\; id="3"\; label="I"\; filenames="HDA0000409474410000011.png"\; state="\{\{state\}\}">I</figure-callout>}}_3{+\tilde{q}}_d\end{array}\right]{\mathrm{\&omega;}}_d,$ Q in formula _0d, q _dbe respectively mark portion and the vector part of expectation hypercomplex number, for q _dantisymmetric matrix,

(2.2) design association attitude is controlled middle control law ω _m: ω _m=A _bdω _d-kq _e, A _bdfor satellite, expect attitude angle body coordinate and be tied to the transition matrix of the actual body coordinate system of satellite, k is positive definite control coefrficient matrix; q _eby association's attitude quaternion error equation $\left\{\begin{array}{c}{q}_{e0}=q_0{q}_{0d}+q^T{q}_d\\ q_e=q_{0d}q-q_0{q}_d+\tilde{q}{q}_d\end{array}\right.$ Determine q in formula _e0for the mark portion of error quaternion, q ₀, q is respectively mark portion and the vector part of actual hypercomplex number,

antisymmetric matrix for q;

(2.3) the room for manoeuvre simple adaptive control attitude control law T of design association:

$T=\mathrm{Kr}=\left[\begin{array}{ccc}{K}_x& K_u& K_e\end{array}\right]{\left[\begin{array}{ccc}{{\mathrm{\&omega;}}_d}^T& {{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_d}^T& e^T\end{array}\right]}^T,$ K=[K in formula _xk _uk _e] be Self Adaptive Control coefficient matrix, by parameter update law, determined K _xk _uk _efor forming the submatrix of Self Adaptive Control matrix K; R is variable, $r={\left[\begin{array}{ccc}{{\mathrm{\&omega;}}_d}^T& {{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_d}^T& e^T\end{array}\right]}^T,$ E is association's kinetics equation output error, e=ω-ω _mthe attitude angular velocity output of ，ωWei association, parameter update law

for

k (0)=K ₀, K ₀for the initial value of Self Adaptive Control parameter matrix, the Self Adaptive Control matrix that Γ is positive definite, the control coefrficient that σ is positive definite;

(2.4) utilize executing agency, according to the room for manoeuvre simple adaptive control attitude control law T of association of step (2.3) design, association is carried out to attitude control;

(3) according to room for manoeuvre control method, mechanical arm control system is carried out to the room for manoeuvre simple adaptive control contrail tracker design of mechanical arm by kinetics equation and kinematical equation, specific implementation process is as follows:

(3.1) first according to mechanical arm trajectory planning design reference kinetics equation with reference to kinematical equation; Reference driving force is learned equation: $\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_{2m}=A_{2m}{x}_{2m}+B_{2m}{u}_{2m}\\ y_{2m}=C_{2m}{x}_{2m}\end{array},$ State variable x _2m=y _2m=ω _ar,

b _2m=C _2m=I ₇, I ₇for unit matrix, ω _arjoint angle speed for each mechanical arm expectation; With reference to kinematical equation, be direct integral relation:

θ _arfor each joint angle of mechanical arm;

(3.2) control law ω in the middle of design mechanical arm Trajectory Tracking Control _arm:

for kinematics output error,

θ _afor the actual joint angle of mechanical arm, k _afor positive definite control coefrficient matrix;

(3.3) design mechanical arm room for manoeuvre simple adaptive control Trajectory Tracking Control T _a:

$T_a=K_a{r}_a=\left[\begin{array}{ccc}{K}_{\mathrm{xa}}& K_{\mathrm{ua}}& K_{\mathrm{ea}}\end{array}\right]{\left[\begin{array}{ccc}{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {e_2}^T\end{array}\right]}^T,$ K in formula _a=[K _xak _uak _ea] be Self Adaptive Control coefficient matrix, by adaptive law, determined K _xak _uak _eafor forming Self Adaptive Control matrix K _asubmatrix, $r_a={\left[\begin{array}{ccc}{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {e_2}^T\end{array}\right]}^T,$ E ₂for mechanical arm system kinetics equation output error, e ₂=ω _a-ω _arm, ω _afor each angled key output of mechanical arm, adaptive law

for:

k _a(0)=K _a0, K _a0for the initial value of Self Adaptive Control parameter matrix, Γ _afor the Self Adaptive Control matrix of positive definite, σ ₂control coefrficient for positive definite;

(3.4) utilize the executing agency on each joint of mechanical arm to restrain T according to the mechanical arm room for manoeuvre simple adaptive control Trajectory Tracking Control of step (3.3) design _amechanical arm is carried out to Trajectory Tracking Control.

The present invention's beneficial effect is compared with prior art:

(1) the complicated high-precision strong adaptive control method that connects association of space multi-arm proposed by the invention does not rely on the design parameter value of association, without in-orbit parameter being carried out to on-line identification, only need output to survey, controller has strong robustness to parameter uncertainty.

(2) control method that the present invention proposes, is generalized to by simple adaptive control method the controlled device that phase match exponents is the non-approximate Strict Positive Realness of high-order.

(3) during processing machine arm closed chain control problem of the present invention, mechanical arm system closed chain kinematic constraint condition is incorporated in trajectory planning, by trajectory planning, provide the ideal trajectory that each mechanical arm meets kinematic constraint condition, thereby mechanical arm closed chain control problem is reduced to the tracking problem that each mechanical arm system is followed the tracks of the ideal trajectory that meets kinematical constraint.

Accompanying drawing explanation

Tu1Wei association attitude stabilization room for manoeuvre simple adaptive control structure chart;

Fig. 2 is mechanical arm track following room for manoeuvre simple adaptive control structure chart.

The specific embodiment

The invention provides the complicated high-precision strong adaptive control method that connects association of a kind of space multi-arm, the equipment that described method is relied on comprises space report control platform and is arranged on the mechanical arm on the report control platform of space, the attitude control system of space report control platform, mechanical arm control system; Method to as if the complicated association that connects of space multi-arm, concrete implementation step is as follows:

(1) the multi-arm complicated Self Adaptive Control that connects association in space is resolved into the attitude control of association and the Trajectory Tracking Control of mechanical arm, the attitude of association is controlled and is adopted method shown in step (2) to complete, and the Trajectory Tracking Control of mechanical arm adopts method shown in step (3) to complete;

(2) according to the Attitude control model of room for manoeuvre control method ，Jiang association by the regress simple adaptive control attitude controller design of kinetics equation and kinematical equation, as shown in Figure 1, specific implementation process is as follows:

(2.1) first according to association attitude, control and require design reference kinetics equation and with reference to kinematical equation; Reference driving force is learned equation: $\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_m=A_m{x}_m+B_m{u}_m\\ y_m=C_m{x}_m\end{array},$ State variable x wherein _m=y _m=ω _d,

i ₃be 3 dimension unit matrix, ω _dfor expectation attitude angular velocity;

With reference to kinematical equation, be: $\left[\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_{d0}\\ {\stackrel{\&CenterDot;}{q}}_d\end{array}\right]=\frac{1}{2}\left[\begin{array}{c}-{q_d}^T\\ q_{d0}{\mathrm{<figure-callout\; id="3"\; label="I"\; filenames="HDA0000409474410000011.png"\; state="\{\{state\}\}">I</figure-callout>}}_3{+\tilde{q}}_d\end{array}\right]{\mathrm{\&omega;}}_d,$ Q in formula _0d, q _dbe respectively mark portion and the vector part of expectation hypercomplex number, for q _dantisymmetric matrix,

(2.2) design association attitude is controlled middle control law ω _m: ω _m=A _bdω _d-kq _e, A _bdfor satellite, expect attitude angle body coordinate and be tied to the transition matrix of the actual body coordinate system of satellite, k is positive definite control coefrficient matrix; q _eby association's attitude quaternion error equation $\left\{\begin{array}{c}{q}_{e0}=q_0{q}_{0d}+q^T{q}_d\\ q_e=q_{0d}q-q_0{q}_d+\tilde{q}{q}_d\end{array}\right.$ Determine q in formula _e0for the mark portion of error quaternion, q _0dfor (q _0dat 2.1 li, define), q ₀, q is respectively mark portion and the vector part of actual hypercomplex number,

antisymmetric matrix for q;

(2.3) the room for manoeuvre simple adaptive control attitude control law T of design association:

$T=\mathrm{Kr}=\left[\begin{array}{ccc}{K}_x& K_u& K_e\end{array}\right]{\left[\begin{array}{ccc}{{\mathrm{\&omega;}}_d}^T& {{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_d}^T& e^T\end{array}\right]}^T,$ K=[K in formula _xk _uk _e] be Self Adaptive Control coefficient matrix, by parameter update law, determined K _xk _uk _efor forming the submatrix of Self Adaptive Control matrix K; R is variable, $r={\left[\begin{array}{ccc}{{\mathrm{\&omega;}}_d}^T& {{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_d}^T& e^T\end{array}\right]}^T,$ E is association's kinetics equation output error, e=ω-ω _mthe attitude angular velocity output of ，ωWei association, parameter update law

for

k (0)=K ₀, K ₀for the initial value of Self Adaptive Control parameter matrix, the Self Adaptive Control matrix that Γ is positive definite, the control coefrficient that σ is positive definite;

(2.4) utilize executing agency, according to the room for manoeuvre simple adaptive control attitude control law T of association of step (2.3) design, association is carried out to attitude control;

(3) according to room for manoeuvre control method, mechanical arm control system is carried out to the room for manoeuvre simple adaptive control contrail tracker design of mechanical arm by kinetics equation and kinematical equation, as shown in Figure 2, specific implementation process is as follows:

(3.1) first according to mechanical arm trajectory planning design reference kinetics equation with reference to kinematical equation; Reference driving force is learned equation: $\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_{2m}=A_{2m}{x}_{2m}+B_{2m}{u}_{2m}\\ y_{2m}=C_{2m}{x}_{2m}\end{array},$ State variable x _2m=y _2m=ω _ar,

b _2m=C _2m=I ₇, I ₇for unit matrix, ω _arjoint angle speed for each mechanical arm expectation; With reference to kinematical equation, be direct integral relation:

θ _arfor each joint angle of mechanical arm;

(3.2) control law ω in the middle of design mechanical arm Trajectory Tracking Control _arm:

for kinematics output error,

θ _afor the actual joint angle of mechanical arm, k _afor positive definite control coefrficient matrix;

(3.3) design mechanical arm room for manoeuvre simple adaptive control Trajectory Tracking Control T _a:

$T_a=K_a{r}_a=\left[\begin{array}{ccc}{K}_{\mathrm{xa}}& K_{\mathrm{ua}}& K_{\mathrm{ea}}\end{array}\right]{\left[\begin{array}{ccc}{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {e_2}^T\end{array}\right]}^T,$ K in formula _a=[K _xak _uak _ea] be Self Adaptive Control coefficient matrix, by adaptive law, determined K _xak _uak _eafor forming Self Adaptive Control matrix K _asubmatrix,, $r_a={\left[\begin{array}{ccc}{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {e_2}^T\end{array}\right]}^T,$ E ₂for mechanical arm system kinetics equation output error, e ₂=ω _a-ω _arm, ω _afor each angled key output of mechanical arm, adaptive law

for: k _a(0)=K _a0, K _a0for the initial value of Self Adaptive Control parameter matrix, Γ _afor the Self Adaptive Control matrix of positive definite, σ ₂control coefrficient for positive definite;

(3.4) utilize the executing agency on each joint of mechanical arm to restrain T according to the mechanical arm room for manoeuvre simple adaptive control Trajectory Tracking Control of step (3.3) design _amechanical arm is carried out to Trajectory Tracking Control.

Embodiment: getting one is example with 3 the complicated connection of 7 degree-of-freedom manipulators associations, coupling system dynamics and trajectory planning, the whole process that the target acquistion of system, mass property parameter identification and target are reclaimed is carried out numerical simulation.In system, the quality/inertia parameter of each body is as shown in table 1, and in table, inertia and static moment are all described in the body coordinate system of each body.

Quality/the inertia parameter of each body in table 1 system

?	Quality (Kg)	Inertia (kg.m2)	Static moment (kg.m)
				Satellite body	3600	diag(1040，1178，1222)	[0，0，0] T
Target star	800	diag(149，139，160)	[0，0，0] T
				1 grade of arm	5	diag(1.979，1.979，1.025)×10 -2	[0，0，0.25] T
2 grades of arms	25	diag(0.05318.34980349)	[-12.5，0，0] T
				3 grades of arms	25	diag(0.053111.03611.036)	[14.375，0，0] T
4 grades of arms	3.5	diag(0.02940.02940.0107)	[0，0，-0.2625] T

[0044]?

5 grades of arms	3.5	diag(0.01070.02940.0294)	[0.2625，0，0] T
				6 grades of arms	2	diag(0.00790.00410.0079)	[0，-0.1，0] T
7 grades of arms	6	diag(0.18380.18380.0123)	[0，0，-0.9] T

The flexible parameter information of system is as shown in table 2.

Flexible parameter in table 2 system

?	The 2nd joint arm	The 3rd joint arm
			Length (m)	1	1.15
Quality (kg)	25	25
			Elastic modelling quantity	4.5E+10	7E+10
Fundamental frequency (Hz)	39.89347	40.47306
			Second order frequency (Hz)	39.89347	40.47306
Three order frequencies (Hz)	233.4357	240.5640
			Quadravalence frequency (Hz)	233.4357	240.5640

(1) the initial acquisition stage

The expectation attitude quaternion of initial acquisition stage association's attitude is q _d=[1 00 0] ^t, expectation attitude angular velocity is 0, the expectation joint angle of mechanical arm is provided by mechanical arm trajectory planning.The control method proposing according to the present invention, designs respectively attitude control law and mechanical arm Trajectory Tracking Control rule.Controller coefficient is as follows:

Association's attitude control law coefficient:

K ₁=0.2,Γ _e=-diag([111])×10 ⁸

K _e(0)=zeros(3,3)

σ=0.01

Mechanical arm Trajectory Tracking Control rule coefficient:

K ₂=diag([1?1?1?1?1?1?1])×0.5,Γ _ea=diag([1?1?1?1?1?1])×10 ⁸

Γ _xa=diag([1?1?1?1?1?1?1])×10 ²,Γ _ua=diag([1?1?1?1?1?1?1])×10 ²

K _ea(0)=zeros(7,7),K _xa(0)=zeros(7,7),K _ua(0)=zeros(7,7)

σ ₂=0.01

(2) accurate acquisition phase

The initial value of accurately catching is the final state of initial acquisition, and controller coefficient is as follows:

Association's attitude control law coefficient:

K ₁=0.3,Γ _e=-diag([111])×10 ¹²

K _e(0)=zeros(3,3)

σ=0.01

Mechanical arm Trajectory Tracking Control rule coefficient:

K _1a=diag([1?1?1?1?1?1?1])×0.5,Γ _ea=diag([111111])×10 ¹⁰

Γ _xa=diag([1111111])×10 ²,Γ _ua=diag([1111111])×10 ²

K _ea(0)=zeros(7,7),K _xa(0)=zeros(7,7),K _ua(0)=zeros(7,7)

σ ₂=0.01

(3) recovery stage

The initial value of recovery stage is for accurately catching or the final state in identification stage, and controller coefficient is as follows:

Association's attitude control law coefficient:

K ₁=0.3,Γ _e=-diag([111])×10 ¹⁰

K _e(0)=zeros(3,3)

σ=0.01

Mechanical arm Trajectory Tracking Control rule coefficient:

K _1a=diag([1?1?1?1?1?1])×0.3,Γ _ea=diag([11111])×10 ⁸

Γ _xa=diag([1?1?1?1?1?1])×10 ²,Γ _ua=diag([111111])×10 ²

K _ea(0)=zeros(6,6),K _xa(0)=zeros(6,6),K _ua(0)=zeros(6,6)

σ ₂=0.01

The content not being described in detail in description of the present invention belongs to those skilled in the art's known technology.

Claims (1)

1. multi-arm complexity in space connects association's self-adaptation control method, it is characterized in that step is as follows:

(1) the multi-arm complicated Self Adaptive Control that connects association in space is resolved into the attitude control of association and the Trajectory Tracking Control of mechanical arm, the attitude of association is controlled and is adopted method shown in step (2) to complete, and the Trajectory Tracking Control of mechanical arm adopts method shown in step (3) to complete;

(2) according to the Attitude control model of room for manoeuvre control method ，Jiang association by the regress simple adaptive control attitude controller design of kinetics equation and kinematical equation, specific implementation process is as follows:

(2.1) first according to association attitude, control and require design reference kinetics equation and with reference to kinematical equation; Reference driving force is learned equation: $\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_m=A_m{x}_m+B_m{u}_m\\ y_m=C_m{x}_m\end{array},$ State variable x wherein _m=y _m=ω _d,

i ₃be 3 rank unit matrix, ω _dfor expectation attitude angular velocity;

With reference to kinematical equation, be: $\left[\begin{array}{c}{\stackrel{\&CenterDot;}{q}}_{d0}\\ {\stackrel{\&CenterDot;}{q}}_d\end{array}\right]=\frac{1}{2}\left[\begin{array}{c}-{q_d}^T\\ q_{d0}{I}_3{+\tilde{q}}_d\end{array}\right]{\mathrm{\&omega;}}_d,$ Q in formula _0d, q _dbe respectively mark portion and the vector part of expectation hypercomplex number,

for q _dantisymmetric matrix,

(2.2) design association attitude is controlled middle control law ω _m: ω _m=A _bdω _d-kq _e, A _bdfor satellite, expect attitude angle body coordinate and be tied to the transition matrix of the actual body coordinate system of satellite, the control coefrficient matrix that k is positive definite; q _eby association's attitude quaternion error equation $\left\{\begin{array}{c}{q}_{e0}=q_0{q}_{0d}+q^T{q}_d\\ q_e=q_{0d}q-q_0{q}_d+\tilde{q}{q}_d\end{array}\right.$ Determine q in formula _e0for the mark portion of error quaternion, q ₀, q is respectively mark portion and the vector part of actual hypercomplex number,

antisymmetric matrix for q;

(2.3) the room for manoeuvre simple adaptive control attitude control law T of design association:

$T=\mathrm{Kr}=\left[\begin{array}{ccc}{K}_x& K_u& K_e\end{array}\right]{\left[\begin{array}{ccc}{{\mathrm{\&omega;}}_d}^T& {{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_d}^T& e^T\end{array}\right]}^T,$ K=[K in formula _xk _uk _e] be Self Adaptive Control coefficient matrix, by parameter update law, determined K _xk _uk _ebe respectively the submatrix that forms Self Adaptive Control matrix K; R is variable, $r={\left[\begin{array}{ccc}{{\mathrm{\&omega;}}_d}^T& {{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_d}^T& e^T\end{array}\right]}^T,$ E is association's kinetics equation output error, e=ω-ω _mthe attitude angular velocity output of ，ωWei association, parameter update law

for

k (0)=K ₀, K ₀for the initial value of Self Adaptive Control parameter matrix, the Self Adaptive Control matrix that Γ is positive definite, the control coefrficient that σ is positive definite;

(2.4) utilize executing agency, according to the room for manoeuvre simple adaptive control attitude control law T of association of step (2.3) design, association is carried out to attitude control;

(3) according to room for manoeuvre control method, mechanical arm control system is carried out to the room for manoeuvre simple adaptive control contrail tracker design of mechanical arm by kinetics equation and kinematical equation, specific implementation process is as follows:

(3.1) first according to mechanical arm trajectory planning design reference kinetics equation with reference to kinematical equation; Reference driving force is learned equation: $\begin{array}{c}{\stackrel{\&CenterDot;}{x}}_{2m}=A_{2m}{x}_{2m}+B_{2m}{u}_{2m}\\ y_{2m}=C_{2m}{x}_{2m}\end{array},$ State variable x _2m=y _2m=ω _ar,

b _2m=C _2m=I ₇, I ₇for unit matrix, ω _arjoint angle speed for each mechanical arm expectation; With reference to kinematical equation, be direct integral relation:

θ _arfor each joint angle of mechanical arm;

(3.2) control law ω in the middle of design mechanical arm Trajectory Tracking Control _arm:

for kinematics output error,

θ _afor the actual joint angle of mechanical arm, k _afor positive definite control coefrficient matrix;

(3.3) design mechanical arm room for manoeuvre simple adaptive control Trajectory Tracking Control T _a:

$T_a=K_a{r}_a=\left[\begin{array}{ccc}{K}_{\mathrm{xa}}& K_{\mathrm{ua}}& K_{\mathrm{ea}}\end{array}\right]{\left[\begin{array}{ccc}{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {e_2}^T\end{array}\right]}^T,$ K in formula _a=[K _xak _uak _ea] be Self Adaptive Control coefficient matrix, by adaptive law, determined K _xak _uak _eafor forming Self Adaptive Control matrix K _asubmatrix, $r_a={\left[\begin{array}{ccc}{{\stackrel{\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {{\stackrel{\&CenterDot;\&CenterDot;}{\mathrm{\&theta;}}}_{\mathrm{ar}}}^T& {e_2}^T\end{array}\right]}^T,$ E ₂for mechanical arm system kinetics equation output error, e ₂=ω _a-ω _arm, ω _afor each angled key output of mechanical arm, adaptive law

for:

k _a(0)=K _a0, K _a0for the initial value of Self Adaptive Control parameter matrix, Γ _afor the Self Adaptive Control matrix of positive definite, σ ₂control coefrficient for positive definite;

(3.4) utilize the executing agency on each joint of mechanical arm to restrain T according to the mechanical arm room for manoeuvre simple adaptive control Trajectory Tracking Control of step (3.3) design _amechanical arm is carried out to Trajectory Tracking Control.

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