CN106055818B - A kind of variable geometry truss robot modelling localization method - Google Patents

A kind of variable geometry truss robot modelling localization method Download PDF

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CN106055818B
CN106055818B CN201610406881.6A CN201610406881A CN106055818B CN 106055818 B CN106055818 B CN 106055818B CN 201610406881 A CN201610406881 A CN 201610406881A CN 106055818 B CN106055818 B CN 106055818B
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敬忠良
徐启敏
胡士强
杨永胜
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Shanghai Jiaotong University
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Abstract

The invention discloses one kind to be based on variable geometry truss robot differential kinematics model location method, step 1, within the scope of operating space, initiation parameter θ0, L0, X0；Step 2, active pole length differential variable dL is designed；Step 3, differential is obtained according to variable geometry truss robot structural constraint equation and maps expression formulaStep 4, it calculates affine dependent on the differential of angleSimilar obtains about the affine of node QStep 5, determine that the differential at structure end center maps according to differential chain ruleStep 6, closing speed Jacobian matrix is extracted, variable geometry truss robot structure differential kinematics equation, discretization structure differential kinematics system are established；Step 7, the data provided with reference to the measuring device of mechanical arm platform carry out measurement node process tracking, obtain the measurement model of the variable geometry truss robot structure.Step 8, by setting gap error function, the comprehensive structure Differential Model and measurement model, the accurate positioning that target expected pose error offsets is realized.

Description

A kind of variable geometry truss robot modelling localization method
Technical field
The invention belongs to space-based field of space technology, in particular to a kind of variable geometry truss robot models localization method.
Background technique
Space platform mechanical arm has more bodies, big flexibility inherent characteristics.Under space-based background, become geometry purlin using the truss Frame structure intrinsic differentiation mapping relations, can obtain the speed Jacobian matrix an of closed form.It is micro- by variable geometry truss robot Componental movement input/output relation realizes the transmitting from kinematics to differential kinematics, inquires into a kind of triple octahedra change geometry The differential kinematics modeling method of truss.Measurement node process is carried out with reference to the data that the measuring device of mechanical arm platform provides Tracking, obtains the measurement model of the variable geometry truss robot structure, by setting gap error function, the comprehensive structure Differential Model with Measurement model realizes the accurate positioning that target expected pose error offsets.
Through the literature search of existing technologies, variable geometry truss robot in three-dimensional space can be long by manipulation drive rod Reach any bending of itself configuration, so that variable geometry truss robot structure can be realized the positioning of preset bearing.Based on space mechanism The in-orbit Aerospace Satellite platform operation scheme of arm is chiefly used in cooperative target, GPS, camera and radar and forms.Such as U.S. NASA DART (Demonstration of Autonomous Rendezvous Technology), rail are demonstrated in transmitting in 2005 Road express, the ATV (Transfer Autonomous Vehicle) of European Space Agency, Japanese ETS engineering test satellite (ETS-7) etc..But It is that this variable geometry truss robot structural system that is based on is installed on satellite there are the inaccurate problem of operation precision, may cause sky Room machine arm operating platform, which tracks cooperative target super close distance, to be lost.
Summary of the invention
It is an object of the present invention to provide one kind to be based on variable geometry truss robot differential kinematics model location method.
The technical scheme is that a kind of variable geometry truss robot models localization method, comprising the following steps: step 1, In the reachable opereating specification of variable geometry truss robot active pole length, the parameter of input is initialized, parameter includes θ0、L0And X0, θ0It indicates to correspond to angle parameter set Θ={ θ1,θ2,θ3Original state, L0It indicates to correspond to the long parameter sets L of driving lever ={ L1,L2,L3Original state, L1=| | A2B2| | indicate A2B2Length, L2=| | B2C2| | indicate B2C2Length, L3=| |A2C2| | indicate A2C2Length,
X0Indicate the center vector parameter set X={ X for corresponding to motion arm mobile platformi| i=1 ..., n just Beginning state, n rely on asymmetric single module number,
The physical relationship of initiation parameter is as shown in Figure 2；
By being translated, being rotated to variable geometry truss robot structure, scaled, affine transformation is to keep platform local feature not Denaturation；
Step 2, one expected path of data setting planned according to spatial measurement platform, setting variable geometry truss robot structure is most Neighbouring connecting rod extension distance and time neighbouring connecting rod extension distance error, calculation formula:
DL=Lk-Lk-1,Lmin≤Lk≤Lmax,
Wherein, LminFor connecting rod L maximum collapse distance, LmaxFor connecting rod L maximum extension distance；
Step 3, it is limited according to variable geometry truss robot structural constraint equation, it is several by becoming using Newton-Raphson method What truss structure direct kinematics relationship calculates the differential Jacobian matrix of Θ and L, obtains differential and maps expression formulaIt is counted Calculation process are as follows:
(1) it is based on variable geometry truss robot structure Basic Constraint Equation:
F1(Θ)=c1+c2+Ac1c2-2As1s2+ B=0
F2(Θ)=c2+c3+Ac2c3-2As2s3+ C=0
F3(Θ)=c3+c1+Ac3c1-2As3s1+ D=0
(2) Jacobian matrix is expressed using Newton-Raphson iterative process:
JδΘk=-Fi(Θk)
Wherein,
(3) Θ is calculatedk+1=Θk+δΘk, until | | δ Θk| | < ε, for the Jacobian matrix of the variable geometry truss robot structure For
Wherein, K1=KBs1+KEc1,K2=KCs1+KFc1,K3=KAs2+KDc2,
K4=KCs2+KFc2,K5=KAs3+KDc3,K6=KBs3+KEc3
KA=-(1+Ac1),KB=-(1+Ac2),KC=-(1+Ac3),
KD=-2As1,KE=-2As2,KF=-2As3
Step 4, as shown in Fig. 2, the angle parameter { θ defined according to step 11,θ2,θ3, further calculate node Qi,
Q1=(Ns1,O1y+Nc1,0)T
Wherein,Indicate the bottom end planar central of variable geometry truss robot structure and the intermediate normal direction of the end plane line of centres Amount,Definition imply variable geometry truss robot structure with certain centre symmetry,
Calculate the active node Q for depending on angle1Differential is affine
Calculate the intermediate normal vector for depending on angleDifferential is affine
Wherein,It is vectorThe vector of x-axis direction is corresponded to based on inertial coodinate system O-xyz,It is vectorIt is based on Inertial coodinate system O-xyz corresponds to the vector in y-axis direction,It is vectorZ-axis direction is corresponded to based on inertial coodinate system O-xyz Vector；
Step 5, structure end center and the long parameter sets L={ L of driving lever are determined according to implicit function existence result1,L2, L3Differential mappingCalculating process:
In order to determine that variable geometry truss robot structure end center pose X is obtained according to variable geometry truss robot construction geometry symmetric relation To the closure equation of following distal center pose:
Wherein,If Jacobian matrix is closure parsing, variable geometry truss robot structure differential kinematics Model meets
Wherein, J (Θ, L) is the speed Jacobian matrix of parsing.In fact, we obtain according to implicit function theo- rem Functional relation
The Jacobian matrix solved by above equation realizes variable geometry truss robot structural kinetics to differential kinematics Space transmitting, that is, the physics converted between service speed space and the connecting rod velocity space is disclosed by speed Jacobian matrix Meaning；
Step 6, in order to overcome model is uncertain to influence, closing speed Jacobi square is extracted using implicit function theo- rem Battle array will become geometry structural kinetics model conversation as its differential kinematics model, and calculating transformation for mula is as follows,
Wherein, u=[L1,L2,L3]TIt is input control variable,
The calculating of discretization structure differential kinematics system is as follows:
Xk=Juk
Step 7, the data provided with reference to the measuring device of mechanical arm platform carry out measurement node process tracking, obtain the change The measurement model of geometry truss structure,
Firstly, the data of the measuring device offer with reference to mechanical arm platform, set measuring node pose
Q1=Q1(p), Q2=Q2(p), Q3=Q3(p),
Measurement node process tracking is carried out, the measurement model of the variable geometry truss robot structure is obtained,
Yk=C (p) uk
ek=r-Yk
Wherein, C (p) be about with ukUnrelated node measurement functions, ukIt is input control variable, ekReference input with The error of measurement node information, r are reference inputs；
Step 8, by setting gap error function, the comprehensive structure Differential Model and measurement model, target expectation is realized The accurate positioning that position and attitude error offsets, process be,
Using variable geometry truss robot structure node feature, interstitial position error function is set,
wk=d (uk)
The comprehensive structure Differential Model and measurement model,
In order to realize accurate positioning that target expected pose error offsets, design of feedback controller,
uk=Φ Xk
Using the feedback controller of design, realize that variable geometry truss robot structure end pose is accurately positioned.
The present invention determines the variable geometry truss robot structure differential kinematics model state pose of low coverage Aerospace Satellite target Position.Become geometry intrinsic differentiation mapping relations using the truss, obtains the speed Jacobian matrix an of closed form.It proposes The differential kinematics modeling method of a kind of triple octahedra variable geometry truss robots.With reference to mechanical arm platform measuring device provide Data carry out measurement node process tracking, obtain the measurement model of the variable geometry truss robot structure, by setting gap error function, The comprehensive structure Differential Model and measurement model realize the accurate positioning that target expected pose error offsets.
The present invention utilizes computer vision technique, allows the robot for space of single platform to the progress of target with respect to appearance The measurement of state improves measurement accuracy, final to realize to Aerospace Satellite land identification, tracking and maintenance.It works for the aerospace on ground Personnel provide various technical supports.Using multiple triple octahedra variable geometry truss robot combined machine arms constituted to space station Waste and old satellite recycling, satellite capture task can be carried out, satellite is not only can detect by mechanical arm platform and damages component, can also pass through The platform data real-time tracking cooperative target of robotic arm path planning plays a significant role to space tasks are completed.In addition, passing through Variable geometry truss robot construction machine arm differential kinematics modeling analysis, it is further proposed that the structure accurate positioning method, improves space The precision of noncooperative target measurement, provides important convenient for the problems such as subsequent space manipulator kinetic stability and active control strategies Theory support.
The present invention is directed under spatial complex background, has the ability of certain adaptation space operating environment, and height is adaptive Should be able to power space variable geometry truss robot mechanical arm, provide and realize the Satellite Targets relative pose for meeting certain requirement of real-time Accurate positioning.Assisting or replace astronaut to complete some space operations using such mechanical arm, (in-orbit maintenance task: generaI investigation is too Empty rubbish, the recycling of waste and old satellite, satellite capture).The present invention helps to push the hair of the research of manned space flight space science and application Exhibition.
Detailed description of the invention
Fig. 1 is flow chart of the present invention；
Fig. 2 is that the present invention is based on variable geometry truss robot structure chained blocks and its structural unit analysis diagram；
Fig. 3 is that the present invention is based on the forward directions of variable geometry truss robot construction module, inverse kinematics analysis path figure；
Fig. 4 is that the present invention is based on the space reflections between variable geometry truss robot structure driving lever speed and service speed；
Fig. 5 is that the present invention is based on variable geometry truss robot structure differential kinematics models in the opposite fortune of its state variable of XOY section The tracking result of dynamic rail mark；
Fig. 6 is that the present invention is based on variable geometry truss robot structure differential kinematics models in the opposite fortune of its state variable of YOZ section The tracking result of dynamic rail mark；
Fig. 7 is that the present invention is based on variable geometry truss robot structure differential kinematics models in the opposite fortune of its state variable of XOZ section The tracking result of dynamic rail mark；
Fig. 8 is variable geometry truss robot structure MATLAB simulated environment Differential Model system emulation flow chart of the present invention.
Specific embodiment
Elaborate below to the embodiment of the present invention: the present embodiment carries out under the premise of the technical scheme of the present invention Implement, the detailed implementation method and specific operation process are given, but protection scope of the present invention is not limited to following implementation Example.
As shown in Figure 1, provided in this embodiment be based on variable geometry truss robot differential kinematics model accurate positioning method, pass through MATLAB emulates data and semi-physical simulation image data, and the data of totally two aspects carry out actual test, and implementation steps are as follows:
Step 1, the parameter of input is initialized respectively first.
Utilize major parameter θ0, L0, X0, θ0It indicates to correspond to angle parameter set Θ={ θ1,θ2,θ3Original state, L0 It indicates to correspond to the long parameter sets L={ L of driving lever1,L2,L3Original state, L1=| | A2B2| | indicate A2B2Length, L2 =| | B2C2| | indicate B2C2Length, L3=| | A2C2| | indicate A2C2Length, X0It indicates to correspond to motion arm mobile platform Center vector parameter set X={ Xi| i=1 ..., n } original state, n relies on asymmetric single module number, initialization The physical relationship of parameter is as shown in Figure 2.Variable geometry truss robot structure is translated, is rotated, is scaled, affine transformation is to keep platform The invariance of local feature.
Step 2, one expected path of data schema provided according to space platform, setting variable geometry truss robot structure are closest Connecting rod extension distance and time neighbouring connecting rod extension distance error.
Its calculating process are as follows:
DL=Lk-Lk-1,Lmin≤Lk≤Lmax,
Wherein, LminFor connecting rod L maximum collapse distance, LmaxFor connecting rod L maximum extension distance.
Step 3, it is limited according to variable geometry truss robot structural constraint equation, Newton-Raphson method is utilized, passes through change Geometry truss structure direct kinematics relationship calculates the differential Jacobian matrix of Θ and L, calculating process are as follows:
Newton-Raphson method uses implicit function theo- rem, need to be from variable geometry truss robot structure direct kinematics relationship It sets out, using Newton-Raphson iterative process, analyzes dihedral angle Θ and become the implication relation between length of connecting rod L.It solves Process is as follows:
(1) it is based on variable geometry truss robot structure Basic Constraint Equation:
F1(Θ)=c1+c2+Ac1c2-2As1s2+ B=0
F2(Θ)=c2+c3+Ac2c3-2As2s3+ C=0
F3(Θ)=c3+c1+Ac3c1-2As3s1+ D=0
(2) Jacobian matrix is expressed using Newton-Raphson iterative process:
JδΘk=-Fi(Θk)
Wherein,
(3) Θ is calculatedk+1=Θk+δΘk, until | | δ Θk| | < ε, for the Jacobian matrix of the variable geometry truss robot structure For
Step 4, as shown in Fig. 2, the angle parameter { θ defined according to step 11,θ2,θ3, further calculate node Qi,
Q1=(Ns1,O1y+Nc1,0)T
Wherein,Indicate the bottom end planar central of variable geometry truss robot structure and the intermediate normal direction of the end plane line of centres Amount,Definition imply variable geometry truss robot structure with certain centre symmetry,
Calculate separately the active node Q dependent on angle1Differential is affine
Calculate the intermediate normal vector for depending on angleDifferential is affine
Wherein,It is vectorThe vector of x-axis direction is corresponded to based on inertial coodinate system O-xyz,It is vectorBased on used Property coordinate system O-xyz corresponds to the vector in y-axis direction,It is vectorThe arrow in z-axis direction is corresponded to based on inertial coodinate system O-xyz Amount；
A series of variable geometry truss robot structural parameters are inputted using differential chain type criterion based on Newton-Raphson method, it is main To include intrinsic parameter, the variable geometry truss robot structure end pose etc. of variable geometry truss robot structural electromotor, find out variable geometry truss robot structure Intermediate parametersBQiWithΘ best estimate about dihedral angle.
Step 5, according to implicit function existence result, structure end center and the long parameter sets L={ L of driving lever are determined1, L2,L3Differential mappingThe input/output relation for describing mechanical arm platform movement speed, to realize variable geometry truss robot Transmitting Space Reconstruction of the structural kinetics to differential kinematics.
In order to determine variable geometry truss robot structure end center pose X, obtained according to variable geometry truss robot construction geometry symmetric relation To the closure equation of following distal center pose:
Wherein,If Jacobian matrix is closure parsing, variable geometry truss robot structure differential kinematics Model meets
Wherein, J (Θ, L) is the speed Jacobian matrix of parsing.In fact, we obtain according to implicit function theo- rem Functional relation
Variable geometry truss robot structural kinetics are realized to differential kinematics from the Jacobian matrix that above equation solves Space transmitting.That is, disclosing the physics converted between service speed space and the connecting rod velocity space by speed Jacobian matrix Meaning.
Step 6, in order to overcome model is uncertain to influence, closing speed Jacobi square is extracted using implicit function theo- rem Variable geometry truss robot structural kinetics model conversation is its differential kinematics model by battle array, and calculating transformation for mula is as follows,
Wherein, u=[L1,L2,L3]TIt is input control variable.
Discretization variable geometry truss robot structure differential kinematics system calculates as follows:
Xk=Juk
The step 7 sets measuring node pose with reference to the data of the measuring device offer of mechanical arm platform
Q1=Q1(p), Q2=Q2(p), Q3=Q3(p),
Measurement node process tracking is carried out, the measurement model of the variable geometry truss robot structure is obtained.
Yk=C (p) uk
ek=r-Yk
Wherein, C (p) be about with ukUnrelated node measurement functions, ukIt is input control variable, r is reference input, ek It is the error of reference input Yu measurement node information.
The step 8 sets interstitial position error function using variable geometry truss robot structure node feature,
wk=d (uk)
The comprehensive structure Differential Model and measurement model,
In order to realize accurate positioning that target expected pose error offsets, design of feedback controller,
uk=Φ Xk
Using the feedback controller of design, realize that variable geometry truss robot structure end pose is accurately positioned.
It is provided in this embodiment to be based on variable geometry truss robot construction machine arm differential kinematics model, further study the structure Accurate positioning method.This method establishes multiple known variables using the truss variable geometry truss robot structure intrinsic differentiation mapping relations Differential chain rule, and then obtain the speed Jacobian matrix of a closed form.The final triple octahedrons of one kind of establishing become several The differential kinematics model of what truss.This method carries out measurement node mistake with reference to the data that the measuring device of mechanical arm platform provides Journey tracking, obtains the measurement model of the variable geometry truss robot structure, by setting gap error function, the comprehensive structure Differential Model With measurement model, the accurate positioning that target expected pose error offsets is realized.In addition this method research has certain adaptation too The ability of idle job environment, and the space variable geometry truss robot mechanical arm of height adaptive ability provide and realize satisfaction centainly The accurate positioning of the Satellite Targets relative pose of requirement of real-time is necessary.This kind of space manipulator platform not only can detect It repairs satellite and damages component, it can also be based on the platform data real-time tracking cooperative target that robotic arm path is planned, it can be achieved that space Satellite platform identification, tracking and maintenance.This invention is also convenient for subsequent space manipulator kinetic stability and active control strategies The problems such as important theory support is provided.Therefore in the fields such as satellite maintenence, space trash removing, space situation awareness It is widely used.

Claims (1)

1. a kind of variable geometry truss robot models localization method, which comprises the following steps:
Step 1, in the reachable opereating specification of variable geometry truss robot active pole length, the parameter of input is initialized, parameter Including θ0、L0And X0,
θ0Indicate corresponding angle parameter sets Θ={ θ1,θ2,θ3Original state,
L0It indicates to correspond to the long parameter sets L={ L of driving lever1,L2,L3Original state,
L1=| | Q1Q2| | indicate Q1Q2Distance, L2=| | Q2Q3| | indicate Q2Q3Distance, L3=| | Q3Q1| | indicate Q3Q1Away from From,
X0Indicate the center vector parameter set X={ X for corresponding to motion arm mobile platformi| i=1, L, n } initial shape State, n rely on asymmetric single module number, and support rod length is defined as N；
By being translated, being rotated to variable geometry truss robot structure, scaled, affine transformation is to keep the structure platform local feature Invariance；
Step 2, one expected path of data setting planned according to spatial measurement platform, setting variable geometry truss robot structure are closest Connecting rod extension distance and time neighbouring connecting rod extension distance error, calculation formula:
DL=Lk-Lk-1,Lmin≤Lk≤Lmax, (1)
Wherein, LminFor connecting rod L maximum collapse distance, LmaxFor connecting rod L maximum extension distance, closest connecting rod extension distance LkIt is fixed Justice are as follows: the practical extension distance of kth moment drive connecting rod；
Step 3, will be become according to variable geometry truss robot structure dynamics restrict (1) according to Newton-Raphson method The dynamic constrained relationship of geometry truss structure direct kinematics, and the differential mapping relations of Θ and L can be further calculatedIts Calculating process are as follows:
(1) it is based on variable geometry truss robot structure Basic Constraint Equation:
F1(Θ)=c1+c2+Ac1c2-2As1s2+ B=0 (2)
F2(Θ)=c2+c3+Ac2c3-2As2s3+ C=0 (3)
F3(Θ)=c3+c1+Ac3c1-2As3s1+ D=0 (4)
Wherein, c1=cos θ1,c2=cos θ2,c3=cos θ3,
s1=sin θ1,s2=sin θ2, s3=sin θ3,
(2) Jacobian matrix is expressed using Newton-Raphson iterative process:
JδΘk=-Fi(Θk) (5)
Wherein,
(3) Θ is calculatedk+1=Θk+δΘk, until | | δ Θk| | < ε, 0 < ε < 1, for the Jacobi of the variable geometry truss robot structure Matrix is
Wherein, K1=KBs1+KEc1,K2=KCs1+KFc,K3=KAs2+KDc,
K4=KCs2+KFc2,K5=KAs3+KDC, K6=KBs3+KEc
KA=-(1+Ac1),KB=-(1+A2c),KC=-(1+Ac3),
KD=-2As1,KE=-2As2,KF=-2As3
Step 4, the angle parameter { θ defined according to step 11,θ2,θ3, further calculate node Qi,
Wherein, parameter O1y,O2y,O3y,O2z,O3z, when being usually set to the fixation of VGT structure floor, the midpoint corresponding bottom surface Bian Xing Corresponding coordinate, i.e. O1yFor the end B bottom surface side shape B1B2Midpoint O1Y-axis coordinate value, O2yFor the end B bottom surface side shape B2B3Midpoint O2Y-axis Coordinate value, O3yFor the end B bottom surface side shape B3B1Midpoint O3Y-axis coordinate value, O2zFor the end B bottom surface side shape B2B3Midpoint O2Z-axis coordinate Value, O3zFor the end B bottom surface side shape B3B1Midpoint O3Z-axis coordinate value,Indicate variable geometry truss robot structure bottom end planar central with The intermediate normal vector of the end plane line of centres,Definition imply variable geometry truss robot structure with certain central symmetry Property,
Wherein, the bottom surface VGT platform is expressedBQi, i=1,2,3, it is corresponding node Qi, i=1,2,3, U1x,U1y,U1zIt is expressed asX, y, z coordinate value,
Calculate angular-dependent θ1Active node Q1Differential is affine
Calculate the intermediate normal vector of angular-dependent ΘDifferential mapping
Wherein,For vectorThe vector of x-axis direction is corresponded to based on inertial coodinate system O-xyz,For vectorIt is sat based on inertia Mark system O-xyz corresponds to the vector in y-axis direction,For vectorThe vector in z-axis direction is corresponded to based on inertial coodinate system O-xyz；
Step 5, structure end center and the long parameter sets L={ L of driving lever are determined according to implicit function existence result1,L2,L3} Differential mappingCalculating process:
In order to determine variable geometry truss robot structure end center vectorAccording to variable geometry truss robot construction geometry symmetric relation, obtain To the closure equation of following distal center pose:
Wherein,S is expressed as the structure interval dissipation distance at node, r be expressed as VGT structure floor center with The distance at intermediate active plane center,It is expressed for VGT bottom center initial time vector, if Jacobian matrix is closure Parsing, variable geometry truss robot structure differential kinematics model meets
Wherein, J (Θ, L) is that the speed Jacobian matrix of parsing obtains functional relation according to implicit function theo- rem
The Jacobian matrix solved by above equation realizes space of the variable geometry truss robot structural kinetics to differential kinematics Transmitting, that is, the physical significance of speed Jacobi discloses inherent transforming relationship between service speed space and the connecting rod velocity space, Such as Fig. 4；
Step 6, in order to overcome model is uncertain to influence, closing speed Jacobian matrix is extracted using implicit function theo- rem, it will For change geometry structural kinetics model conversation into its differential kinematics model, calculating transformation for mula is as follows,
Wherein, u=[L1,L2,L3]TIt is input control variable, J is expressed as J (Θ, L),
The calculating of discretization structure differential kinematics system is as follows:
Xk=Juk (17)
Wherein, indicate that differential system (15)-(16) are the discretized system indicated after kth T moment discrete sampling, sampling period For T=1s；
Step 7, the data provided with reference to the measuring device of mechanical arm platform carry out measurement node process tracking, obtain the change geometry The measurement model of truss structure,
Firstly, the data p of the measuring device offer with reference to mechanical arm platform, sets measuring node pose
Q1=Q1(p), Q2=Q2(p), Q3=Q3(p),
Measurement node process tracking is carried out, the measurement model of the variable geometry truss robot structure is obtained,
Yk=C (p) uk (19)
ek=rd-Yk (20)
Wherein, C (p) be about with ukUnrelated node measurement functions, ukIt is input control variable, ekIt is reference input and measurement The error of nodal information, rdFor reference input；
Step 8, by setting gap error function, the comprehensive structure Differential Model and measurement model, target expected pose is realized The accurate positioning that error offsets, process are as follows:
Using variable geometry truss robot structure node feature, interstitial position error function is set,
wk=d (uk) (21)
The comprehensive structure Differential Model and measurement model,
In order to realize accurate positioning that target expected pose error offsets, design of feedback controller,
uk=Φ Xk (23)
Wherein, Φ is the feedback oscillator of system (22),
Using the feedback controller of design, input control instruction realizes that variable geometry truss robot structure end pose is accurately positioned.
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