Research Article A Novel Flexible Virtual Fixtures for ...mode [ ] (OPAM) and two pipes assisted mode (TPAM). e former mode used the xed VFs [ ]toguidetherobot EE but in our method

Research ArticleA Novel Flexible Virtual Fixtures for Teleoperation

Guanglong Du and Ping Zhang

South China University of Technology Guangzhou 510000 China

Correspondence should be addressed to Ping Zhang pzhangscuteducn

Received 15 October 2013 Accepted 31 December 2013 Published 11 February 2014

Academic Editors M Gobbi K-C Liu and J Xiang

Copyright copy 2014 G Du and P ZhangThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

This paper proposed a novel spatial-motion-constraints virtual fixtures (VFs) method for the human-machine interfacecollaborative technique In our method two 3D flexible VFs have been presented warning pipe and safe pipe And a potential-collision-detection method based on two flexible VFs has been proposed The safe pipe constructs the safe workspace dynamicallyfor the robot which makes it possible to detect the potential collision between the robot and the obstacles By calculating thespeed and the acceleration of the robot end-effecter (EE) the warning pipe can adjust its radius to detect the deviation fromthe EE to the reference path These spatial constraints serve as constraint conditions for constrained robot control The approachenables multiobstacle manipulation task of telerobot in precise interactive teleoperation environment We illustrate our approachon a teleoperative manipulation task and analyze the performance results The performance-comparison experimental resultsdemonstrate that the control mode employing our method can assist the operator more precisely in teleoperative tasks Due tothe properties such as collision avoidance and safety operators can complete the tasks more efficiently along with reduction inoperating tension

1 Introduction

The concept of virtual fixtures is presented by Kikuuwe [1]from Stanford University in 1993 to solve the delay problemand to improve the operability of the teleoperation systemRosenberg constructed 8 types of virtual fixtures in a peg-and-hole task and found out that they can decrease operationtime at some extent and increase efficiency by 20 to 70Because virtual fixtures have a broad application backgroundin teleoperation human-machine cooperative system andmedicine fine production and other fields there are manythorough researches about it

Most of these researches are focused on two types of vir-tual fixtures guidance virtual fixtures and forbidden regionvirtual fixtures Guidance virtual fixtures are needed when arobotic manipulator is needed to move along with a plannedpath precisely Forbidden region virtual fixtures are used toprevent a robotic manipulator entering some specific regionin order to avoid some damage Bettini et al [2] studiedthe performance of real-time video feedback virtual fixturesBased on this research Kang Park and Ewing studied theperformance of video and tactile feedback virtual fixtures

Nowadays with the help of some techniques such as virtualfixtures (VFs) high precise manipulation task is finished byrobotic assistants The surgeon is capable of more precisesurgery in robotic-assisted procedures VFs are algorithmswhich limit a robotic manipulator into restricted regions [3ndash7] andor direct a roboticmanipulator tomove alongwith theplanned path [8ndash10] This following literature has discussedVFs References [8 11ndash13] are for telerobots and [9 14ndash17] arefor cooperative robots

FRVFs (forbidden region virtual fixtures) are used torestrict the surgical tool into certain region in workspaceBeasley and Howe [18] set an active constraint to guide therobot to cut femur and tibia within a permitted region inprosthetic knee surgery Park et al [19] developed VFs basedon sensor that limit the robotrsquos motion or direct the surgeonto move the surgical instruments in a planned path usinghaptic feedbackDuring a teleoperated coronary bypass thereis a virtual wall guiding a surgeonrsquos instrument based on thelocation of the internal mammary artery obtained from apreoperative computer tomography scan

Bettini et al [9] concentrated on researches for guidanceVFsThey used vision information to generateVFs examined

Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 897242 10 pageshttpdxdoiorg1011552014897242

2 The Scientific World Journal

the hard and soft VFs and worked on the application tovitreoretinal surgery Marayong et al [20] demonstratedmotion constraints by varying compliance that was describedfor the general spatial case In these researches admittancecontrol laws are used to implement VFs A passive arm withdynamic constraints (PADyc) has been developed by Li et al[15 17 21] for pericardial puncture They implement VFs torestrict surgical tools to move along planned paths or awayfrom forbidden regions by using electrical motors to choosea clutching system for freewheelsThemain advantage of thismethod is that the robot cannot providemotive force withoutthe help of the surgeon This has been considered as onesafety advantage because it can prevent a robot from losingcontrol But there are some limitations including mechanicalcomplexity and loss of the robotrsquos ability to actively assistin surgical procedures A robotic system for fully automatedparanasal sinus surgery is developed byWurm et al [22]Thissystem uses preoperative CT to direct the robotrsquos autonomousmotion and it allows being remote controlled by a joystick A mechatronic system for FESS (functional endoscopicsinus surgery) has been presented by Luethrsquos group [23ndash25]According to a 3D model from CT data they planned a safeworking space preoperatively In the middle of the operationthe shaver is automatically turned onoff according to theposition of the shaver tip In the safe area the shaver reacts tosignals from the surgeon When the tip of the shaver movesoutside the safe area an electrical pulse will stop the shaverby interrupting its automatic drive control This navigation-based system is only concerned with the position of shavertip

In this paper we present an online obstacle-avoidancemethod for serial robot in geometrically complex environ-ments We extend Lirsquos work [15] to generate VFs for obstacleavoidance and a new potential collision-constraint-detectionmethod has been proposed In this method two pipes (thewarning pipe and the safe pipe) are automatically generatedfrom 3D reference path in real time The safe pipe serves asspatial constraints for constrained robot controlThewarningpipe adjusts the radius to detect the deviation of the robotEE from the reference path by calculating the speed and theacceleration of the robot EE In our experiment (Figure 1)two assisted modes were implemented one pipe assistedmode [15] (OPAM) and two pipes assisted mode (TPAM)The former mode used the fixed VFs [15] to guide the robotEE but in our method (the latter mode) two types of VFswere used to guide and constrain the robot EE When therobot EE collides with the pipes our systemwill give warninginformation based on vision to the operator changing thecolor of the pipes Due to the warning pipe our new spatial-motion-constraints method enables multiobstacle manipu-lation task of telerobot in precise interactive teleoperationenvironment

The remainder of the paper is organized as followsSection 2 provides a brief summary of path and the pipesbuilding algorithm In Section 3 we introduce the dynamicadjustment algorithm of the safe pipe and the warning pipeIn Section 4 we report the experiment results of two controlmodes We conclude the paper and discuss possible futureextensions in Section 5

Safe pipe

Platform

Warning pipe

Peg Hole

Figure 1 Geometric relation for spatial motion constraints

2 Path and Pipes

The path is a possible route obtained by the robot pathplanning Path planning is a kind of algorithmwhich finds outa collision-free path in all generalized coordinates of a robotwith some valuation criteria by the given initial positions andorientations of the robot A pipe gives the robot a safe space inwhich the robot can move freely without collision The pipesare built based on the paths They can divide the safe spacesand can also guide and give active early warnings

The pipes take the paths as medial axis and the path isformed by a series of path points Thus the pipes are formedby discrete pipe units

The pipes are built by many pipe units The pipe unitsare formed by two cross sections and a cylinder The shapeof cross section is decided by the predefined shape of thepipes Cross section is formed by polygon and circle sectionis formed by polygon which has more sides

21 Choosing a Starting Point of Cross Section As we know apolygon can be finalized by the given central point the centralaxis and the starting point How to choose the starting pointdepends on the origin of the coordinate system There is acentral point119875 a central axis 119871 and an origin point119874 Firstlyconnect the original point and the central point to get thereference vector 119874119875 The vertical vector 119876 can be calculated

119876 = 119874119875 times 119871 (1)

Unitize119876 and then get 119905119876 119878 is the point which is 119903 lengthfrom 119875 along the direction of

119878 = 119875 + 119905119876 sdot 119903 (2)

When there is an overlap between the central point andthe origin point we can take the unit vector of 119883 axis to bethe reference vector

22 Constructing a Polygon The key to create a polygon is todetermine the vertexes of the polygon Assume that there isa polygon with 119899 sides Then the radius angle of two adjacentvertices is

120579 = 2 sdot120587

119899 (3)

The Scientific World Journal 3

After the starting point and the central axis were knownthe second point can be obtained through rotating the centralaxis by 120579 degrees

Below is the transformation matrix of the next pointwhich revolves around the previous point Assuming that thecoordinate of the previous point isA(1198601 1198602 1198603) the centralaxis isB(1198611 1198612 1198613) To revolve aroundB axisA shouldmoveto the origin Then revolves around the 120579 degrees of thecentral axis by 120579 degrees and move it inversely Thus thistransformation matrix T is

T = [[[

11989811 11989812 11989813 1198601 minus 11989811 sdot 1198601 minus 11989812 sdot 1198602 minus 11989813 sdot 119860311989821 11989822 11989823 1198602 minus 11989821 sdot 1198601 minus 11989822 sdot 1198602 minus 11989823 sdot 119860311989831 11989832 11989833 1198603 minus 11989831 sdot 1198601 minus 11989832 sdot 1198602 minus 11989833 sdot 11986030 0 0 1

]]

]

(4)

In this equation we have

11989811 = 119905 sdot 1198611 sdot 1198611 + 119888

11989812 = 119905 sdot 1198611 sdot 1198612 + 119904 sdot 1198613

11989813 = 119905 sdot 1198611 sdot 1198613 minus 119904 sdot 1198612


11989822 = 119905 sdot 1198612 sdot 1198612 + 119888

11989823 = 119905 sdot 1198752 sdot 1198753 + 119904 sdot 119875

11989831 = 119905 sdot 1198611 sdot 1198613 + 119904 sdot 1198612


11989833 = 119905 sdot 1198613 sdot 1198613 + 119888

119888 = cos 120579

119904 = sin 120579

119905 = 1 minus cos 120579

(5)

The next A1015840 can be obtained by

A1015840 = T sdot A (6)

After determining the 119899minus1 points the whole vertexes canbe determined Correspondingly cross section is determinedAnd then next step should be the construction of cylinders

23 Constructions of Cylinders To enable pipes to detect col-lision in virtual environment pipes are formed by trianglesIn this algorithm cylinders are formed by connecting twovertexes of two adjacent cross sections

The rule of constructing triangles is to pick up andconnect the three adjacent points in each row like1 2 3 2 3 4 119899 minus 1 119899 119899 + 1 which means the(119899 + 1)th point is completely overlapped with the first pointand then that makes sure that cylinders are joined together

24 Splicing of Pipe Units If there are two pipe orifices whichhave the same shape the algorithmof splicing pipe units is thesame as above (algorithm of constructing cylinders) When

Obstacle

r

Safe pipe

Central axis

PathTarget4r

4r

Figure 2 Result of dynamic safe pipe adjustment

the shapes of two pipe orifices are different there need tobe splicing pipe units to join those pipes The algorithm ofcreating the splicing pipe is introduced below

Assume that the shape of the cross section of the pipe 1is a polygon which has 1198991 sides And assume that for pipe2 the cross section is 1198992 So there also needs to be a linkingpipe to connect pipe 1 and pipe 2This paper chooses 1198993 sidespolygon here 1198993 is the common multiple of 1198991 and 1198992 as thecross section of the linking pipe

1198993 = 119892119888119889 (1198991 1198992) (7)

Here 119892119888119889 means the common multiple of the two num-bers

When connecting two pipes the trianglesrsquo numberingrule needs to be adjusted because the shapes of two polygonsare different As we know 1198993 can be divisible by 1198991 or1198992 When numbering the triangles many-to-one mappingstrategy is employed

3 Dynamic Pipe Adjustment Algorithm

Pipes which are generated by this generation algorithm canbe changed dynamically according to the given path andradius Here are two dynamic pipe adjustment algorithmsThe first one is dynamic pipe scaling algorithm It generatesthe extended safe pipe which plays a guide role and dividessafe region The robot EE can reach its destination safely aslong as it does not exceed the range of pipe region and movesalong the direction of the pipe

The second one is pipe early warning method Thismethod would generate two pipes The first pipe is the safepipe which cannot be extended dynamically but can guidethe operators and provide the safe region The second pipeis the early warning pipe It gives a real-time warning oncethere was any muscles jitter of the operators during the robotcontrolling

31 Dynamic Extension Algorithm Safe extended pipes needto be adjusted dynamically according to how far the robotEE strays from the path One capability of the safe extendedpipes is to provide a safe region to protect robot EE fromcolliding with other objects as long as it moves within thesafe region (Figure 2)That requires the safe extended pipes toadjust dynamically and to give the operator an early warningThe safe pipe region should be big enough for the robot EE


to move around Safe extended pipe keeps extending untilit reaches around the obstacles If the robot EE crosses thesafe extended pipe The system will issue a warning that therobot EE is in a dangerous region Safe extended pipes alsofunctioned as guidance In this method safe extended pipe isdesigned as a pipe from thick to spindly which can lead therobot EE to move towards the target

Given a safe path the robot EE is at the starting point ofthe safe path Assume that the diameter of the robot EErsquos crosssection is 119896 the length of the path is 119866 and also 119866 gt 4119896 Theinitial point is 1198750 and 1198754119896 is the point which is 4119896 away from1198750 At 1198750 the cross section diameter of the safe extended pipeis 4119896 and at 1198754119896 it changes to 2119896 Thus for any point 119875119899 thecross section cross-sectional diameter is

119889 =

4119896 minus

100381610038161003816100381611987511989911987501003816100381610038161003816

4119896sdot 2119896

100381610038161003816100381611987511989911987501003816100381610038161003816 lt 4119896

211989610038161003816100381610038161198751198991198750

1003816100381610038161003816 gt 4119896

(8)

When the robot EE strays from the safe path the safeextended pipe needs to be adjusted accordingly to fit thechanged working space of the robot EE To display thedirection and the rate of deviation of the robot EE intuitivelydynamic self-adaptive adjustment strategy is employed Herewe take the extended direction of the safe pipe to be 119884 andthe extended amount to be119863

Assume that robot EE strays from safe path in 119910 directionand its offset is 119909 According to the self-adaptive adjustmentstrategy the cross-sectional centre of the safe extended pipeat the initial point is the centre of the robot EE and the cross-sectional radius is 2119896 + 119909 Thus the other centre points of thesafe extended pipe 1198751015840are adjusted as follows

1198751015840=

119875119888 +(119909 minus

1003816100381610038161003816100381610038161003816

997888rarr

1198751198881198750

1003816100381610038161003816100381610038161003816

4119896sdot (119909)) sdot 120575

100381610038161003816100381611987511988811987501003816100381610038161003816 lt 4119896

11987511988810038161003816100381610038161198751198881198750

1003816100381610038161003816 gt 4119896

(9)

Here 120575 is a unit normal vector and119875119888 is the original centerpoint of the safe extended pipe

Cross-sectionalrsquos radius of 1198751015840 is adjusted as follows

119889 =

(4119896 + 2119909) minus

1003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816

4119896sdot (2119896 + 2119909)

1003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816lt 4119896

21198961003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816gt 4119896

(10)

32 Initiative Early Warning Algorithm of Safe Pipes In theinitiative warning algorithm there are two pipes The outerone is a safe pipe and the inner one is an early warningpipe Formula (8) can be a reference to the generationalgorithm of safe pipe The difference between the safe pipeand the safe extended pipe is that the safe pipe cannot beextended dynamically Early warning pipe is used to monitorthe deviation of the robot EE and it needs to be adjustedaccording to the deviation of the robot EE (Figure 3) Ifthe robot EE crosses warning pipe the system will alarm awarning report operator that the robot EE is in dangerousregionThe safe extended pipe is designed as a pipe from thickto spindly which can lead the robot EE to the target

Given a path the robot EE is at the initial point of the pathAssuming that the cross-sectional diameter is ℎ the length ofthe path is 119877 and 119877 gt 4ℎ The initial point is1198620 and1198624ℎ is thepoint which is 4ℎ away from 1198750 The cross-sectional diameterat 1198620 is 4ℎ and the diameter is ℎ when at 1198754ℎ Thus for anypoint 119862 its cross-sectional diameter is

119889119904 =

4ℎ minus

100381610038161003816100381611986211986201003816100381610038161003816

4ℎsdot 2ℎ

100381610038161003816100381611986211986201003816100381610038161003816 lt 4ℎ

2ℎ10038161003816100381610038161198621198620

1003816100381610038161003816 gt 4ℎ

(11)

When the robot EE strays from the path the earlywarning pipe needs to adjust itself accordingly so that it cangive a real-time warning when the robot EE crosses safe pipe

Assuming that the robotrsquos current moving speed is V itsacceleration is 119886 Then the robotrsquos displacement at the nextmoment is

119904 = V119905 +1

21198861199052 (12)

Here 119905 is time intervalThe diameter of early pipe is

119889119908 =

(4ℎ minus 2119904) minus

100381610038161003816100381611986211986201003816100381610038161003816

4ℎsdot (2ℎ minus 2119904)

100381610038161003816100381611986211986201003816100381610038161003816 lt 4ℎ

2ℎ10038161003816100381610038161198621198620

1003816100381610038161003816 gt 4ℎ

(13)

33 Collision Detection In order to detect whether therobot EE passes through the pipe this paper uses K-DOPsalgorithm [26] to detect the collision between the robot EEand the pipes K-DOPs can detect the collision in real time Inorder to use K-DOPs the pipe is designed as a set of trianglesIn addition K-DOPs can calculate the collision point andthe collision direction When the robot EE passes throughthe pipe K-DOPs will calculate the crossing position and thedirection and then the operator can adjust the robot EE tothe negative direction

34 Analysis of Time Complexity Assuming the sides of thepipe units are 1198991015840 and the number of discrete points of thepipe path is 119898 then the frequency of choosing initial pointsis 119898 the frequency of constructing polygon is 161198991015840119898 thefrequency of constructing cylinder is 119898(1198991015840 minus 1) and thefrequency of connecting pipe units is 31198991015840(119898 minus 1) Thus thetotal frequency of constructing pipes is

119891 (1198991015840) = 119898 + 16119899

1015840119898 + 119898(119899

1015840minus 1) + 3119899

1015840(119898 minus 1)

= 201198981198991015840minus 31198991015840

(14)

Its time complexity is

119879 (1198991015840) = 119874 (119898119899

1015840) (15)

In the dynamic pipes adjustment algorithm radius ofeach pipe unit is only updated once And for every point inthe pipe its coordinates are needed to be recalculated onceThen the total frequency is

1198911 (1198991015840) = 16119899

1015840119898 (16)


Target

S

Safe pipe

Early warning pipe

PathVelocity

Acceleration a

Figure 3 Result of dynamic early warning pipes adjustment

Network

InstructionInstruction

Video

Peg

Hole

Camera

Local site Remote site

Video

Feedback video Virtual system

Figure 4 System structure


1198791 (1198991015840) = 119874 (119898119899

1015840) (17)

4 Evaluation

Considering of all the described pipes and their effect a seriesof tests are proposed to evaluate this teleoperation assistanceThe test is performed on grabbing an object from a cabinedbox in a 3D environment The experiments were carried outby 6 individual computer experts who were men and womenbetween 22 and 30 years old

41 Experimentation Environment A teleoperation platformbased on virtual reality is built up (see Figure 4) In the localsite a virtual emulator system (VES) and a video feedbacksystem (VFS) are built up to feed back the information tothe operator The video is serial images which are from thecameras fitted in the remote site The remote cameras areused to watch the state of the real robot In this experimentconsidering the real environment of teleoperation the systemlimits bandwidth to 30 kBs and the delay time is approx-imately 3 seconds The robot is a GOOGOL GRB606 with6 DOF Firstly the teleoperated robot is about 80 cm fromthe table The aim of the task is inserting the peg into thehole without collidingwith the table A 6-DOF force feedbackdevice (FFD PHANTOM DESKTOP) is used as the inputinterface device so that the operator can move and orient

the robot EE A camera with a resolution of 640 times 480 pixelsis mounted to feed the visible scene back to the operatoras the output interface device (OID) The feedback and thevirtual display consist of a 161 in 1280 times 1024 pixel resolutionmonitor The peg was cylinder with 75mm in radius and50mm long The radius of the hole was 19mm The robotEE consisted of a square block and two claws The size ofthe block was 100mm (119882) times 100mm (119871) times 80mm (119867) andthat of the claw was 100mm (119882) times 100mm (119871) times 10mm (119867)TheOIDprograms run on an Intel(R) Core(TM)PC Figure 7shows the experimental environmentThe workspace of FFDwas 160mm (119883)times 130mm (119884)times 130mm (119885) and the positionresolution of it was 02mm

42 Grabbing Object Experiment There are two modes tocarry out the task two pipes assisted mode (TPAM) andone pipe assisted mode (OPAM) [15] In the local site avirtual system and a video feedback system were designedto assist the operator The operator can make serial safemovements in the virtual system and send the instructionto the telerobot The operator can carry out the task bycontinuous instructionsWhen there is any collision betweenthe virtual pipes and the virtual box the operator must makeall the instructions over again

In OPAM a fixed VF [15] was designed to assist theoperator to insert the peg into the hole The fixed VF wasa symmetrical pipe and one end of it is thick but the otherone is thin The radius of the one end closed to the robot EE


Table 1 The results of the safe pipe

Time Joints values1198631mm 1198632mm PorN

1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(

∘)11th 013 minus9425 minus6433 035 minus9445 minus044 18 20 N12th 016 minus9442 minus6414 041 minus9463 minus016 13 10 N13th 021 minus9441 minus6434 036 minus6046 minus034 08 10 Y14th 031 minus9431 minus6454 033 minus6042 minus021 11 10 N15th 041 minus9421 minus6423 031 minus6041 minus013 15 10 NPorN pass through or not

Table 2 The results of the warning pipe


1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(


was 100mm and the other end closed to the hole was 19mmThe operator could control the FFD to move and orient therobot EE to control the peg along with the pipe In this modethe operator monitored the virtual window and the feedbackvideo window to catch the state of the remote robot Whenthe robot EE was close to the hole the operator must be verycareful because the robot EEwould have collidedwith the boxeasily

In TPAM two pipes were designed automatically to helpthe operator to locate the robot EE without any collisionIn our method we did not need to design the pipes Thething we needed to do was set the path In the experimentwe drew a safe path from the EE to the center of the holeand then the system created two pipes automatically thesafe pipe and the warning pipe The safe pipe could expanduntil the safe pipe collided with the edge of the hole andthe warning pipe would adjust the radius of itself In thismode the operator monitored the virtual window and thefeedback video window to catch the state of the remote robotAs the operator moves the robot toward the hole the safepipe changes continuously to make sure the robot EE will notcollide with the edge of the hole

There were two steps in each experiment approachingand inserting In the period of approaching the workspace ofthe robot was 800mm times 800mm times 800mm but in the periodof inserting it was 80mm times 80mm times 80mm Since theworkspace of FFD was 160mm (119883) times 130mm (119884) times 130mm(119885) and the position resolution of it was 02mm the accuracyof the robot control was 110mm (119883) times 123mm (119884) times123mm (119885) and 010mm (119883) times 012mm (119884) times 012mm (119885)in the period of approaching and inserting respectively Theexperiments were carried out by 6 individual operators whowere men and women between 23 and 30 years old

43 Result The results of the peg-into-hole under TPAMandOPAM are shown in Tables 1 and 2 and Figure 5 (Test 3)

The 3D paths of the robot EE in TPAM and OPAM aswell as the reference path for the entire test 3 are shown inFigure 5(a) Figures 5(b)ndash5(d) show the displacements of therobot EE positions There are three circles on each curve ofthe reference paths From the beginning to the first circle isthe period of closing to the hole from the first circle to thesecond circle is the period of inserting the peg and from thesecond circle to the third circle is the period of departing fromthe hole The period of closing to the hole was from 1st s to9th s and the period of inserting the peg into the hold wasfrom 9th s to 13th s as well as the period of departing fromthe hole was from 13th s to the 17th s

In order to evaluate the goodness of the path thedeviation from the reference path was introduced as patherrors

Supposing that the sampling point of the reference path is119882119896(119909119896 119910119896 119911119896) and 119881119896(119909

1015840119896 1199101015840119896 1199111015840119896) is the sampling point of the

practice path where 119896 = 1 2 119873 and 119873 is the number ofthe sample points the path errors can be defined as follows

The deviation between two paths in 119909 119910 119911 is

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119909119896 minus 119909

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119910119896 minus 119910

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119911119896 minus 119911

1015840119896

10038171003817100381710038171003817)

119873

(18)

And the 3D path error is defined as follows

119890119901 =radic(1198902119909 + 119890

2119910 + 1198902119911)

(19)

Errors in paths for the test 3 were shown in Figures5(e)ndash5(g) which ranged from 1577 to +1845mm in119883 fromminus1555mm to +1591mm in 119884 and from 1919 to +1597mm


0 200 400 600 8001000

100150200250300350400450

minus200minus800minus700

minus600minus500

minus400minus300

P(x)(mm)

P(y) (mm)

P(z)

(mm

)

(a)

0 10 20 30 40 50

0

500

1000

X (m

m)

minus500

(b)

0 10 20 30 40 50

Y (m

m)

minus800

minus700

minus600

minus500

minus400

minus300

(c)

0 10 20 30 40 50100

200

300

400

500

Z (m

m)

(d)

0 10 20 30 40 50

0

50

100

Dev

iatio

n x

(mm

)

minus100

minus50

(e)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n y

(mm

)

minus100

minus50

Reference pathTPAM path

OPAM path

(f)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n z

(mm

)

minus100

minus50


OPAM path

(g)

Figure 5 Analysis of the experiment


in119885 from the deviation of the reference path and the path inthe TPAM respectively And in the OPAM the errors rangedfrom minus1839 to +2545mm in 119883 from minus2055 to +2968mmin 119884 and from minus2419 to +2852mm in 119885 The mean absoluteerrors in TPAM were 331mm in 119883 335mm in 119884 and370mm in 119885 with standard deviations (SDs) of 021mm032mm and 033mm Compared with the mean absoluteerrors in OPAM 968mm in119883 956mm in 119884 and 1087mmin 119885 with standard deviations (SDs) of 067mm 047mmand 043mm the errors in TPAM were very low Duringthe object manipulation tasks some minor correction ofthe position and the orientation for overshoot was requiredmainly preceding a gripper inserting the peg into the hole asshown in Figures 5(b)ndash5(d)

The safe pipewas designed to detect the potential collisionand the warning pipe constrained the robot EE to follow thereferenced path The robot EE should be in the safe pipe andthe warning pipe When the robot EE passed through thesafe pipe the system should give a warning to the operatorto adjust hisher operation Tables 1 and 2 gave the results ofthe pipes

The manipulation task required that the robot EE needsto get close to the table so that it could insert the peg into thehole When the robot EE got close to the table the safe pipeexpanded to create more safe space to protect the robot EEwithout collision In order tomake sure the space inside of thesafe pipe was safe the obstacles should be outside of the safepipeWhen the safe pipe expanded and encountered the edgeof the hole it would stop to expand So if the robot EE keptmoving and passed through the safe pipe it would collidewith the edge of the hole Table 1 shows the results of thevariety of the safe pipe and Figure 6 shows the definition ofthe distances During the period from 1st s to 9th s the robotEE got close to the hole continuously From the 11th s therobot started to insert the peg into the hole At the 13th s thedistance between the robot EE and the obstacle was 08mmbut it was 10mm away from the safe pipe and the obstacleAt that time the robot EE passed through the safe pipe andwould collidewith the obstacle and the system gave awarningto the operator After the operator adjusted the operation(positions and orientation) the robot EE moved into the safepipe again it was 11mm away from the obstacle which islarger than the distance (10mm) between the safe pipe andthe edge of the hole

The purpose of the warning pipe was to detect thedeviation from the reference path When the robot EEdeviated from the deviation the system would predict thesafe distance through the speed and the acceleration andchange the radius of warning pipeWhen the robot EE passedthrough the warning pipe the systemwould give the operatorwarningThe initial purpose was that the warning pipe coulddetect the potential dangers and adjust the real path in timeThe greater the deviation was the larger the safe distancepredictedwas and the radius of thewarning pipewas smallerDuring the manipulation proceeding the robot EE shouldfollow the reference But due to muscle tremors or operatemiss the robot EE deviated from the reference some timeTable 2 shows the results of the radius changes of the warningpipe At the 13th s the deviation was 87mm along with

Hole

Safe pipe

Peg

D1 D2

(a)

Warning pipe

Peg

D3 D4

Hole

(b)

Figure 6 Definition of the distances 1198631 the distance between thepeg and the edge of the hole 1198632 the distance between the pipeand the edge of the hole 1198633 the sum of the radius of peg andthe deviation of the peg from the reference path 1198634 radius of thewarning pipe

83mm in the radius of the warning pipe So the system gavethe warning to the operator to remind him to adjust theoperation in time

The main purpose of the experiments is to evaluatethe improvement of the operatorrsquos manipulating with thevirtual fixtures derived from complex geometry comparedwith nonassisted instrument manipulation Our constrainedcontrol method works for the traditional master-slave tele-operation We evaluated the userrsquos performance of peg-into-hole with both OPAM and TPAM We simply used anavailable PHANTOMDESKTOP as the teleoperation masterhand controller

The experimentswere completed by 6 operatorswith bothOPAM and TPAM The mean absolute errors between thereference path and the robot path were shown in Tables 3 and4 In OPAM mode the mean absolute errors (MAEs) for thesix tests in the period of approaching ranged from 924mmto 1244mm in 119883 821mm to 990mm in 119884 and 956mm to1390mm in 119885 and the mean errors (MEs) were 1029mm in119883 941mm in119884 1211mm in119885 and 1856mm in 3Dpathwithstandard deviations (SDs) of 106mm 057mm 168mm and115mm MAEs in TPAM ranged from 272mm to 449mmin 119883 168mm to 553mm in 119884 and 370mm to 489mm in119885 and the MEs were 347mm in 119883 320mm in 119884 406mmin119885 and 632mm in 3D path with SDs of 035mm 146mm020mm and 044mm In the period of inserting theMEs inOPAM were 138mm in 119883 158mm in 119884 162mm in 119885 and269mm in 3D path Comparing with the OPAM the MEsin path drop 147mm in TPAM The results show that theoperating errors are lower in TPAM than those in OPAMwhich is due to the assisted pipes making the manipulationmore precise

The operating time is longer in OPAM than in TPAM asshown in Figure 7 Without the aid of the warning pipe theoperators needed to make more minor correction to adjustthe orientation The operating time in OPAM ranged from21 s to 24 s with the average time being 2256 s Comparedwith the OPAM the time drops to 168 s in TPAM whichranged from 16 s to 18 s


Table 3 Mean absolute errors (MAEs) for 6 tests measured by the robot in the period of approaching

Times OPAM TPAM119883mm 119884mm 119885mm Pathmm 119883mm 119884mm 119885mm Pathmm

1 1054 plusmn 089 987 plusmn 055 956 plusmn 056 1732 plusmn 013 287 plusmn 032 168 plusmn 054 382 plusmn 034 507 plusmn 048






MEs 1029 plusmn 106 941 plusmn 057 1211 plusmn 168 1856 plusmn 115 347 plusmn 035 320 plusmn 146 406 plusmn 020 632 plusmn 044

Table 4 Mean absolute errors (MAEs) for 6 tests measured by the robot in the period of inserting









1 2 3 4 5 60

5

10

15

20

25

30

35

Ope

ratio

n tim

e (s)

Number of operator

OPAMTPAM

Figure 7 Operation time

5 Conclusion

This paper has developed a real-time task-based controlmethod of a telerobot in a precise interactive teleopera-tion environment Computer guidance (remote teleoperativecontrol) employing spatial motion constraints generated byvirtual fixtures can assist the operators in skilled manipu-lation tasks The virtual fixtures can provide the desirableproperties such as safety and collision avoidance

The results of the experiments demonstrate that theTPAM is better in shortening the operating time and theaccuracy improvement The experimental results show that

there is remarkable reduction in operating tension on avoid-ing collision of the instrument which can improve themanipulation efficient

In this paper the comparison has been taken concerningthe performance of OPAM and TPAM in a complicatedworking volume The performance-comparison experimentresults show that the TPAM operation is more intuitive foroperator to use The execution time with TPAM operationis shorter than OPAM as it is also more precise thanOPAM The experiment comparison shown here is intendedto demonstrate the improvement of our spatial constraintsmethod in TPAM

The primary focus of this paper is to develop a techniquefor controlling the motion of teleoperated robots via simplereal-time geometric virtual fixtures In the future work wewill use hybrid feedback patterns (force and vision) to assistthe operator

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] R KikuuweN Takesue andH Fujimoto ldquoA control frameworkto generate nonenergy-storing virtual fixtures use of simulatedplasticityrdquo IEEE Transactions on Robotics vol 24 no 4 pp 781ndash793 2008

[2] A Bettini P Marayong S Lang A M Okamura and G DHager ldquoVision-assisted control for manipulation using virtualfixturesrdquo IEEE Transactions on Robotics vol 20 no 6 pp 953ndash966 2004


[3] L B Rosenberg Virtual fixtures [PhD thesis] Department ofMechanical Engineering Stanford University Stanford CalifUSA 1994

[4] F Lai and R D Howe ldquoEvaluating control modes for con-strained robotic surgeryrdquo in Proceedings of the IEEE Interna-tional Conference on Robotics and Automation (ICRA rsquo00) pp603ndash609 April 2000

[5] M A Peshkin J Edward Colgate W Wannasuphoprasit C AMoore R Brent Gillespie and P Akella ldquoCobot architecturerdquoIEEE Transactions on Robotics and Automation vol 17 no 4pp 377ndash390 2001

[6] S Payandehand and Z Stanisic ldquoOn application of virtualfixture as an aid for telemanipulation and trainingrdquo in Pro-ceedings of the 10th Symposium on Haptic Interfaces for VirtualEnvironment and Teleoperator Systems pp 18ndash23 2002

[7] J Ren K A McIsaac R V Patel and T M Peters ldquoApotential field model using generalized sigmoid functionsrdquoIEEE Transactions on Systems Man and Cybernetics B vol 37no 2 pp 477ndash484 2007

[8] D Burschka J J Corso M Dewan et al ldquoNavigating innerspace 3-D assistance for minimally invasive surgeryrdquo Roboticsand Autonomous Systems vol 52 no 1 pp 5ndash26 2005


[10] A Bettini S Lang A Okamura and G Hager ldquoVision assistedcontrol for manipulation using virtual fixturesrdquo in Proceedingsof the IEEERSJ International Conference on Intelligent Robotsand Systems pp 1171ndash1176 November 2001

[11] J Aleotti S Caselli and M Reggiani ldquoEvaluation of virtualfixtures for a robot programming by demonstration interfacerdquoIEEE Transactions on Systems Man and Cybernetics A vol 35no 4 pp 536ndash545 2005

[12] S Ekvall D Aarno and D Kragic ldquoOnline task recognitionand real-time adaptive assistance for computer-aided machinecontrolrdquo IEEE Transactions on Robotics vol 22 no 5 pp 1029ndash1033 2006

[13] G S Guthart and K J Salisbury Jr ldquoIntuitive telesurgerysystem overview and applicationrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation (ICRArsquo00) pp 618ndash621 April 2000

[14] P Marayong A Bettini and A Okamura ldquoEffect of virtualfixture compliance on human-machine cooperative manipula-tionrdquo in Proceedings of the IEEERSJ International Conference onIntelligent Robots and Systems pp 1089ndash1095 October 2002

[15] M Li M Ishii and R H Taylor ldquoSpatial motion constraintsusing virtual fixtures generated by anatomyrdquo IEEE Transactionson Robotics vol 23 no 1 pp 4ndash19 2007

[16] J Troccaz M A Peshkin and B L Davies ldquoThe use oflocalizers robots and synergistic devices inCASrdquo inProceedingsof the 1st Joint Conference Computer Vision Virtual Realityand Robotics in Medicine and Medical Robotics and Computer-Assisted Surgery CVRMed and MRCAS pp 727ndash736 1997

[17] J Ren R V Patel K A McIsaac G Guiraudon and T MPeters ldquoDynamic 3-D virtual fixtures for minimally invasivebeating heart proceduresrdquo IEEE Transactions on Medical Imag-ing vol 27 no 8 pp 1061ndash1070 2008

[18] R A Beasley and R D Howe ldquoIncreasing accuracy in image-guided robotic surgery through tip tracking and model-basedflexion correctionrdquo IEEE Transactions on Robotics vol 25 no2 pp 292ndash302 2009

[19] S Park R D Howe and D F Torchiana ldquoVirtual fixturesfor robotic cardiac surgeryrdquo in Proceedings of the InternationalConference onMedical Image Computing and Computer AssistedIntervention pp 1419ndash1420 2001

[20] P Marayong M Li A M Okamura and G D Hager ldquoSpa-tial motion constraints theory and demonstrations for robotguidance using virtual fixturesrdquo in Proceedings of the IEEEInternational Conference on Robotics and Automation pp 1954ndash1959 September 2003

[21] O Schneider and J Troccaz ldquoA six-degree-of-freedom Pas-sive Arm with Dynamic Constraints (PADyC) for cardiacsurgery application preliminary experimentsrdquoComputer AidedSurgery vol 6 no 6 pp 340ndash351 2001

[22] J Wurm H Steinhart K BummM Vogele C Nimsky and HIro ldquoA novel robot system for fully automated paranasal sinussurgeryrdquo International Congress Series vol 1256 pp 633ndash6382003

[23] G Strauss K Koulechov R Richter A Dietz C Trantakisand T Luth ldquoNavigated control in functional endoscopic sinussurgeryrdquo The International Journal of Medical Robotics andComputer Assisted Surgery vol 1 no 3 pp 31ndash41 2005

[24] K Koulechov G Strauss R Richter C Trantakis and T CLueth ldquoMechatronical assistance for paranasal sinus surgeryrdquoInternational Congress Series vol 1281 pp 636ndash641 2005

[25] K Koulechov G Strauss A Dietz M Strauss M Hofer andT Lueth ldquoFESS control realization and evaluation of navigatedcontrol for functional endoscopic sinus surgeryrdquo ComputerAided Surgery vol 11 no 3 pp 147ndash159 2006

[26] J T Klosowski M Held J S B Mitchell H Sowizral andK Zikan ldquoEfficient collision detection using bounding volumehierarchies of k-DOPsrdquo IEEE Transactions on Visualization andComputer Graphics vol 4 no 1 pp 21ndash36 1998

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



the hard and soft VFs and worked on the application tovitreoretinal surgery Marayong et al [20] demonstratedmotion constraints by varying compliance that was describedfor the general spatial case In these researches admittancecontrol laws are used to implement VFs A passive arm withdynamic constraints (PADyc) has been developed by Li et al[15 17 21] for pericardial puncture They implement VFs torestrict surgical tools to move along planned paths or awayfrom forbidden regions by using electrical motors to choosea clutching system for freewheelsThemain advantage of thismethod is that the robot cannot providemotive force withoutthe help of the surgeon This has been considered as onesafety advantage because it can prevent a robot from losingcontrol But there are some limitations including mechanicalcomplexity and loss of the robotrsquos ability to actively assistin surgical procedures A robotic system for fully automatedparanasal sinus surgery is developed byWurm et al [22]Thissystem uses preoperative CT to direct the robotrsquos autonomousmotion and it allows being remote controlled by a joystick A mechatronic system for FESS (functional endoscopicsinus surgery) has been presented by Luethrsquos group [23ndash25]According to a 3D model from CT data they planned a safeworking space preoperatively In the middle of the operationthe shaver is automatically turned onoff according to theposition of the shaver tip In the safe area the shaver reacts tosignals from the surgeon When the tip of the shaver movesoutside the safe area an electrical pulse will stop the shaverby interrupting its automatic drive control This navigation-based system is only concerned with the position of shavertip

In this paper we present an online obstacle-avoidancemethod for serial robot in geometrically complex environ-ments We extend Lirsquos work [15] to generate VFs for obstacleavoidance and a new potential collision-constraint-detectionmethod has been proposed In this method two pipes (thewarning pipe and the safe pipe) are automatically generatedfrom 3D reference path in real time The safe pipe serves asspatial constraints for constrained robot controlThewarningpipe adjusts the radius to detect the deviation of the robotEE from the reference path by calculating the speed and theacceleration of the robot EE In our experiment (Figure 1)two assisted modes were implemented one pipe assistedmode [15] (OPAM) and two pipes assisted mode (TPAM)The former mode used the fixed VFs [15] to guide the robotEE but in our method (the latter mode) two types of VFswere used to guide and constrain the robot EE When therobot EE collides with the pipes our systemwill give warninginformation based on vision to the operator changing thecolor of the pipes Due to the warning pipe our new spatial-motion-constraints method enables multiobstacle manipu-lation task of telerobot in precise interactive teleoperationenvironment

The remainder of the paper is organized as followsSection 2 provides a brief summary of path and the pipesbuilding algorithm In Section 3 we introduce the dynamicadjustment algorithm of the safe pipe and the warning pipeIn Section 4 we report the experiment results of two controlmodes We conclude the paper and discuss possible futureextensions in Section 5

Safe pipe

Platform

Warning pipe

Peg Hole

Figure 1 Geometric relation for spatial motion constraints

2 Path and Pipes

The path is a possible route obtained by the robot pathplanning Path planning is a kind of algorithmwhich finds outa collision-free path in all generalized coordinates of a robotwith some valuation criteria by the given initial positions andorientations of the robot A pipe gives the robot a safe space inwhich the robot can move freely without collision The pipesare built based on the paths They can divide the safe spacesand can also guide and give active early warnings

The pipes take the paths as medial axis and the path isformed by a series of path points Thus the pipes are formedby discrete pipe units

The pipes are built by many pipe units The pipe unitsare formed by two cross sections and a cylinder The shapeof cross section is decided by the predefined shape of thepipes Cross section is formed by polygon and circle sectionis formed by polygon which has more sides

21 Choosing a Starting Point of Cross Section As we know apolygon can be finalized by the given central point the centralaxis and the starting point How to choose the starting pointdepends on the origin of the coordinate system There is acentral point119875 a central axis 119871 and an origin point119874 Firstlyconnect the original point and the central point to get thereference vector 119874119875 The vertical vector 119876 can be calculated

119876 = 119874119875 times 119871 (1)

Unitize119876 and then get 119905119876 119878 is the point which is 119903 lengthfrom 119875 along the direction of

119878 = 119875 + 119905119876 sdot 119903 (2)

When there is an overlap between the central point andthe origin point we can take the unit vector of 119883 axis to bethe reference vector

22 Constructing a Polygon The key to create a polygon is todetermine the vertexes of the polygon Assume that there isa polygon with 119899 sides Then the radius angle of two adjacentvertices is

120579 = 2 sdot120587

119899 (3)




T = [[[


]]

]

(4)


11989811 = 119905 sdot 1198611 sdot 1198611 + 119888

11989812 = 119905 sdot 1198611 sdot 1198612 + 119904 sdot 1198613



11989822 = 119905 sdot 1198612 sdot 1198612 + 119888

11989823 = 119905 sdot 1198752 sdot 1198753 + 119904 sdot 119875

11989831 = 119905 sdot 1198611 sdot 1198613 + 119904 sdot 1198612


11989833 = 119905 sdot 1198613 sdot 1198613 + 119888

119888 = cos 120579

119904 = sin 120579

119905 = 1 minus cos 120579

(5)


A1015840 = T sdot A (6)





Obstacle

r

Safe pipe

Central axis

PathTarget4r

4r




1198993 = 119892119888119889 (1198991 1198992) (7)










119889 =

4119896 minus

100381610038161003816100381611987511989911987501003816100381610038161003816

4119896sdot 2119896

100381610038161003816100381611987511989911987501003816100381610038161003816 lt 4119896

211989610038161003816100381610038161198751198991198750

1003816100381610038161003816 gt 4119896

(8)



1198751015840=

119875119888 +(119909 minus

1003816100381610038161003816100381610038161003816

997888rarr

1198751198881198750

1003816100381610038161003816100381610038161003816

4119896sdot (119909)) sdot 120575

100381610038161003816100381611987511988811987501003816100381610038161003816 lt 4119896

11987511988810038161003816100381610038161198751198881198750

1003816100381610038161003816 gt 4119896

(9)



119889 =

(4119896 + 2119909) minus

1003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816

4119896sdot (2119896 + 2119909)

1003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816lt 4119896

21198961003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816gt 4119896

(10)



119889119904 =

4ℎ minus

100381610038161003816100381611986211986201003816100381610038161003816

4ℎsdot 2ℎ

100381610038161003816100381611986211986201003816100381610038161003816 lt 4ℎ

2ℎ10038161003816100381610038161198621198620

1003816100381610038161003816 gt 4ℎ

(11)



119904 = V119905 +1

21198861199052 (12)


119889119908 =


100381610038161003816100381611986211986201003816100381610038161003816


100381610038161003816100381611986211986201003816100381610038161003816 lt 4ℎ

2ℎ10038161003816100381610038161198621198620

1003816100381610038161003816 gt 4ℎ

(13)



119891 (1198991015840) = 119898 + 16119899

1015840119898 + 119898(119899

1015840minus 1) + 3119899

1015840(119898 minus 1)

= 201198981198991015840minus 31198991015840

(14)


119879 (1198991015840) = 119874 (119898119899

1015840) (15)


1198911 (1198991015840) = 16119899

1015840119898 (16)


Target

S

Safe pipe

Early warning pipe

PathVelocity

Acceleration a


Network


Video

Peg

Hole

Camera


Video




1198791 (1198991015840) = 119874 (119898119899

1015840) (17)

4 Evaluation









1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(




1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(












119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119909119896 minus 119909

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119910119896 minus 119910

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119911119896 minus 119911

1015840119896

10038171003817100381710038171003817)

119873

(18)


119890119901 =radic(1198902119909 + 119890

2119910 + 1198902119911)

(19)



0 200 400 600 8001000

100150200250300350400450


minus600minus500

minus400minus300

P(x)(mm)

P(y) (mm)

P(z)

(mm

)

(a)

0 10 20 30 40 50

0

500

1000

X (m

m)

minus500

(b)

0 10 20 30 40 50

Y (m

m)

minus800

minus700

minus600

minus500

minus400

minus300

(c)

0 10 20 30 40 50100

200

300

400

500

Z (m

m)

(d)

0 10 20 30 40 50

0

50

100

Dev

iatio

n x

(mm

)

minus100

minus50

(e)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n y

(mm

)

minus100

minus50


OPAM path

(f)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n z

(mm

)

minus100

minus50


OPAM path

(g)







Hole

Safe pipe

Peg

D1 D2

(a)

Warning pipe

Peg

D3 D4

Hole

(b)

























1 2 3 4 5 60

5

10

15

20

25

30

35

Ope

ratio

n tim

e (s)

Number of operator

OPAMTPAM


5 Conclusion








References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












T = [[[


]]

]

(4)


11989811 = 119905 sdot 1198611 sdot 1198611 + 119888

11989812 = 119905 sdot 1198611 sdot 1198612 + 119904 sdot 1198613



11989822 = 119905 sdot 1198612 sdot 1198612 + 119888

11989823 = 119905 sdot 1198752 sdot 1198753 + 119904 sdot 119875

11989831 = 119905 sdot 1198611 sdot 1198613 + 119904 sdot 1198612


11989833 = 119905 sdot 1198613 sdot 1198613 + 119888

119888 = cos 120579

119904 = sin 120579

119905 = 1 minus cos 120579

(5)


A1015840 = T sdot A (6)





Obstacle

r

Safe pipe

Central axis

PathTarget4r

4r




1198993 = 119892119888119889 (1198991 1198992) (7)










119889 =

4119896 minus

100381610038161003816100381611987511989911987501003816100381610038161003816

4119896sdot 2119896

100381610038161003816100381611987511989911987501003816100381610038161003816 lt 4119896

211989610038161003816100381610038161198751198991198750

1003816100381610038161003816 gt 4119896

(8)



1198751015840=

119875119888 +(119909 minus

1003816100381610038161003816100381610038161003816

997888rarr

1198751198881198750

1003816100381610038161003816100381610038161003816

4119896sdot (119909)) sdot 120575

100381610038161003816100381611987511988811987501003816100381610038161003816 lt 4119896

11987511988810038161003816100381610038161198751198881198750

1003816100381610038161003816 gt 4119896

(9)



119889 =

(4119896 + 2119909) minus

1003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816

4119896sdot (2119896 + 2119909)

1003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816lt 4119896

21198961003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816gt 4119896

(10)



119889119904 =

4ℎ minus

100381610038161003816100381611986211986201003816100381610038161003816

4ℎsdot 2ℎ

100381610038161003816100381611986211986201003816100381610038161003816 lt 4ℎ

2ℎ10038161003816100381610038161198621198620

1003816100381610038161003816 gt 4ℎ

(11)



119904 = V119905 +1

21198861199052 (12)


119889119908 =


100381610038161003816100381611986211986201003816100381610038161003816


100381610038161003816100381611986211986201003816100381610038161003816 lt 4ℎ

2ℎ10038161003816100381610038161198621198620

1003816100381610038161003816 gt 4ℎ

(13)



119891 (1198991015840) = 119898 + 16119899

1015840119898 + 119898(119899

1015840minus 1) + 3119899

1015840(119898 minus 1)

= 201198981198991015840minus 31198991015840

(14)


119879 (1198991015840) = 119874 (119898119899

1015840) (15)


1198911 (1198991015840) = 16119899

1015840119898 (16)


Target

S

Safe pipe

Early warning pipe

PathVelocity

Acceleration a


Network


Video

Peg

Hole

Camera


Video




1198791 (1198991015840) = 119874 (119898119899

1015840) (17)

4 Evaluation









1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(




1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(












119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119909119896 minus 119909

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119910119896 minus 119910

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119911119896 minus 119911

1015840119896

10038171003817100381710038171003817)

119873

(18)


119890119901 =radic(1198902119909 + 119890

2119910 + 1198902119911)

(19)



0 200 400 600 8001000

100150200250300350400450


minus600minus500

minus400minus300

P(x)(mm)

P(y) (mm)

P(z)

(mm

)

(a)

0 10 20 30 40 50

0

500

1000

X (m

m)

minus500

(b)

0 10 20 30 40 50

Y (m

m)

minus800

minus700

minus600

minus500

minus400

minus300

(c)

0 10 20 30 40 50100

200

300

400

500

Z (m

m)

(d)

0 10 20 30 40 50

0

50

100

Dev

iatio

n x

(mm

)

minus100

minus50

(e)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n y

(mm

)

minus100

minus50


OPAM path

(f)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n z

(mm

)

minus100

minus50


OPAM path

(g)







Hole

Safe pipe

Peg

D1 D2

(a)

Warning pipe

Peg

D3 D4

Hole

(b)

























1 2 3 4 5 60

5

10

15

20

25

30

35

Ope

ratio

n tim

e (s)

Number of operator

OPAMTPAM


5 Conclusion








References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












119889 =

4119896 minus

100381610038161003816100381611987511989911987501003816100381610038161003816

4119896sdot 2119896

100381610038161003816100381611987511989911987501003816100381610038161003816 lt 4119896

211989610038161003816100381610038161198751198991198750

1003816100381610038161003816 gt 4119896

(8)



1198751015840=

119875119888 +(119909 minus

1003816100381610038161003816100381610038161003816

997888rarr

1198751198881198750

1003816100381610038161003816100381610038161003816

4119896sdot (119909)) sdot 120575

100381610038161003816100381611987511988811987501003816100381610038161003816 lt 4119896

11987511988810038161003816100381610038161198751198881198750

1003816100381610038161003816 gt 4119896

(9)



119889 =

(4119896 + 2119909) minus

1003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816

4119896sdot (2119896 + 2119909)

1003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816lt 4119896

21198961003816100381610038161003816100381611987510158401198750

10038161003816100381610038161003816gt 4119896

(10)



119889119904 =

4ℎ minus

100381610038161003816100381611986211986201003816100381610038161003816

4ℎsdot 2ℎ

100381610038161003816100381611986211986201003816100381610038161003816 lt 4ℎ

2ℎ10038161003816100381610038161198621198620

1003816100381610038161003816 gt 4ℎ

(11)



119904 = V119905 +1

21198861199052 (12)


119889119908 =


100381610038161003816100381611986211986201003816100381610038161003816


100381610038161003816100381611986211986201003816100381610038161003816 lt 4ℎ

2ℎ10038161003816100381610038161198621198620

1003816100381610038161003816 gt 4ℎ

(13)



119891 (1198991015840) = 119898 + 16119899

1015840119898 + 119898(119899

1015840minus 1) + 3119899

1015840(119898 minus 1)

= 201198981198991015840minus 31198991015840

(14)


119879 (1198991015840) = 119874 (119898119899

1015840) (15)


1198911 (1198991015840) = 16119899

1015840119898 (16)


Target

S

Safe pipe

Early warning pipe

PathVelocity

Acceleration a


Network


Video

Peg

Hole

Camera


Video




1198791 (1198991015840) = 119874 (119898119899

1015840) (17)

4 Evaluation









1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(




1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(












119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119909119896 minus 119909

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119910119896 minus 119910

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119911119896 minus 119911

1015840119896

10038171003817100381710038171003817)

119873

(18)


119890119901 =radic(1198902119909 + 119890

2119910 + 1198902119911)

(19)



0 200 400 600 8001000

100150200250300350400450


minus600minus500

minus400minus300

P(x)(mm)

P(y) (mm)

P(z)

(mm

)

(a)

0 10 20 30 40 50

0

500

1000

X (m

m)

minus500

(b)

0 10 20 30 40 50

Y (m

m)

minus800

minus700

minus600

minus500

minus400

minus300

(c)

0 10 20 30 40 50100

200

300

400

500

Z (m

m)

(d)

0 10 20 30 40 50

0

50

100

Dev

iatio

n x

(mm

)

minus100

minus50

(e)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n y

(mm

)

minus100

minus50


OPAM path

(f)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n z

(mm

)

minus100

minus50


OPAM path

(g)







Hole

Safe pipe

Peg

D1 D2

(a)

Warning pipe

Peg

D3 D4

Hole

(b)

























1 2 3 4 5 60

5

10

15

20

25

30

35

Ope

ratio

n tim

e (s)

Number of operator

OPAMTPAM


5 Conclusion








References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Target

S

Safe pipe

Early warning pipe

PathVelocity

Acceleration a


Network


Video

Peg

Hole

Camera


Video




1198791 (1198991015840) = 119874 (119898119899

1015840) (17)

4 Evaluation









1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(




1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(












119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119909119896 minus 119909

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119910119896 minus 119910

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119911119896 minus 119911

1015840119896

10038171003817100381710038171003817)

119873

(18)


119890119901 =radic(1198902119909 + 119890

2119910 + 1198902119911)

(19)



0 200 400 600 8001000

100150200250300350400450


minus600minus500

minus400minus300

P(x)(mm)

P(y) (mm)

P(z)

(mm

)

(a)

0 10 20 30 40 50

0

500

1000

X (m

m)

minus500

(b)

0 10 20 30 40 50

Y (m

m)

minus800

minus700

minus600

minus500

minus400

minus300

(c)

0 10 20 30 40 50100

200

300

400

500

Z (m

m)

(d)

0 10 20 30 40 50

0

50

100

Dev

iatio

n x

(mm

)

minus100

minus50

(e)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n y

(mm

)

minus100

minus50


OPAM path

(f)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n z

(mm

)

minus100

minus50


OPAM path

(g)







Hole

Safe pipe

Peg

D1 D2

(a)

Warning pipe

Peg

D3 D4

Hole

(b)

























1 2 3 4 5 60

5

10

15

20

25

30

35

Ope

ratio

n tim

e (s)

Number of operator

OPAMTPAM


5 Conclusion








References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(




1205791(∘) 1205792(

∘) 1205793(∘) 1205794(

∘) 1205795(∘) 1205796(












119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119909119896 minus 119909

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119910119896 minus 119910

1015840119896

10038171003817100381710038171003817)

119873

119890119909 =

(sum119873

119896=1

10038171003817100381710038171003817119911119896 minus 119911

1015840119896

10038171003817100381710038171003817)

119873

(18)


119890119901 =radic(1198902119909 + 119890

2119910 + 1198902119911)

(19)



0 200 400 600 8001000

100150200250300350400450


minus600minus500

minus400minus300

P(x)(mm)

P(y) (mm)

P(z)

(mm

)

(a)

0 10 20 30 40 50

0

500

1000

X (m

m)

minus500

(b)

0 10 20 30 40 50

Y (m

m)

minus800

minus700

minus600

minus500

minus400

minus300

(c)

0 10 20 30 40 50100

200

300

400

500

Z (m

m)

(d)

0 10 20 30 40 50

0

50

100

Dev

iatio

n x

(mm

)

minus100

minus50

(e)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n y

(mm

)

minus100

minus50


OPAM path

(f)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n z

(mm

)

minus100

minus50


OPAM path

(g)







Hole

Safe pipe

Peg

D1 D2

(a)

Warning pipe

Peg

D3 D4

Hole

(b)

























1 2 3 4 5 60

5

10

15

20

25

30

35

Ope

ratio

n tim

e (s)

Number of operator

OPAMTPAM


5 Conclusion








References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










0 200 400 600 8001000

100150200250300350400450


minus600minus500

minus400minus300

P(x)(mm)

P(y) (mm)

P(z)

(mm

)

(a)

0 10 20 30 40 50

0

500

1000

X (m

m)

minus500

(b)

0 10 20 30 40 50

Y (m

m)

minus800

minus700

minus600

minus500

minus400

minus300

(c)

0 10 20 30 40 50100

200

300

400

500

Z (m

m)

(d)

0 10 20 30 40 50

0

50

100

Dev

iatio

n x

(mm

)

minus100

minus50

(e)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n y

(mm

)

minus100

minus50


OPAM path

(f)

0 10 20 30 40 50

0

50

100

Sampling points

Dev

iatio

n z

(mm

)

minus100

minus50


OPAM path

(g)







Hole

Safe pipe

Peg

D1 D2

(a)

Warning pipe

Peg

D3 D4

Hole

(b)

























1 2 3 4 5 60

5

10

15

20

25

30

35

Ope

ratio

n tim

e (s)

Number of operator

OPAMTPAM


5 Conclusion








References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














Hole

Safe pipe

Peg

D1 D2

(a)

Warning pipe

Peg

D3 D4

Hole

(b)

























1 2 3 4 5 60

5

10

15

20

25

30

35

Ope

ratio

n tim

e (s)

Number of operator

OPAMTPAM


5 Conclusion








References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




























1 2 3 4 5 60

5

10

15

20

25

30

35

Ope

ratio

n tim

e (s)

Number of operator

OPAMTPAM


5 Conclusion








References






























RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









Documents

Research Article A Novel Flexible Virtual Fixtures for ...mode [ ] (OPAM) and two pipes assisted mode (TPAM). e former mode used the xed VFs [ ]toguidetherobot EE but in our method