ForwardandInverseKinematics

MEEN 491 – 512 Aggie-Challenge Instructor: Dr. Langari

MalikAldabbaghTemiBalogunMauraCadiganNathanDunkelbergerTylerJohnsonJesseJamesPerez

ProblemIntroduction•  GiventheEinalroboticarmdesignandthemotionofalltheactuators,Eindthepositionoftheendeffector

•  Requiresknowledgeofkinematicstosolvecorrectly•  Importantfortheinverseportion

•  GiventheconEigurationoftheendeffector,EindtheconEigurationoftheroboticarm

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Denavit-Hartenberg(D-H)Convention

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Denavit-Hartenberg(D-H)Convention

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FinalDHTableforForwardKinematics

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Link ai αi di θi

1 0 -90° 0 θ1*

2 0 100° d2* 0

3 0 60° r1+b1tan(10°) θ3*

4 0 100° 0 θ4*

5 0 -40° -(r2+b2/cos(50°)) θ5*

6 0 90° b2tan(50°)+b3+b4 θ6*

7 0 0° -b5 0

ExoskeletonWorkspace• Workspaceistherangeofmotionofthesystem,orthesectionofspaceinwhicheachpartofthesystemcanoperatewithoutinterference

•  Aworkspaceislimitedbyseveralfactors

•  Knowingtheworkspaceofasystemiscriticalwhenapplyingitintherealworld

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Exoskeleton Workspace

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Inverse Kinematics

•  Theprocessofdeterminingasystem’sconEigurationfromtheendeffector

•  MoredifEicultthanforwardkinematics •  Nosetwayforeveryproblem •  Canbesolvednumericallyoranalytically •  Maynotbeabletobesolvedatall

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InverseKinematics•  Twomethods

•  Analytical:asymbolicrepresentationthatworksformostconEigurations

•  Numerical:numericalsolutionthatonlyworksforaspeciEicconEiguration

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GeometricSolution(Analytical) •  Whileitwillbepartiallysolvedanalytically,solvingforanyvariablegeometricallywillproducemoreaccurateresultsandwillallowforquickercalculations

•  Thelesscomplextheanalyticalequations,thebetter

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GeometricSolution

•  TheEinalcolumnof 𝑅↓7↑0 doesnotdependonΘ7*

𝑅↓7↑0 = █𝑟↓11 &𝑟↓12 &𝑟↓13 @𝑟↓21 &𝑟↓22 &𝑟↓23 @𝑟↓31 &𝑟↓32 &𝑟↓33  

•  LastcolumncanbeusedtosolveforΘ3*,Θ4*.Θ5*analytically

•  Θ7*isthelastvariableandthereare9equationsthatcanbeusedtosolveforit

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NumericalInverseKinematics•  Canbeusedwhenthereisnopossibleanalyticalsolution•  Doesnotprovidedirectequations•  Forwardkinematicshelpchecksolution

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Gradient Method (Numerical) •  GradientMethod:𝑞↑𝑘+1  = 𝑞↑𝑘 + α∗𝐽↓𝑟↑𝑇 (𝑞↑𝑘 ) [𝑟↓𝑑 − 𝑓↓𝑟 (𝑞↑𝑘 )]•  q–guessofparameters•  k–index•  α–stepsize•  J–Jacobianoperator•  rd–desiredoutput•  fr–functions

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Problems with Numerical Methods

•  Highcomputationtime•  Mustchangeparameterswhichaffecttheoutput

– Notstraightforward•  Mustkeeptrackofcurrentandpastiterations

– Easytomessup•  Complicatedtokeeptrackofallvariables

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Future Goals for the Project

•  Finishtheinversekinematicsportion •  Solidifytheworkspace,completearangeofmotionforthesystem

•  Developcontrolalgorithms

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Overall experience

•  HowhasitcomparedtootherResearchcourses? •  Whatdidwelearnfromtheexperience? •  Howhastheexperiencehelpedus?

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