Forward and Inverse Kinematics - TAMU College of Engineering...Forward and Inverse Kinematics MEEN...
Transcript of Forward and Inverse Kinematics - TAMU College of Engineering...Forward and Inverse Kinematics MEEN...
ForwardandInverseKinematics
MEEN 491 – 512 Aggie-Challenge Instructor: Dr. Langari
MalikAldabbaghTemiBalogunMauraCadiganNathanDunkelbergerTylerJohnsonJesseJamesPerez
ProblemIntroduction• GiventheEinalroboticarmdesignandthemotionofalltheactuators,Eindthepositionoftheendeffector
• Requiresknowledgeofkinematicstosolvecorrectly• Importantfortheinverseportion
• GiventheconEigurationoftheendeffector,EindtheconEigurationoftheroboticarm
2
Denavit-Hartenberg(D-H)Convention
3
Denavit-Hartenberg(D-H)Convention
4
FinalDHTableforForwardKinematics
5
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
6
Exoskeleton Workspace
7
Inverse Kinematics
• Theprocessofdeterminingasystem’sconEigurationfromtheendeffector
• MoredifEicultthanforwardkinematics • Nosetwayforeveryproblem • Canbesolvednumericallyoranalytically • Maynotbeabletobesolvedatall
8
InverseKinematics• Twomethods
• Analytical:asymbolicrepresentationthatworksformostconEigurations
• Numerical:numericalsolutionthatonlyworksforaspeciEicconEiguration
9
GeometricSolution(Analytical) • Whileitwillbepartiallysolvedanalytically,solvingforanyvariablegeometricallywillproducemoreaccurateresultsandwillallowforquickercalculations
• Thelesscomplextheanalyticalequations,thebetter
10
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
11
NumericalInverseKinematics• Canbeusedwhenthereisnopossibleanalyticalsolution• Doesnotprovidedirectequations• Forwardkinematicshelpchecksolution
12
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
13
Problems with Numerical Methods
• Highcomputationtime• Mustchangeparameterswhichaffecttheoutput
– Notstraightforward• Mustkeeptrackofcurrentandpastiterations
– Easytomessup• Complicatedtokeeptrackofallvariables
14
Future Goals for the Project
• Finishtheinversekinematicsportion • Solidifytheworkspace,completearangeofmotionforthesystem
• Developcontrolalgorithms
15
Overall experience
• HowhasitcomparedtootherResearchcourses? • Whatdidwelearnfromtheexperience? • Howhastheexperiencehelpedus?
16