RobotikTraining.ppt

RobotVision BasicTrainingCourse Contents BasicMathematicsCoordinatesandFramesRobotsRobotVision 2Dand3DCalibration RobotVision BasicTrainingCourse BasicMathematics VectorsandMatrices vector matrix row column additionandsubtraction VectorsandMatrices Multiplication a d b e c f x b f e ca f d ca e b d A B Caution A B B A MatrixMath BasicRules A B B AA BonlypossibleifnumberofrowsofA numberofcolumnsofBandnumberofcolumnsofB numberofrowsofAnumberofrowsofA B numberofrowsofAnumberofcolumnsofA B numberofcolumnsofBA A 1 1A 1 A MatrixEquations EquationA B C D E FmultiplicationofbothsideswiththesamematrixfromthesamesidewithC 1fromtherightsideA B C C 1 D E F C 1A B 1 D E F C 1A B D E F C 1orwithA 1fromtheleftsideA 1 A B C A 1 D E FB C A 1 D E F RobotVision BasicTrainingCourse CoordinatesandFrames SomeExpressions CoordinateSystem Coordinate FrameCoordinatesystemattachedtoanobjectoraspecificpointPoseDescribesthepositionandorientationofaframewithrespecttoacoordinatesystem orframe TransformationDescribestherelationbetweentwoframesTransformsaposefromoneframetoanother 3D 2D 3D 6degreesoffreedom d o f 3translationsalongand3orientationsaroundthe3cartesianaxes2D 3d o f 2translationsalongthe2cartesianaxesand1orientationintheplane2Disaspecialcaseof3DAll3Dmathematicsisalsovalidfor2D Onetranslationandtwoanglesarealwayszeroin2D Descriptionofapointinspace x y z CP CyP CxP CzP C CxP CxP CxP CyP CzP T PositioninframeCofpointP coordinatexinframeCofpointP CxPCyPCzP Descriptionofapose frameinspace Translation x y z CyA CxA CzA C CxP CxA CxA CyA CzA T PositioninframeCoforiginofframe poseAonlytranslationoftheframe pose CxACyACzA A x y z Descriptionofapose frameinspace Rotation Orientation x y z C A x y z Rot x Rot y Rot z vectorof3angles 3angleswhichdescribetheorientationofpose frameAwithrespecttoframeCCAUTION differentdefinitionsexistandareusedindifferentrobotcontrollers rotationmatrix Possiblerepresentationsoforientations matrixwhichcontainsthe3unitvectorsn o aofframeAexpressedinframeC nz nx ny 1 quaternion q0q1q2q3 angleandaxisinCwhichdescriberotationofAinanormalizedform q0 q1 q2 q3 CRA CQA C A C C C A A A Descriptionofapose frameinspace TranslationandOrientation x y z C Rot x Rot y Rot z CxA CyA CzA firsttranslatethenrotate RepresentationofTranslationandRotation 6dimensionalvectorT MatrixQuaternionand3dimensionalvector xyzRot xRot yRot z nxoxaxpxnyoyaypynzozazpz0001 orientation translation orientation orientation translation translation DefinitionoftheOrientationVectorusedbyISRA x y z x z y z orderofrotations rotatearoundrotatedaxes righthandrule positivedirectionofaxis directionofthumb directionoffingers positivedirectionofangle thumb finger axis OtherDefinitionsoftheOrientationVector OtherorderofnotationOtherorderofrotationRotationaroundfixedaxes Euler angles Thedifferentdefinitionsarenotcompatible Theconversionfromeachofthosedefintionstoarotationmatrixorquaternionandviceversaisdifferent Ingeneralitisnotpossibletoperformcalculationswiththe3dimensionalorientationvector Itisonlyusedfortherepresentationininterfaces especiallytheuserinterface asitisverydifficulttohaveanimaginationofthemeaningofarotation matrixoraquaternion Howeverallcalcualtionsinasystemareperformedinternallyeitherinrotationmatrices T matricesorinquaternionsandtranslationalvectors CommonRobotInterfacesandDefinitions FANUCRepresentationoforientations rotationaroundfixedaxesorderofrotations x y znotation W Rot x P Rot y R Rot zInterfaceVersion1 commonintheUS 6dimensionalvectorVersion2 commoninEuropeandAsia T matrixABBRepresentationoforientations rotationaroundrotatedaxes asISRA orderofrotations z y x asISRA notation A Rot x B Rot y C Rot zInterfaceVersion1 6dimensionalvectorVersion2 quaternionand3dimensionaltranslationvector WPR Surprizinglythisresultsinthesameanglesasweuse althoughthedefinitionisdifferent canbetreatedasthesame ABC dependsoncontrollerversion CommonRobotInterfacesandDefinitions ctd KUKARepresentationoforientations rotationaroundrotatedaxes asISRA orderofrotations z y x asISRA notation A Rot z B Rot y C Rot x ISRAbackwards Interface6dimensionalvector ABC TransformationofPoints x y z CP CyP CxP CzP C CxP ATC APC CxPpositionofpointPdescribedinframeCAxPpositionofpointPdescribedinframeAAPCdescriptionofframeAinC positionandorientation ATPtransformationfromAtoC AxP TheT matrixwhichdescribesthepositionandorientationofframeAinframeCtransformsthedescriptionofapointinAtoadescriptionofthesamepointinC AxP AzP AyP TransformationofPoints Math usingT matrices Cx CTA Axusingquaternions notusedinISRA systems usethequaternion calculus C C A A TransformationofFrames x y z ByR B x y z C APC ATC BPC BTC ATB APB APBpositionandorientationofframeBdescribedinframeABPCpositionandorientationofframeCdescribedinframeBAPCpositionandorientationofframeCdescribedinframeAATBtransformationfromBtoA TheT matrixwhichdescribesthepositionandorientationofframeBinframeAtransformsthedescriptionofaframedescribedinBtoadescriptionofthesameframeinA TransformationofFrames Math usingT matrices APC ATB BPCusingquaternions notusedinISRA systems usethequaternion calculus A B B C A C AsthenotationsofposesandtransformationsarethesameitisverycommontonamebothTandcallbothtransformations InverseTransformation x y z ByR B x y z C ATC BTC ATB BTC ATB 1 ATC Inversetransformation transformationintheopositedirection InverseTransformation Math ATB ATB 1 BTA ATB ATB 1 ATB 1 ATB 1 notransformation MultipleTransformations x y z ByR B ATE BTD ATB ETC CTD ATC ATC ATB BTD CTD 1 ATC ATE ETC ATC CTD ATB BTD ATB BTD CTD 1 ETC 1 ATE 1 1 2DTransformationasspecialcaseof3D xy000Rot z nxox0pxnyoy0py00100001 orientation onlyrotationaroundz translation noz translation standardcase x yplane 6dimensionalvector T matrix Transformations Examples x y z BR ByR BxR BzR B AxR AxP ATC APC CTB CPB ATB APB RobotVision BasicTrainingCourse Robots Robot Expressions base hand tool gripper load link joint axis Robot FramesandTransformations baseframe worldframe userbaseframe handframe usertoolframe baseoffset tooloffset positionoftoolinworld positionoftoolinuserframe ExampleUserBaseFrame worldframe userbaseframe movethescreeninaframeattachedtothescreenopening Robot PossibilitiestoDrivetheRobot x y z z x y x y z A1 A2 A3 A4 A5 A6 world base tool Commonframestodrivein world base userbase tool jointThejoint frame isnotreallyaframe Inthejointframetherobotdrivesitsaxesseparately joint toolcenterpointTCP RobotMotions TCP startpointofmotion endpointofmotion linearmotionLIN pointtopointmotionPTP linearmotion TheTCPmovesonalinearpathfromthestartingpointtotheendpointpointtopointmotion allaxesaredriveninawaythattheyarriveatthesametimeattheirendlocation ThepathoftheTCPisnotdefined RobotVision BasicTrainingCourse RobotVision 2Dand3D RobotVision from2Dto3D 2DfindanobjectinaplaneORIS21 2DfindanobjectinaplaneanddetermineORISthedistancetotheobject3DmonocularfindanobjectinspacewithonecameraCAPMESperview3DstereofindanobjectinspacewithtwoVIAMEScamerasperview3Dselectived o f sfindandobjectinspacebutdetermineVIAMESonlypartofthed o f s Examples2D depaletizingofcylinderheads 21 2D findthelayerinwhichthecylinderheadislocatedandfindthepositionandorientationinthelayerORIS takeboxesfromaconveyor 2Dmovingline findtheboxontheconveyorwithrespecttoamovingframeattachedtotheconveyorORIS Examples3D locatecarbodyinspraypaintingline 3DmonocularfixedcamerasCAPMES locatebodypartsinarackforunloading 3Dstereomovingcamerasonrobotrestrictedd o f sVIAMES RobotVision BasicTrainingCourse Calibration PurposeofCamera Calibration Purpose Determinationofcamerapositioninspacex y z Determinationofcameraparameterspicturesize lenseinfluencesDeterminationofcommoncoordinatesforrobotandvisionMethod MeasurementofknownpointsinspacebythecamerasCalculationofparameters CoordinateFrames robot cabin carbody robot robotpath poi