Static calibration and dynamic compensation of the SCORBOT robot using sensor fusion and LSTM networks

ABSTRACTThis paper presents both static calibration and dynamics compensation to reduce the positioning errors of the SCORBOT robot. First, a sensor fusion scheme is proposed to estimate the position and attitude of the end-effector of a robot instead of using laser trackers or coordinate measuring machines. The scheme integrates an extended Kalman filter (EKF) with the models of an inertial measurement unit (IMU) and a depth camera. Second, a static calibration scheme is presented to reduce the mechanism errors of robots. The scheme modifies the Denavit-Hartenberg (D-H) parameters provided by the manufacturer based on the least squares method. Third, a dynamic compensation scheme is proposed to reduce the errors caused by robot motions. The scheme establishes a long short-term memory (LSTM) network to compensate the joint angles, where the robot dynamics is integrated into the scheme. Finally, both simulations and experiments are performed to validate the proposed schemes.CO EDITOR-IN-CHIEF: Kuo, Cheng-ChienASSOCIATE EDITOR: Su, Shun-FengKEYWORDS: Static calibrationdynamic compensationsensor fusionLSTM network Nomenclature iAj=transformation matrix form coordinate systems i to jaidiαi=D-H parameters of the ith joint axisariami=actual and measured linear accelerations of the ith joint axisbaibωi=signal biases of linear accelerations and angular velocitiesbfbibcbo=biases of LSTM networkscDHcDH0=of D-H parameters and nominal D-H parameterscisi=cosine and sine functions of rotating angle of the ith joint axisE[]=expected valueFw=matrix and vector in the continuous-time state equationFDK=position vector of the end-effector by direct kinematicsG=gravitational force vectorHv=matrix and vector in the measurement equationJ=objective functionK=Kalman filter gainM=inertia matrixnainωi=signal noises of linear accelerations and angular velocitiesP=covariance matrix of the statesp=position vector of the end-effectorq=generalized coordinatesqi=rotating angle of the ith joint axis.T=generalized force vector.t=discrete timeu, v, w=vectors to describe the orientation of the end-effectorV=Centrifugal and Coriolis force vectorWfWiWcWo=weights of LSTM networksx=state vectorxtht=input and output of LSTM arrays(Xi,Yi,Zi)=ith coordinate systemz=measurementsΔcDH=variations of D-H parameter vectorΔt=sampling timeΦη=matrix and vector in the discrete-time state equationϕθψ=Euler anglesωriωmi=actual and measured angular velocities⋅2=2-normAcknowledgmentsThis work was supported in part by the Ministry of Science and Technology, Taiwan, under Grant MOST 109-2221-E-011-068.Disclosure statementNo potential conflict of interest was reported by the author(s).Additional informationFundingThe work was supported by the Ministry of Science and Technology, Taiwan [MOST 109-2221-E-011-068].