Modeling of an external force estimator for an end-effector of a robot by neural networks

ABSTRACTThis paper proposes a method to estimate external forces at the tip of a robot end-effector by using a neural network model. In order to avoid the use of an expensive force sensor in the training purpose, the proposed method implements the indirect training method by including the inverse dynamic model of the robot manipulator to the training algorithm with available information from a default robot system. In this method, the robot dynamics equations are necessary for the training, therefore a disturbance observer is adopted to deal with the existing uncertainties and errors. The performance of the proposed estimation method is evaluated through experiments of a 5-DOF robotic experimental platform, comparing to another existing estimation method using recurrent neural network with a type-1 disturbance observer for the external force estimation. The estimation results show that the behavior of the estimated external forces strongly correlates with the applied external forces and the proposed method is superior to the other method.CO EDITOR-IN-CHIEF: Kuo, Cheng-ChienASSOCIATE EDITOR: Zhang, XuefengKEYWORDS: external force estimationindirect trainingdisturbance observerneural networks (NNs) Nomenclature e=the error between the actual and estimated applied torquesε=the loss functionFextand Fˆext=the actual and estimated external force, respectivelyg=the gradient vector of the loss function with respect to the weighting parametersH=the Hessian matrix of the loss function with respect to the weighting parametersI=the identity matrixJ=the Jacobian matrix of the robot kinematicsk=the epoch indexλ=the positive damping factorM=the robot mass inertia matrixΔM=the modeling errors and parameter uncertainties in the matrix Mn=the number of the degree of freedomni, nh, and no=the number of nodes in the input, hidden, and output layers, respectivelyn=the torque vector contributed by the centrifugal, Coriolis, gravitational, and friction effectsΔn=the modeling errors and parameter uncertainties in the vector nN=the number of datasetsq˙,q,andq¨=the angular displacement, velocity, and acceleration of the robot system, respectivelyτ and τˆ=the actual and estimated applied torques, respectivelyτdand τˆd=the actual and estimated internal disturbances, respectivelyw=the weighting parameters in the NN modelDisclosure statementNo penitential conflict of interest was reported by the authors.Additional informationFundingThis work was supported in part by the Advanced Institute of Manufacturing with High-tech Innovations (AIM-HI) from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan and was also supported in part by the National Science and Technology Council, Taiwan, ROC, under Grants NSTC 111-2218-E-194-005 and NSTC 111-2221-E-194 -039 -MY2.