Backpropagation through links: a new approach to kinematic control of serial manipulators

We present a new approach to neural control of serial manipulators, based on the sequential nature of the forward kinematics equations. A neural network is trained to compute the angle between two adjacent links, using the location error of the connecting joint as an input. This angle is then used to derive the location of the next joint, according to a single link kinematic equation. The procedure is repeated until all the links angles are computed. When embedded in a closed loop controller, this algorithm provides smooth operation of a serial manipulator with any number of links. The neural network is trained by backpropagating the end-effector location error through the links equations, in a similar way to backpropagation through time. The training procedure does not involve known solutions of the inverse kinematics problem. Moreover, no retraining of the network is required when adding or removing links. Several examples demonstrate the manipulator performance for three, four and six link robot arms.