A discrete-time stochastic model for the motion of a robotic manipulator system is introduced. The input vector consists of the voltages to the joint motors, and the output vector has the velocities (positions) of the gripper expressed in the world (xyz) coordinate system as the components. The model is a linear multivariate autoregressive model with external input. The unknown parameters of the model can be calculated recursively on-line by the least squares algorithm. An adaptive self-tuning type controller is then designed by minimizing the expected value of a quadratic criterion. This performance index penalizes the deviations of the actual path of the gripper from the desired values expressed in the Cartesian coordinate system and the use of the energy associated with the input vector. Digital simulation results using the parameter estimation and the control algorithms are presented, and discussed.

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