A unified formulation for the calibration of both serial-link robots and robotic mechanisms having kinematic closed-loops is presented and applied experimentally to two 6-degree-of-freedom devices: the RSI 6-DOF hand controller and the MEL "modified Stewart platform". The unification is based on an equivalence between end-effector measurements and constraints imposed by the closure of kinematic loops. Errors are allocated to the joints such that the loop equations are satisfied exactly, which eliminates the issue of equation scaling and simplifies the treatment of multi-loop mechanisms. For the experiments reported here, no external measuring devices are used; instead we rely on measurements of displacements in some of the passive joints of the devices. Using a priori estimates of the statistics of the measurement errors and the parameter errors, the method estimates the parameters and their accuracy, and tests for unmodeled factors.
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