Parameter Identification and Nonparametric Calibration of the Tri-Pyramid Robot

The Tri-pyramid Robot is a 3-degree-of-freedom overconstrained parallel robot designed for the rapid flexible forming of three-dimensional thin sheets without geometry-specific dies used in conventional forming processes. In this article, a combined parametric and nonparametric calibration method for the geometric and nongeometric errors of the Tri-pyramid Robot is presented. The geometry-based inverse and forward kinematic equations are derived. With the actuator values and the relative end-effector positions measured through experiments, the real structural parameters are identified using the nonlinear least-squares method. A neural network is trained to further calibrate the position- and direction-dependent nongeometric errors, such as backlash and link deformations. Combining the end-effector position calculated from the kinematic model and the nongeometric errors predicted with the trained neural network, the end-effector positions can be predicted. The validation experiments show that the accuracy of the robot can be improved by 60% with the proposed method.