Parameter Identification and Nonparametric Calibration of the Tri-Pyramid Robot

Shuheng Liao, Qiang Zeng, Kornel F. Ehmann, Jian Cao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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.

Original languageEnglish (US)
Article number9112686
Pages (from-to)2309-2317
Number of pages9
JournalIEEE/ASME Transactions on Mechatronics
Issue number5
StatePublished - Oct 2020


  • Geometry-based kinematics
  • Tri-pyramid Robot
  • neural network
  • nongeometric error
  • robot calibration

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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