A minimal kinematic model for serial robot calibration using POE formula

Development of a compact continuum tubular robotic system for nasopharyngeal biopsy

“…(10) can be further approximated by [34,38] where log() logarithmically maps a transformation matrix to its twist matrix.…”

“…Using adjoint transformation, we have where Here, A i is given by [34,38] where By defining combining (13)- (19), and comparing with (12), we have where Based on the Jacobian matrix, the inverse kinematics can be solved through an iterative procedure given an initial estimation and an updating rule. If the Jacobian matrix is full rank, the updating rule can be simply (13) …”

A position independent geometric errors identification and correction method for five-axis serial machines based on screw theory

“…are identified, the actual twists need to be calculated according to their geometric definition [23,24]. For translational axes, the directional vector…”

“…The screw theory allows a global description of rigid body motion, so that there is no need to build local frames on each drive module as required by the HTMs method. Although it has been widely used in the robotics area [23,24], only limited use of screw theory has been reported for five-axis machine tools' geometric errors modeling. Moon et al [25] developed a methodology to predict machining error caused by geometric errors and also presented an approximate error compensation method through the inverse Jacobian matrix based on the screw theory.…”

Positional error similarity analysis for error compensation of industrial robots

“…Hayati [5] added a rotational parameter on the basis of D-H model and proposed modified D-H model, which is widely used in kinematic calibration by later researchers [6][7][8][9][10]. Besides, product of exponentials (POE) formula [11] was also used in the robot kinematic model to perform robot calibration [12,13].…”