A novel solution for $\mathbf{AX}=\mathbf{YB}$ sensor calibration problem using dual Lie algebra

A Comparative Review of Hand-Eye Calibration Techniques for Vision Guided Robots

“…The simultaneous solutions provide a way of solving for the rotation and translation parameters simultaneously, either analytically or by way of numerical optimisation. Representative implementations based on analytical approach include Quaternions [55], Screw motion [56], Dual quaternions [57], Kronecker product [58], Dual Tensor [59], and Dual Lie algebra [60], while implementations based on numerical optimisation include Gradient/Newton optimisation method [61], Linear-matrix-inequality [62], Alternative linear programming [63], and Pseudo-inverse [64]. These methods can generate highly accurate results and generally avoid the problem stated earlier for the separated solutions.…”

A Minimal Parameterization of Rigid Body Displacement and Motion Using a Higher-Order Cayley Map by Dual Quaternions

“…Although classical, studying the motion of rigid solid bodies is still an interesting field in robotics [1][2][3][4][5][6][7][8][9], computer vision [10][11][12], kinematic equations and robot manipulation [13], Cosserat media, molecular dynamics, and astrodynamics . The representation of the integration of the translational component with that of the rotational motion of a rigid motion is possible if we consider the rigid motion not only as a motion of points but also as a motion of directed lines.…”

“…In the past decades, theoretical bases were reevaluated, and a different technique emerged from the theory of the dual algebra realm [2][3][4][5][10][11][12][14][15][16]18,[35][36][37][38][39][40][41][42][43][44]. Numerous applications have utilized dual quaternions, developing multiple algorithms for the kinematic equations associated with robotic manipulators [1][2][3][4][5][6][7][8][9], hand-eye calibration [10][11][12], serial and parallel robotic systems control [13], astrodynamics , etc. [10][11][12][14][15][16]18,39,40,[42][43][44][45][46].…”

Simultaneous Calibration of the Hand-Eye, Flange-Tool and Robot-Robot Relationship in Dual-Robot Collaboration Systems

“…Tan used three calibration methods based on nonlinear optimization and evolutionary computation to calibrate the underactuated robotic hand with soft fingers [13]. Condurache designed the simultaneous closed-form solutions for the sensor calibration problem by using an isomorphism between the special Euclidean group SE(3) and the orthogonal dual tensors group SO (3), which are based on the properties of the orthogonal dual tensors [14]. Wu presented a new error formulation using Cayley transform, which allowed for a unified approach for AX=XB and AX=YB simultaneously [15].…”