Omid Heidari, Hamid Daniali, and Alireza Fathi
Special cases of 6R manipulators, characteristic polynomial, Mutable Smart Bee Algorithm
The inverse kinematics of a general 6R serial manipulator leads to atmost 16 real solutions. Researchers have been searching for special cases of this class of manipulator with a reduced-order characteristic polynomial which cause the manipulator to have less than 16 configurations, for a given end-effector (EE) pose. They have given some special cases of the characteristic polynomial by introducing several special geometries of the manipulator structure. Here, we derive the characteristic polynomial in terms of Denavit–Hartenberg (DH) parameters and the pose of the EE given in the dual Euler-angles form. Then, we search for the special cases of the characteristic polynomial in DH parameters space to uncover the special geometries of the manipulator. To this end, we use a swarm-based optimization algorithm, namely Mutable Smart Bee Algorithm, to vanish the coefficient of the term with highest degree in the characteristic polynomial. Finally, we classify the special cases.
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