The Distance Geometry of the Generalized Lobster’s Arm

Conference Article


International Symposium on Advances in Robot Kinematics (ARK)





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This paper proposes a distance-based formulation to solve the inverse kinematics of what is known as the generalized Lobster's arm: a 6R serial chain in which all consecutive revolute axes intersect. Since the solution of the inverse kinematics of a general 6R serial chain comes down to finding the roots of a 16th-degree polynomial, one might think that this polynomial also contains the solutions to the inverse kinematics of 6R serial chains with special geometric parameters as a mere particular case. Nevertheless, under certain geometric circumstances various problems can appear. Some are of numerical nature, but others are fundamental problems of the used method. For that reason, it is still useful to study 6R chains with special geometric parameters, especially when the new formulation leads to a simpler solution, gives new insights, and provides new connections with other problems, as is the case in this paper.



Author keywords

6R serial kinematic chains, inverse kinematics, distance geometry

Scientific reference

F. Thomas and J.M. Porta. The Distance Geometry of the Generalized Lobster’s Arm, 18th International Symposium on Advances in Robot Kinematics, 2022, Bilbao, Vol 24 of Springer Proceedings in Advanced Robotics, pp. 409-417, Springer.