Discussion of “Geometric Algorithms for Robot Dynamics: A Tutorial Review” (F. C. Park, B. Kim, C. Jang, and J. Hong, 2018, ASME Appl. Mech. Rev., 70(1), p. 010803)

Abstract

Lie-theoretic methods provide an elegant way to formulate many problems in robotics, and the tutorial by Park et al. (2018, “Geometric Algorithms for Robot Dynamics: A Tutorial Review,” ASME Appl. Mech. Rev., 70(1), p. 010803) is simultaneously a complete and concise introduction to these methods as they pertain to robot dynamics. The central reason why Lie groups are a natural mathematical tool for robotics is that rigid-body motions and pose changes can be described as Lie groups, and allow phenomena including robot kinematics and dynamics to be formulated in elegant notation without introducing superfluous coordinates. The emphasis of the tutorial by Park et al. (2018, “Geometric Algorithms for Robot Dynamics: A Tutorial Review,” ASME Appl. Mech. Rev., 70(1), p. 010803) is robot dynamics from a Lie-theoretic point of view. Newton–Euler and Lagrangian formulation of robot dynamics algorithms with O(n) complexity were formulated more than 35 years ago using recurrence relations that use the serial structure of manipulator arms. This was done without using the knowledge of Lie theory. But issues such as why the ω× terms in rigid-body dynamics appear can be more easily understood in the context of this theory. The authors take great efforts to be understandable by nonexperts and present extensive references to the differential-geometric and Lie-group-centric formulations of manipulator dynamics. In the discussion presented here, connections are made to complementary methods that have been developed in other bodies of literature. This includes the multibody dynamics, geometric mechanics, spacecraft dynamics, and polymer physics literature, as well as robotics works that present non-Lie-theoretic formulations in the context of highly parallelizable algorithms.