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

摘要

We are grateful to Chirikjian for his in-depth analysis and insightful comments [1] on our tutorial review [2], which complement nicely our main discussion on how Lie group methods can be effectively used for robot dynamics. There is considerable machinery from the theory of Lie groups and differential geometry that impact robot dynamics, and more generally nonlinear mechanics, and Chirikjian's commentary offers a deeper but still very much readable discussion of Lie group essentials that our review paper did not cover. Chirikjian also provides important context to our review by further pointing out the past literature on robot dynamics that is not based on Lie group methods, e.g., recursive methods for inverse and forward dynamics based on classical Denavit-Hartenberg kinematic representations. Finally, the discussion and additional references pointed out by Chirikjian on Lie group methods for modeling constrained multibody systems, and connections with variational integrators and discrete Lagrangian mechanics, provide fitting closure to our review, by pointing the reader to the latest developments and trends in geometric methods for robot and multibody system dynamics. Hopefully having made the case that there are both important analytical and computational benefits to using Lie group methods for multibody dynamics, we would remark that there is still quite a ways to go in this program to "geometrize" classical mechanics, and plenty of new application domains and open problems.