Note on Signature of Trident Mechanisms with Distribution Growth Vector (4,7)
We recall some basic concepts of differential geometry and control theory and their application in robotics, namely we describe so called generalized trident snake robot with four control parameters. Indeed, we are working with a model that combines a robotic snake and Doubin car. We determine the controlling distribution and describe its properties. Consequently, we determine the signature corresponding to the mechanisms with four controlling parameters. This is essential for analysis of the underlying algebraic structure and allows us to choose suitable control model.
KeywordsNon-holonomic system Trident robot Differential geometry Signature
This research was supported by a grant of the Czech Science Foundation no. 17-21360S, “Advances in Snake-like Robot Control” and by a Grant No. FSI-S-17-4464.
- 1.Agracev, A., Barilari, D., Boscain, U.: Introduction to Riemannian and sub-Riemannian geometry. Preprint SISSA (2016)Google Scholar
- 8.Ishikawa, M.: Trident snake robot: locomotion analysis and control. In: NOL-COS, IFAC Symposium on Nonlinear Control Systems, vol. 6 (2004)Google Scholar
- 10.Montgomery, R.: A Tour of Subriemannian Geometries, Their Geodesics and Applications. Mathematical Surveys and Monographs, p. 259. AMS, Providence (2002)Google Scholar
- 11.Murray, R.M., Zexiang, L., Sastry, S.S.: A Mathematical Introduction to Robotic Manipulation. CRC Press, Boca Raton (1994)Google Scholar