(Mechanical systems with complex manifolds.)
Software packages have addressed this inefficiency, and offer automation for the generation of these equations of motion. However, these packages are not designed to work on systems whose dynamics evolve on manifolds, curved surfaces in 3D space. The mathematical framework of the software handles vectors and matrices in pure symbolic form, void of scalar components. Therefor global maneuvers can be handled free of singularity and non-uniqueness issues.
This work is intended to enable a broader study of robotic systems, and to enable novel control design for achieving highly dynamic maneuvers. This tools range and utility has been recently revisited, an updated draft is in the works.
Equations of motions provide the behavior of a mechanical system’s moving parts with respect to time. For a simple mechanical configuration, one can write down the equations via hand computation. For more complex systems, the hand computation intense, laborious and error prone. Automation offers an opportunity for wider exploration of the rich dynamical capabilities of these systems.
Extract Dynamics on Complex Manifolds
How does a cat rotate to land on its feet? How does a satellite rotate in three-dimensional space? How
does a soccer player dribble with finesse through a defense? If the equations of motions for these systems are obtained, these questions can be perfectly answered.