Curves on manifolds arise as data in various modern application areas, but there is a dearth of statistical models suited to such data. Manifold-valued data are challenging because manifolds generally lack a vector space structure, so a common strategy is to employ maps back and forth between the manifold and a vector space, and hence exploit models more easily defined on the latter. In this spirit, we exploit "unrolling" and "rolling" maps, based upon ideas introduced by Jupp and Kent (1987), to define a parametric model for random curves on manifolds. The model is generative, amenable to estimation and simulation, and possesses some desirable invariance properties with respect to choice of coordinate frame. We illustrate with an example from robotics, in which curves on SO(3) describe the orientation of the end effector of a robot arm whilst performing a task.
This is joint work with Karthik Bharath, Alfred Kume and Pablo Lopez-Custodio.
Zoom link: https://uoc-gr.zoom.us/j/97374751400?pwd=UjZ4cUVaSXZ2bnZUT1BNSVhySFlDQT09
