the role of contact Jacobian in reachability analysis.

[pangtao22]

• Does the (bundled) hand Jacobian largely remain constant during one "stroke" of in-hand manipulation maneuver (which corresponds to one edge in the RRT tree)? It would be interesting to generate some plots along successful trajectories.
• Right now, the forward reachable set is computed by the SVD of 2000 one-step rollouts. Can the number of samples needed to compute the 1-step reachable set be reduced by looking instead at the SVD of the bundled contact Jacobian? Can a more rigorous first vs zero order analysis be made, e.g. first order has less variance so fewer samples are needed?