Decoupling vector fields

For mechanical systems in which dynamics is considered, the steering problem becomes complicated by drift. One recent approach is based on establishing that a system is kinematically controllable, which means that the system is STLC on the C-space, if traversed using trajectories that start and stop at zero velocity states [157]. The method finds decoupling vector fields on the C-space. Any path that is the integral curve of a decoupling vector field in the C-space is executable by the full system with dynamics. If a mechanical system admits such vector fields, then it was proved in [157] that a steering method for ${\cal C}$ can be lifted into one for $X$, the phase space of the mechanical system. This idea was applied to generate an efficient LPM in an RRT planner in [224].