  This paper describes a revision of the classic Lazy Probabilistic Roadmaps
algorithm (Lazy PRM), that results from pairing PRM and a novel Branch-and-Cut
(BC) algorithm. Cuts are dynamically generated constraints that are imposed on
minimum cost paths over the geometric graphs selected by PRM. Cuts eliminate
paths that cannot be mapped into smooth plans that satisfy suitably defined
kinematic constraints. We generate candidate smooth plans by fitting splines to
vertices in minimum-cost path. Plans are validated with a recently proposed
algorithm that maps them into finite traces, without need to choose a fixed
discretization step. Trace elements exactly describe when plans cross
constraint boundaries modulo arithmetic precision. We evaluate several planners
using our methods over the recently proposed BARN benchmark, and we report
evidence of the scalability of our approach.
