We present an efficient method for certifying non-collision for
piecewise-polynomial motion plans in algebraic reparametrizations of
configuration space. Such motion plans include those generated by popular
randomized methods including RRTs and PRMs, as well as those generated by many
methods in trajectory optimization. Based on Sums-of-Squares optimization, our
method provides exact, rigorous certificates of non-collision; it can never
falsely claim that a motion plan containing collisions is collision-free. We
demonstrate that our formulation is practical for real world deployment,
certifying the safety of a twelve degree of freedom motion plan in just over a
second. Moreover, the method is capable of discriminating the safety or lack
thereof of two motion plans which differ by only millimeters.Comment: 7 pages, 5 figures, 1 tabl