Design of Admissible Heuristics for Kinodynamic Motion Planning via   Sum-of-Squares Programming
  How does one obtain an admissible heuristic for a kinodynamic motion planning problem? This paper develops the analytical tools and techniques to answer this question. A sufficient condition for the admissibility of a heuristic is presented which can be checked directly from the problem data. This condition is also used to formulate a concave program to optimize an admissible heuristic. This optimization is then approximated and solved in polynomial time using sum-of-squares programming techniques. A number of examples are provided to demonstrate these concepts. 
Brian Paden and Valerio Varriccho and Emilio Frazzoli
cs.RO