Simplicial Label Correcting Algorithms for continuous stochastic shortest path problems

Dmitry S. Yershov, Steven M. LaValle
2013 2013 IEEE International Conference on Robotics and Automation  
The problem of optimal feedback planning under prediction uncertainties among static obstacles is considered. A discrete-time stochastic state transition model is defined over a continuous state space. A relation to a "nearby" deterministic model is shown for small time steps; the cost-to-go function of the stochastic model is approximated with that of the deterministic model, and the approximation error is found to be proportional to the time step. This motivates using numerical methods, which
more » ... are vastly available for solving deterministic problems, to approximate the original stochastic problem. We demonstrate this application on a Simplicial Label Correcting Algorithm, which, assuming a piecewise linear discretization, computes the shortestpath plan on the simplicial complex. Additionally, a theoretical error bound between the approximate solution and the exact solution is derived and confirmed in numerical experiments. This paper provides a rigorous analysis as well as algorithmic and implementation details of the proposed model for the stochastic shortest path problem in continuous spaces with obstacles.
doi:10.1109/icra.2013.6631300 dblp:conf/icra/YershovL13 fatcat:gnykmfekibbwlojn23zzpvpsnm