  Planning under process and measurement uncertainties is a challenging
problem. In its most general form it can be modeled as a Partially Observed
Markov Decision Process (POMDP) problem. However POMDPs are generally difficult
to solve when the underlying spaces are continuous, particularly when beliefs
are non-Gaussian, and the difficulty is further exacerbated when there are also
non-convex constraints on states. Existing algorithms to address such
challenging POMDPs are expensive in terms of computation and memory. In this
paper, we provide a feedback policy in non-Gaussian belief space via solving a
convex program for common non-linear observation models. The solution involves
a Receding Horizon Control strategy using particle filters for the non-Gaussian
belief representation. We develop a way of capturing non-convex constraints in
the state space and adapt the optimization to incorporate such constraints, as
well. A key advantage of this method is that it does not introduce additional
variables in the optimization problem and is therefore more scalable than
existing constrained problems in belief space. We demonstrate the performance
of the method on different scenarios.
