  We propose a novel belief space planning technique for continuous dynamics by
viewing the belief system as a hybrid dynamical system with time-driven
switching. Our approach is based on the perturbation theory of differential
equations and extends Sequential Action Control to stochastic dynamics. The
resulting algorithm, which we name SACBP, does not require discretization of
spaces or time and synthesizes control signals in near real-time. SACBP is an
anytime algorithm that can handle general parametric Bayesian filters under
certain assumptions. We demonstrate the effectiveness of our approach in an
active sensing scenario and a model-based Bayesian reinforcement learning
problem. In these challenging problems, we show that the algorithm
significantly outperforms other existing solution techniques including
approximate dynamic programming and local trajectory optimization.
