  The paper introduces DiSProD, an online planner developed for environments
with probabilistic transitions in continuous state and action spaces. DiSProD
builds a symbolic graph that captures the distribution of future trajectories,
conditioned on a given policy, using independence assumptions and approximate
propagation of distributions. The symbolic graph provides a differentiable
representation of the policy's value, enabling efficient gradient-based
optimization for long-horizon search. The propagation of approximate
distributions can be seen as an aggregation of many trajectories, making it
well-suited for dealing with sparse rewards and stochastic environments. An
extensive experimental evaluation compares DiSProD to state-of-the-art planners
in discrete-time planning and real-time control of robotic systems. The
proposed method improves over existing planners in handling stochastic
environments, sensitivity to search depth, sparsity of rewards, and large
action spaces. Additional real-world experiments demonstrate that DiSProD can
control ground vehicles and surface vessels to successfully navigate around
obstacles.
