  To sidestep the curse of dimensionality when computing solutions to
Hamilton-Jacobi-Bellman partial differential equations (HJB PDE), we propose an
algorithm that leverages a neural network to approximate the value function. We
show that our final approximation of the value function generates near optimal
controls which are guaranteed to successfully drive the system to a target
state. Our framework is not dependent on state space discretization, leading to
a significant reduction in computation time and space complexity in comparison
with dynamic programming-based approaches. Using this grid-free approach also
enables us to plan over longer time horizons with relatively little additional
computation overhead. Unlike many previous neural network HJB PDE approximating
formulations, our approximation is strictly conservative and hence any
trajectories we generate will be strictly feasible. For demonstration, we
specialize our new general framework to the Dubins car model and discuss how
the framework can be applied to other models with higher-dimensional state
spaces.

Machine Learning