  Motion planning under differential constraints, kinodynamic motion planning,
is one of the canonical problems in robotics. Currently, state-of-the-art
methods evolve around kinodynamic variants of popular sampling-based
algorithms, such as Rapidly-exploring Random Trees (RRTs). However, there are
still challenges remaining, for example, how to include complex dynamics while
guaranteeing optimality. If the open-loop dynamics are unstable, exploration by
random sampling in control space becomes inefficient. We describe a new
sampling-based algorithm, called CL-RRT#, which leverages ideas from the RRT#
algorithm and a variant of the RRT algorithm that generates trajectories using
closed-loop prediction. The idea of planning with closed-loop prediction allows
us to handle complex unstable dynamics and avoids the need to find
computationally hard steering procedures. The search technique presented in the
RRT# algorithm allows us to improve the solution quality by searching over
alternative reference trajectories. Numerical simulations using a nonholonomic
system demonstrate the benefits of the proposed approach.
