  We present the Learning for KinoDynamic Tree Expansion (L4KDE) method for
kinodynamic planning. Tree-based planning approaches, such as rapidly exploring
random tree (RRT), are the dominant approach to finding globally optimal plans
in continuous state-space motion planning. Central to these approaches is
tree-expansion, the procedure in which new nodes are added into an
ever-expanding tree. We study the kinodynamic variants of tree-based planning,
where we have known system dynamics and kinematic constraints. In the interest
of quickly selecting nodes to connect newly sampled coordinates, existing
methods typically cannot optimise to find nodes that have low cost to
transition to sampled coordinates. Instead, they use metrics like Euclidean
distance between coordinates as a heuristic for selecting candidate nodes to
connect to the search tree. We propose L4KDE to address this issue. L4KDE uses
a neural network to predict transition costs between queried states, which can
be efficiently computed in batch, providing much higher quality estimates of
transition cost compared to commonly used heuristics while maintaining
almost-surely asymptotic optimality guarantee. We empirically demonstrate the
significant performance improvement provided by L4KDE on a variety of
challenging system dynamics, with the ability to generalise across different
instances of the same model class, and in conjunction with a suite of modern
tree-based motion planners.
