  Safe path planning is a crucial component in autonomous robotics. The many
approaches to find a collision free path can be categorically divided into
trajectory optimisers and sampling-based methods. When planning using occupancy
maps, the sampling-based approach is the prevalent method. The main drawback of
such techniques is that the reasoning about the expected cost of a plan is
limited to the search heuristic used by each method. We introduce a novel
planning method based on trajectory optimisation to plan safe and efficient
paths in continuous occupancy maps. We extend the expressiveness of the
state-of-the-art functional gradient optimisation methods by devising a
stochastic gradient update rule to optimise a path represented as a Gaussian
process. This approach avoids the need to commit to a specific resolution of
the path representation, whether spatial or parametric. We utilise a continuous
occupancy map representation in order to define our optimisation objective,
which enables fast computation of occupancy gradients. We show that this
approach is essential in order to ensure convergence to the optimal path, and
present results and comparisons to other planning methods in both simulation
and with real laser data. The experiments demonstrate the benefits of using
this technique when planning for safe and efficient paths in continuous
occupancy maps.
