  Recent work has demonstrated real-time mapping and reconstruction from dense
perception, while motion planning based on distance fields has been shown to
achieve fast, collision-free motion synthesis with good convergence properties.
However, demonstration of a fully integrated system that can safely re-plan in
unknown environments, in the presence of static and dynamic obstacles, has
remained an open challenge. In this work, we first study the impact that signed
and unsigned distance fields have on optimisation convergence, and the
resultant error cost in trajectory optimisation problems in 2D path planning,
arm manipulator motion planning, and whole-body loco-manipulation planning. We
further analyse the performance of three state-of-the-art approaches to
generating distance fields (Voxblox, Fiesta, and GPU-Voxels) for use in
real-time environment reconstruction. Finally, we use our findings to construct
a practical hybrid mapping and motion planning system which uses GPU-Voxels and
GPMP2 to perform receding-horizon whole-body motion planning that can smoothly
avoid moving obstacles in 3D space using live sensor data. Our results are
validated in simulation and on a real-world Toyota Human Support Robot (HSR).
