  Harmonic potentials provide globally convergent potential fields that are
provably free of local minima. Due to its analytical format, it is particularly
suitable for generating safe and reliable robot navigation policies. However,
for complex environments that consist of a large number of overlapping
non-sphere obstacles, the computation of associated transformation functions
can be tedious. This becomes more apparent when: (i) the workspace is initially
unknown and the underlying potential fields are updated constantly as the robot
explores it; (ii) the high-level mission consists of sequential navigation
tasks among numerous regions, requiring the robot to switch between different
potentials. Thus, this work proposes an efficient and automated scheme to
construct harmonic potentials incrementally online as guided by the task
automaton. A novel two-layer harmonic tree (HT) structure is introduced that
facilitates the hybrid combination of oriented search algorithms for task
planning and harmonic-based navigation controllers for non-holonomic robots.
Both layers are adapted efficiently and jointly during online execution to
reflect the actual feasibility and cost of navigation within the updated
workspace. Global safety and convergence are ensured both for the high-level
task plan and the low-level robot trajectory. Known issues such as oscillation
or long-detours for purely potential-based methods and sharp-turns or high
computation complexity for purely search-based methods are prevented. Extensive
numerical simulation and hardware experiments are conducted against several
strong baselines.
