  Robotic manipulators are essential for future autonomous systems, yet limited
trust in their autonomy has confined them to rigid, task-specific systems. The
intricate configuration space of manipulators, coupled with the challenges of
obstacle avoidance and constraint satisfaction, often makes motion planning the
bottleneck for achieving reliable and adaptable autonomy. Recently, a class of
constant-time motion planners (CTMP) was introduced. These planners employ a
preprocessing phase to compute data structures that enable online planning
provably guarantee the ability to generate motion plans, potentially
sub-optimal, within a user defined time bound. This framework has been
demonstrated to be effective in a number of time-critical tasks. However,
robotic systems often have more time allotted for planning than the online
portion of CTMP requires, time that can be used to improve the solution. To
this end, we propose an anytime refinement approach that works in combination
with CTMP algorithms. Our proposed framework, as it operates as a constant time
algorithm, rapidly generates an initial solution within a user-defined time
threshold. Furthermore, functioning as an anytime algorithm, it iteratively
refines the solution's quality within the allocated time budget. This enables
our approach to strike a balance between guaranteed fast plan generation and
the pursuit of optimization over time. We support our approach by elucidating
its analytical properties, showing the convergence of the anytime component
towards optimal solutions. Additionally, we provide empirical validation
through simulation and real-world demonstrations on a 6 degree-of-freedom robot
manipulator, applied to an assembly domain.
