  Robotic manipulator applications often require efficient online motion
planning. When completing multiple tasks, sequence order and choice of goal
configuration can have a drastic impact on planning performance. This is well
known as the robot task sequencing problem (RTSP). Existing general purpose
RTSP algorithms are susceptible to producing poor quality solutions or fail
entirely when available computation time is restricted. We propose a new
multi-query task sequencing method designed to operate in semi-structured
environments with a combination of static and non-static obstacles. Our method
intentionally trades off workspace generality for planning efficiency. Given a
user-defined task space with static obstacles, we compute a subspace
decomposition. The key idea is to establish approximate isometries known as
$\epsilon$-Gromov-Hausdorff approximations that identify points that are close
to one another in both task and configuration space. Importantly, we prove
bounded suboptimality guarantees on the lengths of trajectories within these
subspaces. These bounding relations further imply that trajectories within the
same subspace can be smoothly concatenated which we show is useful for
determining efficient task sequences. We evaluate our method with several
kinematic configurations in a complex simulated environment, achieving up to 3x
faster motion planning and 5x lower maximum trajectory jerk compared to
baselines.
