  We present a planning and control framework for physics-based manipulation
under uncertainty. The key idea is to interleave robust open-loop execution
with closed-loop control. We derive robustness metrics through contraction
theory. We use these metrics to plan trajectories that are robust to both state
uncertainty and model inaccuracies. However, fully robust trajectories are
extremely difficult to find or may not exist for many multi-contact
manipulation problems. We separate a trajectory into robust and non-robust
segments through a minimum cost path search on a robustness graph. Robust
segments are executed open-loop and non-robust segments are executed with
model-predictive control. We conduct experiments on a real robotic system for
reaching in clutter. Our results suggest that the open and closed-loop approach
results in up to 35% more real-world success compared to open-loop baselines
and a 40% reduction in execution time compared to model-predictive control. We
show for the first time that partially open-loop manipulation plans generated
with our approach reach similar success rates to model-predictive control,
while achieving a more fluent/real-time execution. A video showing real-robot
executions can be found at https://youtu.be/rPOPCwHfV4g.
