  Searching for bindings of geometric parameters in task and motion planning
(TAMP) is a finite-horizon stochastic planning problem with high-dimensional
decision spaces. A robot manipulator can only move in a subspace of its whole
range that is subjected to many geometric constraints. A TAMP solver usually
takes many explorations before finding a feasible binding set for each task. It
is favorable to learn those constraints once and then transfer them over
different tasks within the same workspace. We address this problem by
representing constraint knowledge with transferable primitives and using
Bayesian optimization (BO) based on these primitives to guide binding search in
further tasks. Via semantic and geometric backtracking in TAMP, we construct
constraint primitives to encode the geometric constraints respectively in a
reusable form. Then we devise a BO approach to efficiently utilize the
accumulated constraints for guiding node expansion of an MCTS-based binding
planner. We further compose a transfer mechanism to enable free knowledge flow
between TAMP tasks. Results indicate that our approach reduces the expensive
exploration calls in binding search by 43.60to 71.69 when compared to the
baseline unguided planner.
