  We present a learning-enabled Task and Motion Planning (TAMP) algorithm for
solving mobile manipulation problems in environments with many articulated and
movable obstacles. Our idea is to bias the search procedure of a traditional
TAMP planner with a learned plan feasibility predictor. The core of our
algorithm is PIGINet, a novel Transformer-based learning method that takes in a
task plan, the goal, and the initial state, and predicts the probability of
finding motion trajectories associated with the task plan. We integrate PIGINet
within a TAMP planner that generates a diverse set of high-level task plans,
sorts them by their predicted likelihood of feasibility, and refines them in
that order. We evaluate the runtime of our TAMP algorithm on seven families of
kitchen rearrangement problems, comparing its performance to that of
non-learning baselines. Our experiments show that PIGINet substantially
improves planning efficiency, cutting down runtime by 80% on problems with
small state spaces and 10%-50% on larger ones, after being trained on only
150-600 problems. Finally, it also achieves zero-shot generalization to
problems with unseen object categories thanks to its visual encoding of
objects. Project page https://piginet.github.io/.
