  A factored Nonlinear Program (Factored-NLP) explicitly models the
dependencies between a set of continuous variables and nonlinear constraints,
providing an expressive formulation for relevant robotics problems such as
manipulation planning or simultaneous localization and mapping. When the
problem is over-constrained or infeasible, a fundamental issue is to detect a
minimal subset of variables and constraints that are infeasible. Previous
approaches require solving several nonlinear programs, incrementally adding and
removing constraints, and are thus computationally expensive. In this paper, we
propose a graph neural architecture that predicts which variables and
constraints are jointly infeasible. The model is trained with a dataset of
labeled subgraphs of Factored-NLPs, and importantly, can make useful
predictions on larger factored nonlinear programs than the ones seen during
training. We evaluate our approach in robotic manipulation planning, where our
model is able to generalize to longer manipulation sequences involving more
objects and robots, and different geometric environments. The experiments show
that the learned model accelerates general algorithms for conflict extraction
(by a factor of 50) and heuristic algorithms that exploit expert knowledge (by
a factor of 4).
