Learning Feasibility of Factored Nonlinear Programs in Robotic Manipulation Planning

TL;DR

This paper introduces a graph neural network approach to efficiently identify infeasible variables and constraints in factored nonlinear programs, significantly speeding up robotic manipulation planning tasks.

Contribution

The authors develop a graph neural architecture that predicts infeasibility in Factored-NLPs, enabling faster conflict detection in robotic manipulation planning.

Findings

Model predicts infeasible subgraphs in larger Factored-NLPs than training data

Accelerates conflict extraction algorithms by a factor of 50

Improves heuristic algorithms' speed by a factor of 4

Abstract

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).