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).

翻译：因子化非线性规划（Factored-NLP）显式建模了一组连续变量与非线性约束之间的依赖关系，为机器人操作规划、同步定位与地图构建等相关机器人学问题提供了具有表达力的数学形式。当问题过度约束或不可行时，关键难题是检测导致不可行的最小变量子集与约束子集。现有方法需多次求解非线性规划，通过逐步增删约束进行求解，因此计算代价高昂。本文提出一种图神经网络架构，用于预测哪些变量和约束存在联合不可行性。该模型基于带有标签的因子化非线性规划子图数据集进行训练，重要的是，它能对训练过程中未见过的更大规模的因子化非线性规划做出有效预测。我们在机器人操作规划任务中评估该方法，模型能够泛化至涉及更多物体、机器人的更长操作序列及不同几何环境。实验表明，该学习模型可将通用的冲突提取算法加速50倍，将利用专家知识的启发式算法加速4倍。