iA*: Imperative Learning-Based A* Search for Path Planning

Path planning, which aims to find a collision-free path between two locations, is critical for numerous applications ranging from mobile robots to self-driving vehicles. Traditional search-based methods like A* search guarantee path optimality but are often computationally expensive when handling largescale maps. While learning-based methods alleviate this issue by incorporating learned constraints into their search procedures, they often face challenges like overfitting and reliance on extensive labeled datasets. To address these limitations, we propose Imperative A* (iA*), a novel self-supervised path planning framework leveraging bilevel optimization (BLO) and imperative learning (IL). The iA* framework integrates a neural network that predicts node costs with a differentiable A* search mechanism, enabling efficient self-supervised training via bilevel optimization. This integration significantly enhances the balance between search efficiency and path optimality while improving generalization to previously unseen maps. Extensive experiments demonstrate that iA* outperforms both classical and supervised learning-based methods, achieving an average reduction of 65.7% in search area and 54.4% in runtime, underscoring its effectiveness in robot path planning tasks.