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

TL;DR

The paper tackles the efficiency and generalization limits of traditional A* and supervised learning-based path planning. It proposes Imperative A* (iA*), a self-supervised bilevel framework that couples a neural cost predictor with a differentiable A* search, enabling end-to-end gradient-based training without labeled paths. By formulating a three-component BLO framework (upper-level encoder, differentiable lower-level search, and memory bridge) and using a self-supervised loss derived from actual lower-level outcomes, iA* achieves a better balance between search area and path length while improving generalization. Experimental results across MP, Maze, Matterport3D, and simulated environments demonstrate substantial reductions in search area and runtime and improved robustness to unseen maps, highlighting iA*’s practical impact for robot navigation.

Abstract

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 large-scale 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.

Figures (6)

• Figure 1: The comparison of the searched area of search-based path planning methods. (a), (b), and (c) display the planning results by using A*, Neural A*, and iA* (ours), where the red and green circles represent the start node and goal node, while the red pixels and green pixels represent the generated path and search area.
• Figure 2: The framework of iA* consists of three main components: (1) an upper-level optimization module featuring an instance encoder that processes the map, start, and goal, (2) a lower-level optimization module that integrates a differentiable A* search for node selection and expansion, and (3) a memory storage module that maintains intermediate representations, $H$, $G$, and $F$ to facilitate interaction between the upper and lower level optimizations.
• Figure 3: The calculation of the path length. $\mu$ is the Path Matrix generated from the lower-level optimization, $A * K$ represents the convolution operation between matrix $A$ and kernel $K$, and $D$ is the distance matrix for further path length calculation.
• Figure 4: Selected planning results of different search-based path planning methods in the three datasets, MP dataset (the first two rows), Maze dataset (the middle two rows), and Matterport3D dataset (the last two rows). $\boldsymbol{\mathcal{S},\mathcal{G}}$ indicate the start and goal positions in the given map, respectively. The red pixels indicate the generated path and the green pixels indicate the searched area.
• Figure 5: The trajectories of a mobile robot under given navigation tasks in the simulation environments, Tunnel (the first row) and Indoor (the second row). (a) represents the given instances, start (red circle), and goal (green circle). (b), (c) and (d) represent the trajectories of a mobile robot navigating from start to goal in the simulation environments with Classical A*, Neural A*, and iA*.