From $O(n)$ to $O(1)$: a Novel Learning-Based Approach for Path Planning

Path and motion planning are crucial steps in many practical applications. In this paper, we propose a novel learningbased paradigm to address this challenge. We model path planning as a sequence-to-sequence problem and design an encoderdecoder framework to learn and generate critical vertices along optimal paths. Specifically, we employ ResNet as the encoder and explore both LSTM and Transformer architectures as decoders. Our models achieve constant time complexity <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$O(1)$</tex> for predicting individual vertices, and linear time complexity for generating the entire path-an order of magnitude faster than existing solutions. This approach has the potential to bring groundbreaking improvements to the speed and efficiency of path planning across a wide range of practical applications.