Title: Plan-R1: Safe and Feasible Trajectory Planning as Language Modeling
Primary area: applications to robotics, autonomy, planning
Keywords: Trajectory Planning, Reinforcement Learning, Autonomous Driving

Abstract: Safe and feasible trajectory planning is critical for real-world autonomous driving systems.
However, existing learning-based planners rely heavily on expert demonstrations, which not only lack explicit safety awareness but also risk inheriting undesirable behaviors such as speeding from suboptimal human driving data.
Inspired by the success of large language models, we propose Plan-R1, a two-stage trajectory planning framework that decouples principle alignment from behavior learning.
In the first stage, a general trajectory predictor is pre-trained on expert data to capture diverse, human-like driving behaviors.
In the second stage, the model is fine-tuned with rule-based rewards using Group Relative Policy Optimization (GRPO), explicitly aligning ego planning with principles such as safety, comfort, and traffic rule compliance.
This two-stage paradigm retains human-like behaviors while enhancing safety awareness and discarding undesirable patterns from demonstrations.
Furthermore, we identify a key limitation of directly applying GRPO to planning: group-wise normalization erases cross-group scale differences, causing rare, high-variance safety-violation groups to have similar advantages as abundant low-variance safe groups, thereby  suppressing optimization for safety-critical objectives.
To address this, we propose Variance-Decoupled GRPO (VD-GRPO), which replaces normalization with centering and fixed scaling to preserve absolute reward magnitudes, ensuring that safety-critical objectives remain dominant throughout training.
Experiments on the nuPlan benchmark demonstrate that Plan-R1 significantly improves planning safety and feasibility, achieving state-of-the-art performance, particularly in realistic reactive settings.

TL;DR: We propose Plan-R1, a two-stage framework that decouples planning principle alignment from behavior learning to overcome the limitations of expert data. With VD-GRPO to preserve safety-critical signals, Plan-R1 achieves SOTA results on nuPlan.