Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2505.01589

Phasing Through the Flames: Rapid Motion Planning with the AGHF PDE for Arbitrary Objective Functions and Constraints

Challen Enninful Adu·César E. Ramos Chuquiure·Yutong Zhou·Pearl Lin·Ruikai Yang·Bohao Zhang·Shubham Singh·Ram Vasudevan
View original source ↗Read source document ↗Export metadata ↓

Abstract

The generation of optimal trajectories for high-dimensional robotic systems under constraints remains computationally challenging due to the need to simultaneously satisfy dynamic feasibility, input limits, and task-specific objectives while searching over high-dimensional spaces. Recent approaches using the Affine Geometric Heat Flow (AGHF) Partial Differential Equation (PDE) have demonstrated promising results, generating dynamically feasible trajectories for complex systems like the Digit V3 humanoid within seconds. These methods efficiently solve trajectory optimization problems over a two-dimensional domain by evolving an initial trajectory to minimize control effort. However, these AGHF approaches are limited to a single type of optimal control problem (i.e., minimizing the integral of squared control norms) and typically require initial guesses that satisfy constraints to ensure satisfactory convergence. These limitations restrict the potential utility of the AGHF PDE especially when trying to synthesize trajectories for robotic systems. This paper generalizes the AGHF formulation to accommodate arbitrary cost functions, significantly expanding the classes of trajectories that can be generated. This work also introduces a Phase1 - Phase 2 Algorithm that enables the use of constraint-violating initial guesses while guaranteeing satisfactory convergence. The effectiveness of the proposed method is demonstrated through comparative evaluations against state-of-the-art techniques across various dynamical systems and challenging trajectory generation problems. Project Page: https://roahmlab.github.io/BLAZE/

Explore related subjects

cs.RO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Challen Enninful Adu, César E. Ramos Chuquiure, Yutong Zhou, Pearl Lin, Ruikai Yang, Bohao Zhang, Shubham Singh, Ram Vasudevan. 2025-05-02. Phasing Through the Flames: Rapid Motion Planning with the AGHF PDE for Arbitrary Objective Functions and Constraints. https://arxiv.org/abs/2505.01589

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Physics-Guided Residual Reinforcement Learning for Humanoid Narrow-Path Traversal

Traversing narrow paths is challenging for humanoid robots due to the sparse and safety-critical footholds required. Purely template-based or end-to-end reinforcement learning-based methods suffer from such harsh terrains. This paper proposes a two stage training framework for such narrow path traversing tasks, coupling a template-based foothold planner with a low-level foothold tracker from Stage-I training and a lightweight perception aided foothold modifier from Stage-II training. With the curriculum setup from flat ground to narrow paths across stages, the resulted controller in turn learns to robustly track and safely modify foothold targets to ensure precise foot placement over narrow paths. This framework preserves the interpretability from the physics-based template and takes advantage of the generalization capability from reinforcement learning, resulting in easy sim-to-real transfer. The learned policies outperform purely template-based or reinforcement learning-based baselines in terms of success rate, centerline adherence and safety margins. Validation on a Unitree G1 humanoid robot yields successful traversal of a 0.2m wide and 3m long beam for 20 trials without any failure.

cs.RO↗
arXiv2026

HERMES: A Holistic End-to-End Risk-Aware Multimodal Embodied System with Vision-Language Models for Long-Tail Autonomous Driving

End-to-end autonomous driving models increasingly benefit from large vision-language models for semantic understanding, yet safe and reliable planning under long-tail conditions remains challenging, particularly in mixed-traffic environments involving heterogeneous road users and rare safety-critical interactions. This paper proposes HERMES, a holistic risk-aware end-to-end multimodal driving framework that explicitly incorporates long-tail semantic knowledge into trajectory planning. HERMES employs a foundation-model-assisted annotation pipeline to construct structured Long-Tail Scene Context and Long-Tail Planning Context, capturing hazard-centric scene information, maneuver intent, and risk-aware planning guidance. A Tri-Modal Driving Module then integrates multi-view visual observations, historical ego-motion, and long-tail semantic instructions through intent- and risk-aware conditioning for trajectory generation. Extensive experiments on a large-scale real-world long-tail driving benchmark demonstrate consistent improvements over representative recent baselines in overall planning performance and across diverse safety-critical scenarios. Ablation studies further validate the effectiveness and complementary roles of the major components within HERMES.

cs.RO↗
arXiv2026

StageCraft: Execution Aware Mitigation of Distractor and Obstruction Failures in VLA Models

Large scale pre-training on text and image data along with diverse robot demonstrations has helped Vision Language Action models (VLAs) to generalize to novel tasks, objects and scenes. However, these models are still susceptible to failure in the presence of execution-time impediments such as distractors and physical obstructions in the robot's workspace. Existing policy improvement methods finetune base VLAs to improve generalization, yet they still struggle in unseen distractor settings. To address this problem, we investigate whether internet-scale pretraining of large vision-language models (VLMs) can be leveraged to reason about these impediments and mitigate policy failures. To this end, we propose StageCraft, a training-free approach to improve pretrained VLA policy performance by manipulating the environment's initial state using VLM-based in-context reasoning. StageCraft takes policy rollout videos and success labels as input and leverages VLM's reasoning ability to infer which objects in the initial state need to be manipulated to avoid anticipated execution failures. StageCraft is an extensible plug-and-play module that does not introduce additional constraints on the underlying policy, and only requires a few policy rollouts to work. We evaluate performance of state-of-the-art VLA models with StageCraft and show an absolute 40% performance improvement across three real world task domains involving diverse distractors and obstructions. Our simulation experiments in RLBench empirically show that StageCraft tailors its extent of intervention based on the strength of the underlying policy and improves its performance with more in-context samples. Videos of StageCraft in effect can be found at https://stagecraft-decorator.github.io/stagecraft/ .

cs.RO↗