Searcharxiv⌕ 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

IMLE-VLA: Fast Single-Step Action Generation for Vision-Language-Action Policies

Vision-language-action (VLA) policies leverage pretrained vision-language backbones to achieve strong cross-task generalization. A leading design couples this backbone with a dedicated continuous action head trained via diffusion or flow matching. However, such heads rely on iterative multi-step sampling, for example 10 Euler steps in $\pi_{0.5}$. This creates an inference bottleneck that produces stop-and-go movement in the robot and slower task completion. We introduce IMLE-VLA, which replaces the iterative action head with a single-step conditional generator trained via conditional Implicit Maximum Likelihood Estimation (cIMLE). The cIMLE objective promotes multimodal action coverage, avoiding the mode collapse of naive regression heads while eliminating multi-step sampling entirely. When IMLE-VLA is applied to $\pi_{0.5}$, it increases inference frequency 3.67x (55 Hz vs. 15 Hz), enabling up to 11x higher action throughput. On the 40-task LIBERO benchmark, IMLE-VLA achieves the highest average success rate (98.0%) among all baselines while leading in inference frequency. Under the test-time perturbations of LIBERO-plus, IMLE-VLA retains $\pi_{0.5}$'s robustness while other baselines degrade sharply, confirming that the cIMLE head preserves generalization. Real-world experiments on a Franka Emika Panda across four tasks demonstrate smoother motion (2.2x to 3.0x lower jerk) and faster task completion, with IMLE-VLA outperforming $\pi_{0.5}$ on every task and reducing average VLA inference time per episode by 3.9x to 6.6x. Videos and code are available at https://kianhk6.github.io/IMLE-VLA/

cs.RO↗
arXiv2026

ObstaDiff: Generalizable Diffusion Policy Learning via Obstacle-aware Representations

Imitation learning has achieved impressive results in robotic manipulation, yet most existing approaches assume clean backgrounds and lack explicit mechanisms for obstacle-aware motion generation. Extending such policies to cluttered, real-world scenes with unstructured obstacles remains a key generalization challenge. We present ObstaDiff, a decomposed diffusion-policy framework with a lightweight obstacle-aware visual encoder. ObstaDiff extracts a structured target-obstacle-background representation, enabling the downstream alignment policy to generate end-effector trajectories toward a target-centered bottleneck pose while reasoning about surrounding obstacles. We evaluate ObstaDiff on 61 real-robot greenhouse trials per method (366 executions in total). ObstaDiff achieves 75.41% average task success and 8.20% average obstacle collision rate, outperforming representative imitation-learning baselines and improving generalization in cluttered agricultural scenes.

cs.RO↗
arXiv2026

Testing Between the Test Cases: Proving End-to-End Steering in Conditions You Never Drove

AI-based automated vehicle testing is challenging because a model that passes every test condition can still fail in the real world. Formal verification offers a way to directly address this gap. On a simulated highway and an arterial road we trained two small end-to-end steering networks each in CARLA, one on clear conditions alone and one on clear, fog, night and low sun. All four models were driven against a 2.19 ft lane-departure budget. Without driving again, we used bound propagation, a formal method that reads the trained weights, to compute how far steering can drift at every disturbance strength between two captured images. One calculation covers more than a campaign could drive: on the arterial it spans 133 poses, where ten intensities each would be 10^133 combinations, in minutes on one GPU. Not only did formal verification find conditions that broke the clear-trained policy without simulation testing, it provided some preliminary evidence for potential failures between the test cases. Our overall conclusion is that formal verification is a viable complement to simulation, and could be adopted as a part of verification and validation for automated driving.

cs.RO↗