Efficient Probabilistic Collision Detection for Non-Convex Shapes

Jae Sung Park; Chonhyon Park; Dinesh Manocha

Home/Archive/arXiv

arXiv · 1610.03651

Efficient Probabilistic Collision Detection for Non-Convex Shapes

Jae Sung Park·Chonhyon Park·Dinesh Manocha

View original source ↗Read source document ↗Export metadata ↓

Abstract

We present new algorithms to perform fast probabilistic collision queries between convex as well as non-convex objects. Our approach is applicable to general shapes, where one or more objects are represented using Gaussian probability distributions. We present a fast new algorithm for a pair of convex objects, and extend the approach to non-convex models using hierarchical representations. We highlight the performance of our algorithms with various convex and non-convex shapes on complex synthetic benchmarks and trajectory planning benchmarks for a 7-DOF Fetch robot arm.

Explore related subjects

cs.RO

Keep this discovery

BibTeX RIS

Jae Sung Park, Chonhyon Park, Dinesh Manocha. 2016-10-12. Efficient Probabilistic Collision Detection for Non-Convex Shapes. https://arxiv.org/abs/1610.03651

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↗