Organizations: Kyoto University, Japan · The University of Tokyo, Japan
Abstract
Convex Collision-Free Regions (CCFR) is a collision handling method that explicitly represents local convex feasible regions to enforce non-penetration. Each feasible region is constructed from surrounding mesh primitive configurations, including edge-edge and vertex-face interactions. The resulting convex region represents admissible non-penetrating vertex displacements at the current configuration. Existing collision handling methods for deformable body simulation have largely relied on implicit representations of feasibility, resulting in either compromised robustness for secondary collisions and codimensional contacts or tight coupling with specific nonlinear optimization schemes. Our formulation constructs feasible regions independently for each vertex, defined prior to penetration, inherently accounts not only for primary collisions but also for secondary collisions and codimensional contacts, enabling highly scalable and parallelizable collision handling. These feasible regions encode geometric non-penetration constraints independently of physical contact response models. CCFR does not rely on nonlinear optimization and is compatible with simulation frameworks such as Extended Position-Based Dynamics (XPBD) that do not explicitly maintain interior feasibility during iterative updates. The effectiveness of CCFR is demonstrated across cloth, hair, wire, particle systems, and codimensional contact scenarios, showing versatile and efficient collision handling.
Generating intelligent robot behavior in contact-rich settings is a research problem where zeroth-order methods currently prevail. Developing methods that make use of first/second order information about rigid-body dynamics in the presence of contact holds great promise in terms of increasing the solution speed and computational efficiency. The main bottleneck in this research direction is the difficulty in obtaining gradients and Hessians that are actually useful for numerical optimization, due to pathologies in all three steps of a common simulation pipeline: i) collision detection, ii) contact dynamics, iii) time integration. This abstract proposes a method that aims to address the collision detection part of the puzzle, via a novel pipeline designed from scratch with smooth (i.e. twice) differentiability and massive vectorizability on GPUs as the main priorities. This is in contrast to standard collision detection routines that are instead optimized for runtime on CPUs and minimal memory footprint, but do employ logic and control flow that hinder differentiability and vectorization. The proposed pipeline consists of the following contributions: i) highly expressive and compute efficient SDF representations, ii) differentiable broad-phase and narrow-phase routines that use these representations to generate vertex-SDF and edge-SDF contacts, iii) a differentiable routine for convex decomposition based contact blending.
Approximating collision-free space is fundamental to robot planning in complex environments. Convex geometric representations, such as polytopes and ellipsoids, are widely employed due to their structural properties, which can be easily integrated with convex optimization. Iterative optimization-based inflation methods can generate large volume polytopes in cluttered environments, but their efficiency degrades as the obstacle set becomes more complex or when sensor data are noisy. These methods are also sensitive to initialization and often rely on accurate geometric models. In this paper, we propose the STAR-Filter, a lightweight framework that employs starshaped set construction as a fast filter for convex region generation in collision-free space. By identifying obstacle points as active supporting constraints, the proposed method significantly reduces redundant computation while preserving feasibility and robustness to sensor noise. We provide theoretical and numerical analyses that characterize the structural properties of the starshaped set and proposed pipeline in environments of varying complexity. Simulation results show that the proposed framework achieves the lowest computation time and reduces conservativeness in polytope generation for real-world noisy and large-scale data. We demonstrate the effectiveness of the framework for Safe Flight Corridor (SFC) generation and agile quadrotor planning in noisy environments.
Convex free regions provide a structured and optimization-friendly representation of collision-free space for robot navigation in unknown and cluttered environments. However, existing methods typically enlarge local collision-free regions mainly according to surrounding obstacle geometry. In cluttered environments, such strategies may fail to generate regions that both accommodate robot geometry and preserve traversable extension along candidate motion directions, thereby limiting downstream traversal, especially in narrow passages. Even when such a region is available, safe motion generation remains challenging, because safety checking at discretized trajectory samples does not guarantee continuously collision-free motion when robot geometry is modeled explicitly. To address these issues, we propose a navigation framework that jointly incorporates candidate motion directions and robot geometry into convex free-region generation, and achieves continuously collision-free motion through continuous-safe trajectory generation. Within each region, the framework performs geometry-aware target pose selection and trajectory generation, together with Lipschitz-based continuous safety certification and local refinement. The resulting free regions and candidate motions are maintained in a region-based graph to support incremental planning. Quantitative results in cluttered 2D navigation scenarios show that the proposed method generates free regions better aligned with downstream traversal and enables reliable collision-free navigation, while additional 3D and real-world experiments on a quadrupedal robot and a UAV demonstrate the extensibility and practical applicability of the framework. The open-source project can be found at https://github.com/ZhichengSong6/FRGraph.