{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/probabilistic-occupancy-function-and-sets","title":"Probabilistic Occupancy Function and Sets Using Forward Stochastic Reachability for Rigid-Body Dynamic Obstacles","arxiv_id":"1803.07180","date":"2018-03-19","proceeding":null,"authors":["Abraham P. Vinod","Meeko M. K. Oishi"],"abstract":"We present theory and algorithms for the computation of probability-weighted \"keep-out\" sets to assure probabilistically safe navigation in the presence of multiple rigid body obstacles with stochastic dynamics. Our forward stochastic reachability-based approach characterizes the stochasticity of the future obstacle states in a grid-free and recursion-free manner, using Fourier transforms and computational geometry. We consider discrete-time Markovian switched systems with affine parameter-varying stochastic subsystems (DMSP) as the obstacle dynamics, which includes Markov jump affine systems and discrete-time affine parameter-varying stochastic systems (DPV). We define a probabilistic occupancy function, to describe the probability that a given state is occupied by a rigid body obstacle with stochastic dynamics at a given time; keep-out sets are the super-level sets of this occupancy function. We provide sufficient conditions that ensure convexity and compactness of these keep-out sets for DPV obstacle dynamics. We also propose two computationally efficient algorithms to overapproximate the keep-out sets --- a tight polytopic approximation using projections, and an overapproximation using Minkowski sum. For DMSP obstacle dynamics, we compute a union of convex and compact sets that covers the potentially non-convex keep-out set. Numerical simulations show the efficacy of the proposed algorithms for a modified version of the classical unicycle dynamics, modeled as a DMSP.","url_abs":"https://arxiv.org/abs/1803.07180v2","url_pdf":"https://arxiv.org/pdf/1803.07180v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"probabilistic-occupancy-function-and-sets","repo_url":"https://github.com/unm-hscl/abyvinod-TAC-ProbabilisticOccupancy","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}