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Optimization-based planners typically avoid humans through collision avoidance chance constraints. This allows the planner to optimize performance while guaranteeing probabilistic safety. However, existing real-time methods do not consider the actual probability of collision for the planned trajectory but rather its marginalization, that is, the independent collision probabilities for each planning step and\/or dynamic obstacle, resulting in conservative trajectories. To address this issue, we introduce a novel real-time capable method termed Safe Horizon MPC that explicitly constrains the joint probability of collision with all obstacles over the duration of the motion plan. This is achieved by reformulating the chance-constrained planning problem using scenario optimization and predictive control. Out of sampled realizations of human motion, we identify which cases affect the optimization. This allows us to certify the planned trajectory in real-time. Our method is less conservative than state-of-the-art approaches, applicable to arbitrary probability distributions of the obstacles\u2019 trajectories, computationally tractable and scalable. We demonstrate our proposed approach using a mobile robot and an autonomous vehicle in an environment shared with humans.<\/jats:p>","DOI":"10.1177\/02783649251315203","type":"journal-article","created":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T04:06:44Z","timestamp":1739419604000},"page":"1507-1525","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":16,"title":["Scenario-based motion planning with bounded probability of collision"],"prefix":"10.1177","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6527-7367","authenticated-orcid":false,"given":"Oscar","family":"de Groot","sequence":"first","affiliation":[{"name":"Department of Cognitive Robotics, TU Delft, Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Laura","family":"Ferranti","sequence":"additional","affiliation":[{"name":"Department of Cognitive Robotics, TU Delft, Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dariu M.","family":"Gavrila","sequence":"additional","affiliation":[{"name":"Department of Cognitive Robotics, TU Delft, Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Javier","family":"Alonso-Mora","sequence":"additional","affiliation":[{"name":"Department of Cognitive Robotics, TU Delft, Delft, The Netherlands"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2025,2,13]]},"reference":[{"key":"e_1_3_6_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10514-013-9334-3"},{"key":"e_1_3_6_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00186-019-00691-9"},{"key":"e_1_3_6_4_1","doi-asserted-by":"publisher","DOI":"10.1287\/moor.23.4.769"},{"key":"e_1_3_6_5_1","volume-title":"Wiley Series in Probability and Mathematical Statistics","author":"Billingsley P","year":"1995","unstructured":"Billingsley P (1995) Probability and measure. 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