Chance-Constrained Trajectory Planning with Multimodal Environmental Uncertainty
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866916647969751040 |
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| author | Ren, Kai Ahn, Heejin Kamgarpour, Maryam |
| author_facet | Ren, Kai Ahn, Heejin Kamgarpour, Maryam |
| contents | We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles' uncertain states. Then, we develop a mixed-integer conic approximation to the chance-constrained trajectory planning problem with deterministic linear systems and polyhedral obstacles. When the GMM moments are estimated via finite samples, we develop a tight concentration bound to ensure the chance constraint with a desired confidence. Moreover, to limit the amount of constraint violation, we develop a Conditional Value-at-Risk (CVaR) approach corresponding to the chance constraints and derive a tractable approximation for known and estimated GMM moments. We verify our methods with state-of-the-art trajectory prediction algorithms and autonomous driving datasets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06779 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chance-Constrained Trajectory Planning with Multimodal Environmental Uncertainty Ren, Kai Ahn, Heejin Kamgarpour, Maryam Robotics Systems and Control We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles' uncertain states. Then, we develop a mixed-integer conic approximation to the chance-constrained trajectory planning problem with deterministic linear systems and polyhedral obstacles. When the GMM moments are estimated via finite samples, we develop a tight concentration bound to ensure the chance constraint with a desired confidence. Moreover, to limit the amount of constraint violation, we develop a Conditional Value-at-Risk (CVaR) approach corresponding to the chance constraints and derive a tractable approximation for known and estimated GMM moments. We verify our methods with state-of-the-art trajectory prediction algorithms and autonomous driving datasets. |
| title | Chance-Constrained Trajectory Planning with Multimodal Environmental Uncertainty |
| topic | Robotics Systems and Control |
| url | https://arxiv.org/abs/2503.06779 |