On The Evaluation of Collision Probability along a Path
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914962058772480 |
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| author | Paiola, Lorenzo Grioli, Giorgio Bicchi, Antonio |
| author_facet | Paiola, Lorenzo Grioli, Giorgio Bicchi, Antonio |
| contents | Characterizing the risk of operations is a fundamental requirement in robotics, and a crucial ingredient of safe planning. The problem is multifaceted, with multiple definitions arising in the vast recent literature fitting different application scenarios and leading to different computational approaches. A basic element shared by most frameworks is the definition and evaluation of the probability of collision for a mobile object in an environment with obstacles. We observe that, even in basic cases, different interpretations are possible. This paper proposes an index we call "Risk Density", which offers a theoretical link between conceptually distant assumptions about the interplay of single collision events along a continuous path. We show how this index can be used to approximate the collision probability in the case where the robot evolves along a nominal continuous curve from random initial conditions. Indeed, under this hypothesis the proposed approximation outperforms some well-established methods either in accuracy or computational cost. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_08204 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On The Evaluation of Collision Probability along a Path Paiola, Lorenzo Grioli, Giorgio Bicchi, Antonio Robotics Characterizing the risk of operations is a fundamental requirement in robotics, and a crucial ingredient of safe planning. The problem is multifaceted, with multiple definitions arising in the vast recent literature fitting different application scenarios and leading to different computational approaches. A basic element shared by most frameworks is the definition and evaluation of the probability of collision for a mobile object in an environment with obstacles. We observe that, even in basic cases, different interpretations are possible. This paper proposes an index we call "Risk Density", which offers a theoretical link between conceptually distant assumptions about the interplay of single collision events along a continuous path. We show how this index can be used to approximate the collision probability in the case where the robot evolves along a nominal continuous curve from random initial conditions. Indeed, under this hypothesis the proposed approximation outperforms some well-established methods either in accuracy or computational cost. |
| title | On The Evaluation of Collision Probability along a Path |
| topic | Robotics |
| url | https://arxiv.org/abs/2311.08204 |