Trajectory Optimization Under Stochastic Dynamics Leveraging Maximum Mean Discrepancy
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912477872128000 |
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| author | Sharma, Basant Singh, Arun Kumar |
| author_facet | Sharma, Basant Singh, Arun Kumar |
| contents | This paper addresses sampling-based trajectory optimization for risk-aware navigation under stochastic dynamics. Typically such approaches operate by computing $\tilde{N}$ perturbed rollouts around the nominal dynamics to estimate the collision risk associated with a sequence of control commands. We consider a setting where it is expensive to estimate risk using perturbed rollouts, for example, due to expensive collision-checks. We put forward two key contributions. First, we develop an algorithm that distills the statistical information from a larger set of rollouts to a reduced-set with sample size $N<<\tilde{N}$. Consequently, we estimate collision risk using just $N$ rollouts instead of $\tilde{N}$. Second, we formulate a novel surrogate for the collision risk that can leverage the distilled statistical information contained in the reduced-set. We formalize both algorithmic contributions using distribution embedding in Reproducing Kernel Hilbert Space (RKHS) and Maximum Mean Discrepancy (MMD). We perform extensive benchmarking to demonstrate that our MMD-based approach leads to safer trajectories at low sample regime than existing baselines using Conditional Value-at Risk (CVaR) based collision risk estimate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19045 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Trajectory Optimization Under Stochastic Dynamics Leveraging Maximum Mean Discrepancy Sharma, Basant Singh, Arun Kumar Robotics This paper addresses sampling-based trajectory optimization for risk-aware navigation under stochastic dynamics. Typically such approaches operate by computing $\tilde{N}$ perturbed rollouts around the nominal dynamics to estimate the collision risk associated with a sequence of control commands. We consider a setting where it is expensive to estimate risk using perturbed rollouts, for example, due to expensive collision-checks. We put forward two key contributions. First, we develop an algorithm that distills the statistical information from a larger set of rollouts to a reduced-set with sample size $N<<\tilde{N}$. Consequently, we estimate collision risk using just $N$ rollouts instead of $\tilde{N}$. Second, we formulate a novel surrogate for the collision risk that can leverage the distilled statistical information contained in the reduced-set. We formalize both algorithmic contributions using distribution embedding in Reproducing Kernel Hilbert Space (RKHS) and Maximum Mean Discrepancy (MMD). We perform extensive benchmarking to demonstrate that our MMD-based approach leads to safer trajectories at low sample regime than existing baselines using Conditional Value-at Risk (CVaR) based collision risk estimate. |
| title | Trajectory Optimization Under Stochastic Dynamics Leveraging Maximum Mean Discrepancy |
| topic | Robotics |
| url | https://arxiv.org/abs/2501.19045 |