Stochastic Motion Planning as Gaussian Variational Inference: Theory and Algorithms
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866913908238843904 |
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| author | Yu, Hongzhe Chen, Yongxin |
| author_facet | Yu, Hongzhe Chen, Yongxin |
| contents | We present a novel formulation for motion planning under uncertainties based on variational inference where the optimal motion plan is modeled as a posterior distribution. We propose a Gaussian variational inference-based framework, termed Gaussian Variational Inference Motion Planning (GVI-MP), to approximate this posterior by a Gaussian distribution over the trajectories. We show that the GVI-MP framework is dual to a special class of stochastic control problems and brings robustness into the decision-making in motion planning. We develop two algorithms to numerically solve this variational inference and the equivalent control formulations for motion planning. The first algorithm uses a natural gradient paradigm to iteratively update a Gaussian proposal distribution on the sparse motion planning factor graph. We propose a second algorithm, the Proximal Covariance Steering Motion Planner (PCS-MP), to solve the same inference problem in its stochastic control form with an additional terminal constraint. We leverage a proximal gradient paradigm where, at each iteration, we quadratically approximate nonlinear state costs and solve a linear covariance steering problem in closed form. The efficacy of the proposed algorithms is demonstrated through extensive experiments on various robot models. An implementation is provided in https://github.com/hzyu17/VIMP. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_14985 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stochastic Motion Planning as Gaussian Variational Inference: Theory and Algorithms Yu, Hongzhe Chen, Yongxin Robotics We present a novel formulation for motion planning under uncertainties based on variational inference where the optimal motion plan is modeled as a posterior distribution. We propose a Gaussian variational inference-based framework, termed Gaussian Variational Inference Motion Planning (GVI-MP), to approximate this posterior by a Gaussian distribution over the trajectories. We show that the GVI-MP framework is dual to a special class of stochastic control problems and brings robustness into the decision-making in motion planning. We develop two algorithms to numerically solve this variational inference and the equivalent control formulations for motion planning. The first algorithm uses a natural gradient paradigm to iteratively update a Gaussian proposal distribution on the sparse motion planning factor graph. We propose a second algorithm, the Proximal Covariance Steering Motion Planner (PCS-MP), to solve the same inference problem in its stochastic control form with an additional terminal constraint. We leverage a proximal gradient paradigm where, at each iteration, we quadratically approximate nonlinear state costs and solve a linear covariance steering problem in closed form. The efficacy of the proposed algorithms is demonstrated through extensive experiments on various robot models. An implementation is provided in https://github.com/hzyu17/VIMP. |
| title | Stochastic Motion Planning as Gaussian Variational Inference: Theory and Algorithms |
| topic | Robotics |
| url | https://arxiv.org/abs/2308.14985 |