Chance-Constrained Gaussian Mixture Steering to a Terminal Gaussian Distribution

Naoya Kumagai; Kenshiro Oguri

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arXiv · 2403.16302

Chance-Constrained Gaussian Mixture Steering to a Terminal Gaussian Distribution

Naoya Kumagai·Kenshiro Oguri

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Abstract

We address the problem of finite-horizon control of a discrete-time linear system, where the initial state distribution follows a Gaussian mixture model, the terminal state must follow a specified Gaussian distribution, and the state and control inputs must obey chance constraints. We show that, throughout the time horizon, the state and control distributions are fully characterized by Gaussian mixtures. We then formulate the cost, distributional terminal constraint, and affine/2-norm chance constraints on the state and control, as convex functions of the decision variables. This is leveraged to formulate the chance-constrained path planning problem as a single convex optimization problem. A numerical example demonstrates the effectiveness of the proposed method.

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BibTeX RIS

Naoya Kumagai, Kenshiro Oguri. 2024-03-24. Chance-Constrained Gaussian Mixture Steering to a Terminal Gaussian Distribution. https://arxiv.org/abs/2403.16302

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