Title:
Optimal Motion Planning and Computational Optimal Transport
Optimal Motion Planning and Computational Optimal Transport
Author(s)
Sun, Haodong
Advisor(s)
Kang, Sung Ha
Zhou, Haomin
Zhou, Haomin
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Abstract
In many real life problems, the decision making process is guided by the principle of cost minimization. In this thesis, we focus on analyzing the theoretical properties and designing computational methods under the framework of several classical cost minimization problems, including optimal motion planning and optimal transport (OT). Over the past decades, motion planning has attracted large amount of attention in robotics. Given certain configurations in the environment, we are looking for trajectories which move the robot from one to the other. To produce high-quality trajectories, we propose a new computational method to design smooth and collision-free trajectories for motion planning with one or more robots. The functional cost in model leads to short and smooth trajectories. The designed method can also be generalized to problems with multiple robots. The idea of optimal transport naturally arises from many application scenarios including economy, computer science, etc. Optimal transport provides powerful tools for comparing probability measures in various types. However, obtaining the optimal transport plan is generally a computationally-expensive task. We start with an entropy transport problem as a relaxed version of original optimal transport problem with soft marginals, and propose an efficient algorithm to produce sample approximation for the optimal transport plan. This method can directly output samples from optimal plan between two continuous marginals without any discretization and network training. An inverse problem of OT is also of our interest. We present a computational framework for learning the cost function from the given optimal transport plan. The cost learning problem is reformulated as an unconstrained convex optimization problem and two efficient algorithms are proposed for discrete and continuous cost learning.
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Date Issued
2022-04-28
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Text
Resource Subtype
Dissertation