High-dimensional stochastic optimal control using continuous tensor decompositions
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1611.04706.pdf
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Author(s)
Gorodetsky, Alex Arkady
Karaman, Sertac
Marzouk, Youssef M
Date Issued
February 2018
Journal
International Journal of Robotics Research
Publisher
SAGE Publications
Citation
Gorodetsky, Alex et al. “High-Dimensional Stochastic Optimal Control Using Continuous Tensor Decompositions.” The International Journal of Robotics Research 37, 2–3 (February 2018): 340–377 © 2018 The Author(s)
Version
Author's final manuscript
Abstract
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately, most existing algorithms that guarantee convergence to optimal solutions suffer from the curse of dimensionality: the run time of the algorithm grows exponentially with the dimension of the state space of the system. We propose novel dynamic programming algorithms that alleviate the curse of dimensionality in problems that exhibit certain low-rank structure. The proposed algorithms are based on continuous tensor decompositions recently developed by the authors. Essentially, the algorithms represent high-dimensional functions (e.g. the value function) in a compressed format, and directly perform dynamic programming computations (e.g. value iteration, policy iteration) in this format. Under certain technical assumptions, the new algorithms guarantee convergence towards optimal solutions with arbitrary precision. Furthermore, the run times of the new algorithms scale polynomially with the state dimension and polynomially with the ranks of the value function. This approach realizes substantial computational savings in “compressible” problem instances, where value functions admit low-rank approximations. We demonstrate the new algorithms in a wide range of problems, including a simulated six-dimensional agile quadcopter maneuvering example and a seven-dimensional aircraft perching example. In some of these examples, we estimate computational savings of up to 10 orders of magnitude over standard value iteration algorithms. We further demonstrate the algorithms running in real time on board a quadcopter during a flight experiment under motion capture. Keywords: Stochastic optimal control; motion planning; dynamic programming; tensor decompositions
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
Massachusetts Institute of Technology. Department of Mechanical Engineering
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DOI of Published Version
https://doi.org/10.1177/0278364917753994
