Mori-Zwanzig formalism based reduced-order modeling for decision-making in marine autonomy
Author(s)
Hou, Mengxue
Advisor(s)
Edwards, Catherine R.
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Abstract
This thesis first considers the reduced-order modeling and path planning of a deterministic system, an example application of which is the AUV deterministic planning problem in the ocean flow field. We develop a data-driven reduced-order model of the flow dynamics. The proposed algorithm partitions the flow field into piece-wise constant flow speed, and leverages the real-time AUV measurements to learn the parameters in the reduced-order model. Such abstraction transforms the infinite dimensional planning problem into a mixed integer optimization problem (MIP). We develop an interleaved MIP solution with guaranteed completeness and optimality, and the computation cost is shown to be lower than the existing AUV planning methods. To further reduce the computation cost of solving the MIP, a bounded cost search algorithm is developed to compute a bounded cost sub-optimal solution of the MIP, with proved completeness. Further, we consider the reduced-order modeling and belief space planning of a continuous-state POMDP (partially observable Markov decision process), and develops a belief abstraction method to facilitate symbolic planning in the belief space. As unmodeled residual state has impact on the reduced-order dynamics, the abstracted belief dynamics is non-Markovian. Hence we identify the abstracted belief dynamics using a recurrent neural network, and develops a reduced-order Bayesian law based on the Mori-Zwanzig formalism. Both theoretical analysis and simulation results show that the proposed method provides high fidelity approximation of the belief dynamics. Further, we show through simulation that the belief abstraction reduces the computation cost in solving the planning problem in belief space.
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Date
2022-08-01
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Resource Subtype
Dissertation