Mori-Zwanzig formalism based reduced-order modeling for decision-making in marine autonomy

Committee:

Dr. Fumin Zhang, ECE, Chair, Advisor

Dr. Catherine Edwards, Skidaway Institute of Oceanography, Co-Advisor

Dr. Seth Hutchinson, ECE

Dr. Haomin Zhou, Math

Dr. Enlu Zhou, ISyE

Dr. Ye Zhao, ME

Abstract: Some robotic systems, such as the autonomous underwater vehicles (AUV), are strongly influenced by the environmental processes, which introduces high complexity in system dynamics. For such autonomous systems, directly specifying the full system behavior in real-time can be computationally impractical. Hence it is desired to introduce abstraction of system dynamics and modularity in actions, such that the computation cost can be significantly reduced. However, the abstraction introduces new challenges. First is the mixed-integer type decision-making due to the abstraction of system dynamics and the hierarchical representation of system behaviors. Another challenge is the degraded solution quality due to the model reduction error incurred from the abstraction.  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.