Motion Planning, Partial Observability, and Quantum Mechanics- Advancing the Frontiers of Path Integral Control Theory
Abstract
The Path Integral Control (PIC) is a control algorithm inspired by the Path Integral formulation of quantum mechanics. This algorithm enables decision-makers to compute optimal control inputs in real time by conducting Monte Carlo simulations of open-loop systems. Due to its purely simulator-driven nature, PIC is applicable to high-dimensional, nonlinear, and stochastic optimal control (SOC) problems, where conventional model-based policy synthesis methods often face challenges. Recently, PIC has gained widespread popularity in robotics and autonomy, primarily because its Monte Carlo-based algorithm is amenable to parallel implementations on Graphics Processing Units (GPUs). As PIC s popularity increased, its theoretical and algorithmic limitations became widely acknowledged. For example, PIC is only applicable to a restricted class of SOC problems. This limitation is closely related to the major difficulty in generalizing PIC to partially observable systems. To systematically address these limitations, we propose a series of research tasks that range from motion planning to quantum mechanics, aiming to glean insights from diverse research domains. Specifically, Thrust 1 aims to advance PIC theory in motion planning. We explore innovative applications of PIC for risk-constrained and rationally inattentive path planning. Thrust 2 aims to remove the structural restriction of the current PIC theory and develop a PIC framework for partially observable control systems. In Thrust 3, we identify the class of SOC problems solvable by linear Schrodinger equations and apply PIC to control quantum systems. The successful completion of this project will bridge engineering and physics, advancing the frontiers of PIC theory. The research outcomes will lay foundational groundwork for simulator-driven autonomy to achieve the next-level agility, flexibility, and reliability, which will be a significant asset for AFOSR.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 06, 2025
- Source ID
- FA95502410180
Entities
People
- Takashi Tanaka
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of Texas at Austin