Path Integral Control for Partially Observed Systems with Controlled Sensing
This work provides a theoretical framework for integrating controlled sensing into path integral control, enabling optimal control in partially observed systems for robotics and autonomous systems.
The paper addresses the problem of path integral control in partially observed systems where a fixed observation matrix fails to satisfy a necessary matching condition. By treating the observation matrix as a control variable and constraining it to a measurable selector from the matching set, the authors reduce the Hamilton-Jacobi-Bellman equation to a linear PDE with a Feynman-Kac representation, enabling efficient computation.
Path integral control in Gaussian belief space requires a structural matching condition between the observation-driven diffusion of the belief mean and the actuation authority, which a fixed observation matrix cannot enforce. We treat the observation matrix as a control variable and show that constraining the sensing control to a measurable selector from the resulting matching set reduces the Hamilton-Jacobi-Bellman equation for the belief mean and covariance to a linear PDE with a Feynman-Kac representation.