Reflected Schrödinger Bridge: Density Control with Path Constraints
This work addresses density control with path constraints for applications like safety-critical systems, but it appears incremental as it builds on previous proximal recursion methods.
The paper tackles the problem of steering a joint state probability density function to another over a finite horizon with hard state constraints, such as obstacle avoidance, by extending Schrödinger bridge theory to include reflecting boundary conditions and providing a computational framework based on proximal recursions.
How to steer a given joint state probability density function to another over finite horizon subject to a controlled stochastic dynamics with hard state (sample path) constraints? In applications, state constraints may encode safety requirements such as obstacle avoidance. In this paper, we perform the feedback synthesis for minimum control effort density steering (a.k.a. Schrödinger bridge) problem subject to state constraints. We extend the theory of Schrödinger bridges to account the reflecting boundary conditions for the sample paths, and provide a computational framework building on our previous work on proximal recursions, to solve the same.