Controlling the navigation of self-propelled, Brownian colloids in complex microstructured environments ( e.g., porous media and tumor vasculature) is important to emerging applications ( e.g., enhanced oil recovery and drug delivery). Here, we report a feedback control strategy by which to navigate self-propelled colloids through free space and increasingly complex mazes. Colloid rod position and orientation within mazes is sensed in real time, and instantaneous propulsion along the rod long axis can be actuated via light intensity. However, because uncontrolled rod rotational diffusion determines the propulsion direction, feedback control based on a policy is required to decide how to actuate propulsion magnitude versus colloid position and orientation within mazes. By considering stochastic rod dynamics including self-propulsion, translational-rotational diffusion, and rod-maze interactions, a Markov decision process framework is used to determine optimal control policies to navigate between start and end points in minimal time. The free-space navigation optimal policy effectively reduces to a simple heuristic in which propulsion is actuated only when particles point toward the target. The emergent structure of optimal control policies in mazes is based on the practice of globally following the shortest geometric paths; however, locally, propulsion is actuated to either follow paths toward the target or to produce collisions with maze features as part of generating more-favorable positions and orientations. Findings show how the coupled effects of maze size, propulsion speed, control update time, and relative particle translational and rotational diffusivities influence navigation performance.
Keywords: Markov decision process; active colloids; feedback control; first passage time; fractal mazes.