Message Passing-Based Bayesian Control of a Cart-Pole System

We describe a Bayesian controller for a cart-pole system, a well-known benchmark in control theory. The cart-pole system is characterized by its nonlinear and underactuated nature, and we further complicate the scenario by (1) assuming that the controller lacks knowledge of sensor noise variance, and (2) imposing bounds on the control signal. Traditional control algorithms often struggle to adapt to uncertainties and constraints. However, the Bayesian framework, particularly the active inference framework, smoothly accommodates these complexities. In the proposed controller, the entire computational process consists of online Bayesian inference. This process is streamlined through a toolbox for fast message passing-based inference in factor graphs. We describe the mechanics of message passing in factor graphs, addressing challenges such as non-linear factors, bounded control, and real-time parameter tracking. The primary objective of this paper is to demonstrate that, with the advancement of the active inference framework and the effectiveness of automated inference toolboxes, Bayesian control emerges as an appealing option for application engineers.