The use of estimation techniques on stochastic models to solve control problems is an emerging paradigm that falls under the rubric of Active Inference (AI) and Control as Inference (CAI). In this work, we use probability propagation on factor graphs to show that various algorithms proposed in the literature can be seen as specific composition rules in a factor graph. We show how this unified approach, presented both in probability space and in log of the probability space, provides a very general framework that includes the Sum-product, the Max-product, Dynamic programming and mixed Reward/Entropy criteria-based algorithms. The framework also expands algorithmic design options that lead to new smoother or sharper policy distributions. We propose original recursions such as: a generalized Sum/Max-product algorithm, a Smooth Dynamic programming algorithm and a modified versions of the Reward/Entropy algorithm. The discussion is carried over with reference to a path planning problem where the recursions that arise from various cost functions, although they may appear similar in scope, bear noticeable differences. We provide a comprehensive table of composition rules and a comparison through simulations, first on a synthetic small grid with a single goal with obstacles, and then on a grid extrapolated from a real-world scene with multiple goals and a semantic map.

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We present a unified approach to multi-agent autonomous coordination in complex and uncertain environments, using path planning as a problem context. We start by posing the problem on a probabilistic factor graph, showing how various path planning algorithms can be translated into specific message composition rules. This unified approach provides a very general framework that, in addition to including standard algorithms (such as sum-product, max-product, dynamic programming and mixed Reward/Entropy criteria-based algorithms), expands the design options for smoother or sharper distributions (resulting in a generalized sum/max-product algorithm, a smooth dynamic programming algorithm and a modified versions of the reward/entropy recursions). The main purpose of this contribution is to extend this framework to a multi-agent system, which by its nature defines a totally different context. Indeed, when there are interdependencies among the key elements of a hybrid team (such as goals, changing mission environment, assets and threats/obstacles/constraints), interactive optimization algorithms should provide the tools for producing intelligent courses of action that are congruent with and overcome bounded rationality and cognitive biases inherent in human decision-making. Our work, using path planning as a domain of application, seeks to make progress towards this aim by providing a scientifically rigorous algorithmic framework for proactive agent autonomy.