By dynamic planning, we refer to the ability of the human brain to infer and impose motor trajectories related to cognitive decisions. A recent paradigm, active inference, brings fundamental insights into the adaptation of biological organisms, constantly striving to minimize prediction errors to restrict themselves to life-compatible states. Over the past years, many studies have shown how human and animal behaviors could be explained in terms of active inference - either as discrete decision-making or continuous motor control - inspiring innovative solutions in robotics and artificial intelligence. Still, the literature lacks a comprehensive outlook on effectively planning realistic actions in changing environments. Setting ourselves the goal of modeling complex tasks such as tool use, we delve into the topic of dynamic planning in active inference, keeping in mind two crucial aspects of biological behavior: the capacity to understand and exploit affordances for object manipulation, and to learn the hierarchical interactions between the self and the environment, including other agents. We start from a simple unit and gradually describe more advanced structures, comparing recently proposed design choices and providing basic examples. This study distances itself from traditional views centered on neural networks and reinforcement learning, and points toward a yet unexplored direction in active inference: hybrid representations in hierarchical models.

How can agents infer the intentions of others by simply observing their behavior? And how can they generate fast and accurate actions such as grasping a moving object on the fly? Recent advances in Bayesian model reduction have led to innovative, biologically plausible approaches to actively infer the state of affairs of the world and perform planning with continuous signals. However, reducing the surrounding environment into a small set of simpler hypotheses remains a challenge in highly dynamic contexts. In this study, we propose an approach, based on active inference, that employs dynamic priors sampled from reduced versions of a generative model. Each dynamic prior corresponds to an alternative evolution of the world, which the agent can evaluate by accumulating continuous data. We test our approach on two everyday tasks: inferring a trajectory and grasping a moving object. Our findings reveal how agents can smoothly infer and enact dynamic intentions, and emphasize the key role of intentional gain or precision in motor learning.

Decision-making is often conceptualized as a serial process, during which sensory evidence is accumulated for the choice alternatives until a certain threshold is reached, at which point a decision is made and an action is executed. This decide-then-act perspective has successfully explained various facets of perceptual and economic decisions in the laboratory, in which action dynamics are usually irrelevant to the choice. However, living organisms often face another class of decisions-called embodied decisions-that require selecting between potential courses of actions to be executed timely in a dynamic environment, e.g., for a lion, deciding which gazelle to chase and how fast to do so. Studies of embodied decisions reveal two aspects of goal-directed behavior in stark contrast to the serial view. First, that decision and action processes can unfold in parallel; second, that action-related components, such as the motor costs associated with selecting a particular choice alternative or required to "change mind" between choice alternatives, exert a feedback effect on the decision taken. Here, we show that these signatures of embodied decisions emerge naturally in active inference-a framework that simultaneously optimizes perception and action, according to the same (free energy minimization) imperative. We show that optimizing embodied choices requires a continuous feedback loop between motor planning (where beliefs about choice alternatives guide action dynamics) and motor inference (where action dynamics finesse beliefs about choice alternatives). Furthermore, our active inference simulations reveal the normative character of embodied decisions in ecological settings - namely, achieving an effective balance between a high accuracy and a low risk of missing valid opportunities.