Fig. 2: Diverse navigational strategies dynamically emerge in simulations from the interaction of perceptual and internal model uncertainties during optimal control under uncertainty.

a Participants moving in an environment with landmarks and target locations build up a probabilistic allocentric internal representation by sequentially combining egocentric observations, capturing their uncertain subjective belief regarding their position, heading direction, as well as the expected location of landmarks and goals. b The true state x_t which captures participant’s location, heading direction, as well as the location of goals and landmarks, is not directly accessible, hence participants rely on their probabilistic internal representation b_t = (μ_t, Σ_t), reflecting their subjective spatial uncertainties, which serves as the basis for path planning and is updated by planned motor actions u_t (prediction) alongside noisy sensory observations from perception z_t (state estimation). c The internal subjective belief facilitates the planning of trajectories towards internally represented goal locations and sequential updating of the participant’s allocentric position within the internal representation (vector-based navigation). A goal is considered to be reached by a participant when the belief about self-location matches the belief of the goal location in the internal representation. d In the absence of landmarks, noisy motor actions increase positional and heading uncertainty tracked by the belief state, which may become increasingly discrepant from the actual state x_t (path-integration). e During locomotion towards a visible goal, visual feedback from sensory perception reduces positional errors stemming from noisy motor actions (beaconing). f Initial noisy egocentric observations of objects (distance and bearing) are transformed into an internal allocentric representation taking into account the participant’s positional and observation uncertainties (left: oriented, low uncertainty, right: disoriented, high uncertainty). g The allocentric internal representation, reflects participant’s spatial estimates and uncertainties regarding the location of landmarks and goals in the environment, as well as their own location and heading direction within the environment (cognitive map). h Landmarks in the environment reduce participant’s positional and heading uncertainty and provide orientation (landmark-based navigation). Left: Participant is disoriented, i.e., belief about heading and position is discrepant from true heading and position and highly uncertain. Middle: Landmark observation reduces positional uncertainty allowing participants to re-orient. Right: Movement toward the invisible goal location using landmark observations to correct errors due to noisy motor actions.