Question

In FSM-based behavioral planning, what is the specific mathematical function used to calculate the probability of a surrounding vehicle’s future position based on its current state?

Accepted Answer

In FSM-based behavioral planning, the specific mathematical function used to calculate the probability of a surrounding vehicle’s future position is the Multivariate Gaussian Distribution. This function models the uncertainty of a vehicle&#x27;s motion by representing its predicted position as a two-dimensional probability density surface, where the peak of the bell curve indicates the most likely location and the width indicates the level of uncertainty. The function is defined by a mean vector, which represents the predicted coordinates of the vehicle&#x27;s center, and a covariance matrix, which accounts for the spread of possible positions caused by factors like measurement noise or driver unpredictability. As time progresses, the covariance matrix expands, reflecting that the vehicle&#x27;s potential position becomes less certain the further into the future you predict. To calculate this, the planner uses a state transition model, such as a Constant Velocity or Constant Turn Rate and Velocity model, to estimate the mean, and then applies the Multivariate Gaussian equation to generate a spatial probability map. This map allows the autonomous system to evaluate collision risks by integrating the probability density over the space occupied by the ego vehicle.

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In FSM-based behavioral planning, what is the specific mathematical function used to calculate the probability of a surrounding vehicle’s future position based on its current state?