  Stochastic Model Predictive Control has proved to be an efficient method to
plan trajectories in uncertain environments, e.g., for autonomous vehicles.
Chance constraints ensure that the probability of collision is bounded by a
predefined risk parameter. However, considering chance constraints in an
optimization problem can be challenging and computationally demanding. In this
paper, we present a grid-based Stochastic Model Predictive Control approach.
This approach allows to determine a simple deterministic reformulation of the
chance constraints and reduces the computational effort, while considering the
stochastic nature of the environment. Within the proposed method, we first
divide the environment into a grid and, for each predicted step, assign each
cell a probability value, which represents the probability that this cell will
be occupied by surrounding vehicles. Then, the probabilistic grid is
transformed into a binary grid of admissible and inadmissible cells by applying
a threshold, representing a risk parameter. Only cells with an occupancy
probability lower than the threshold are admissible for the controlled vehicle.
Given the admissible cells, a convex hull is generated, which can then be used
for trajectory planning. Simulations of an autonomous driving highway scenario
show the benefits of the proposed grid-based Stochastic Model Predictive
Control method.
