  In real-time trajectory planning for unmanned vehicles, on-board sensors,
radars and other instruments are used to collect information on possible
obstacles to be avoided and pathways to be followed. Since, in practice,
observations of the sensors have measurement errors, the stochasticity of the
data has to be incorporated into the models. In this paper, we consider using a
genetic algorithm for the constrained optimization problem of finding the
trajectory with minimum length between two locations, avoiding the obstacles on
the way. To incorporate the variability of the sensor readings, we propose a
more general framework, where the feasible regions of the genetic algorithm are
stochastic. In this way, the probability that a possible solution of the search
space, say x, is feasible can be derived from the random observations of
obstacles and pathways, creating a real-time data learning algorithm. By
building a confidence region from the observed data such that its border
intersects with the solution point x, the level of the confidence region
defines the probability that x is feasible. We propose using a smooth penalty
function based on the Gaussian distribution, facilitating the borders of the
feasible regions to be reached by the algorithm.
