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

Genetic Algorithm for Constrained Optimization with Stochastic Feasibility Region with Application to Vehicle Path Planning