Many tools exist to solve constrained path-planning problems. They can be classified as follows. In the older ones, paths are planned in a discretized state space. The most recent, sampling-based path planners can explore the whole state space more efficiently. These path planners are used in many fields, e;g., chemistry, biology, automatic control or robotics. The main contribution of our work is to provide a solution to the path planning problem when uncertainty is present. Modern planning techniques are used in combination with localization algorithms that make it possible to characterize the uncertainty on the system state at a given time. Two approaches are considered. In the first one, the path planner uses a probabilistic representation of the state space at any given time using multivariate Gaussian distributions. An extended Kalman filter is used to propagate the state error. In the second approach, all states that are consistent with bounds on the errors are enclosed in a computable set. Contrary to the previous probabilistic method, this one is able to guarantee the safety of the system moving along the planned path, provided of course that the hypotheses on which it is based are satisfied.
