We consider path-planning problems with an initial uncertainty on the target and/or the global environment. The actual state of the world will be revealed at some “certainty time” T (which itself can be either deterministic or random). We first show how to control the system until then to minimize the expected cost-to-target. We also compare and contrast several notions of “robustness” for these problems (worst-case optimality, worst-case/average-case trade-offs, chance constrained optimization and the distributionally robust optimization to address the model uncertainty). We illustrate our methods on robotic navigation and airplane storm-avoidance examples.