In this thesis, the problem of motion planning under uncertainty is explored.Motion planning under uncertainty is important since even with noise during the execution of the plan, it is desierable to keep the collision risk low.However, for the motion planning to be useful it needs to be possible to perform it in a reasonable time.The introduction of state uncertainty leads to a substantial increase in search time due to the additional dimensions it adds to the search space.In order to alleviate this problem, different approaches to pruning of the search space are explored.The initial approach is to prune states based on having strictly worse uncertainty and path cost than other found states.Having performed this initial pruning, an alternate approach to comparing uncertainties is examined in order to explore if it is possible to achieve a lower search time. The approach taken in order to lower the search time further is to discretize the covariance of a state by using a number of buckets.However, this discretization results in giving up the completeness and optimality of the algorithm.Having implemented these different ways of pruning, their performance is tested on a number of different scenarios.This is done by evaluating the planner using the pruning in several different scenarios including uncertainty and one without uncertainty.It is found that all of the pruning approaches reduce the overall search time compared to when no additional pruning based on the uncertainty is done.Additionally, it is indicated that the bucket based approach reduce the search time to a greater extent than the strict pruning approach.Furthermore, the extensions made results in no increase in cost or a very small increase in cost for the explored scenarios.Based on these results, it is likely that the bucket pruning approach has some potential.However more studies, perticularly with additional scenarios, needs to be made before any definitive conclusions can be made.