When a robot performs a task in an unstructured dynamic environment, it has to account for many factors. It should not only keep the track of where it is and how it should move, but also ensure that the kinematic, dynamic and task specific limitations are observed. It is also important that the robot can effectively avoid collisions with static and moving obstacles. In the current thesis we present design and implementation of an algorithm capable to face all these challenges. The system combines principles of dynamic roadmaps and elastic roadmaps frameworks, both of which are the state-of-art approaches to motion planning problem. The suggested solution is presented in the context of a broad overview of the literature in motion planning domain focusing on methodology of sample-based and feedback planning in dynamic environments. The implemented algorithm is applied to a 7-degree-of-freedom manipulator and is demonstrated and analyzed through a variety of simulated test scenarios. The result is an extensible and future-oriented planning system that can plan and execute movement between a starting and target position while preserving task constraints and reacting to environment changes in real time.