The autonomous execution of mobile manipulation tasks in unstructured, dynamic environments requires the consideration of various motion constraints. The task itself imposes constraints, of course, but so do the kinematic and dynamic limitations of the manipulator, unpredictably moving obstacles, and the global connectivity of the workspace. All of these constraints need to be updated continuously in response to sensor feedback. We present the elastic roadmap framework, a novel feedback motion planning approach capable of satisfying all of these motion constraints and their respective feedback requirements. This framework is validated in simulation and real-world experiments using a mobile manipulation platform and a stationary manipulator.