Mobile manipulation targets applications in dynamic and unstructured environments. Motion generation methods suitable for these applications must account for end-effector task constraints, must reason about environment uncertainty, i.e. the fact that the exact state of the dynamic environment cannot be known to the robot, and should do so only using their on-board sensors. We present the Expected-Shortest-Path Elastic Roadmap (ESPER) planner as a motion generation method suitable for mobile manipulation. It integrates task-constrained, whole-body, reactive motion generation in high-dimensional configuration space with reasoning about uncertainty. In our experiments, we generate task-consistent motion in uncertain environments on a real-world mobile manipulator only relying on on-board sensors.