We describe an approach to the use of case-based techniques for natural language understanding and for action planning in a system for dialogue between a human and a robot, which in our case is a UAV (unmanned aerial vehicle). A single case base and case-based reasoning engine is used both for understanding and for planning actions by the UAV. This approach has been developed through the work on an experimental dialogue system, called CEDERIC. Dialogue experiments where a number of users have solved tasks by dialogue with this system showed very adequate success rates, while at the same time they indicated a few weak points in the system that could then easily be corrected.