A large variety of mobile robots has blossomed recently, made possible by progresses in energy storage, electronics, processing speed, etc. We have seen these robots performing exploration and navigation tasks in different environments, and demonstrating impressive autonomy. However, the actual programming of complex behaviors, in particular when physical interaction takes place be- tween the robot and its environment, has remained tedious. This work often involves writing and tuning complicated state machines and requires a lot of engineering resources. Machine learning, which aims at specifying complex algorithms by leveraging data instead of just expert knowledge, proposes an alternative path. It appears especially useful for robotic tasks, as these often deal with high-dimensional input and output spaces while relying on a lot of contingent parameter values. Our aim is to understand the limits of capabilities that can be achieved with a simple, non-parametric system that learns from demonstration. We want to reduce the number of meta parameters to the minimum, because these ultimately have to be given to the system, while still handling tasks con- sisting of several steps. This paper proposes a system with only ns+ 2 meta parameters, where ns is the number of sensor dimensions. All these parameters are related to the robotic platform and its application, but do not depend on the task. We believe that such a system, should it perform well enough, would be of tremendous help for developing and deploying robotic applications. Indeed, the current requirement of choosing by hand many parameters is a major obstacle to the deployment of programming by demonstration.