  In this paper, we investigate the synthesis of piecewise affine feedback
controllers to address the problem of safe and robust controller design in
robotics based on high-level controls specifications. The methodology is based
on formulating the problem as a collection of reach control problems on a
polytopic state space. Reach control has so far only been developed in theory
and has not been tested experimentally on a real system before. Using a
quadrocopter as our experimental platform, we show that these theoretical tools
can achieve fast, albeit safe and robust maneuvers. In contrast to most
traditional control techniques, the reach control approach does not require a
predefined open-loop reference trajectory or spacial path. Experimental results
on a quadrocopter show the effectiveness and robustness of this control
approach. In a proof-of-concept demonstration, the reach controller is
implemented in one translational direction while the other degrees of freedom
are stabilized by separate controllers.
