* By Jerry Ding, Jeremy H. Gillula, Haomiao Huang, Michael P. Vitus, Wei Zhang, and Claire J. Tomlin © LUSHPIX Toward Reachability-Based Controller Design R obotics has provided the motivation and inspiration for many innovations in planning and control. From nonholonomic motion planning [1] to probabilistic road maps [2], from capture basins [3] to preimages [4] of obstacles to avoid, and from geometric nonlinear control [5], [6] to machine-learning methods in robotic control [7], there Digital Object Identifier 10.1109/MRA.2011.942113 Date of publication: 13 September 2011 1070-9932/11/$26.00ª2011 IEEE is a wide range of planning and control algorithms and methodologies that can be traced back to a perceived need or anticipated benefit in autonomous or semiautonomous systems. Our research has also been inspired by problems in autonomous and semiautonomous systems. We have focused on safety verification and controller synthesis to satisfy safety specifications as well as verification and controller synthesis for guaranteeing that desired targets are reached. Among a group of researchers at the interface of SEPTEMBER 2011 * IEEE ROBOTICS & AUTOMATION MAGAZINE * 33