Autonomous systems offer the promise of providing greater safety and access. However, this positive impact will only be achieved if the underlying algorithms that control such systems can be certified to behave robustly. This talk will describe a pair of techniques grounded in infinite dimensional optimization to address this challenge.
The first technique, which is called Reachability-based Trajectory Design, constructs a parameterized representation of the forward reachable set, which it then uses in concert with predictions to enable real-time, certified, collision checking. This approach, which is guaranteed to generate not-at-fault behavior, is demonstrated across a variety of different real-world platforms including ground vehicles, manipulators, and walking robots. The second technique is a modeling method that allows one to represent a nonlinear system as a linear system in the infinite-dimensional space of real-valued functions. By applying this modeling method, one can employ well-understood linear model predictive control techniques to robustly control nonlinear systems. The utility of this approach is verified on a soft robot control task.