Historically, scalability has been a major challenge for the successful application of
semidefinite programming in fields such as machine learning, control, and robotics. In this …

Conic optimization has recently emerged as a powerful tool for designing tractable and
guaranteed algorithms for power system operation. On the one hand, tractability is crucial …

We consider the problem of generating motion plans for a robot that are guaranteed to
succeed despite uncertainty in the environment, parametric model uncertainty, and …

In recent years, optimization theory has been greatly impacted by the advent of sum of
squares (SOS) optimization. The reliance of this technique on large-scale semidefinite …

This paper is concerned with polynomial optimization problems. We show how to exploit
term (or monomial) sparsity of the input polynomials to obtain a new converging hierarchy of …

This paper presents initial results towards a realizable framework for the safety critical
controlled invariance of cyber-physical systems. The main contribution of this paper is the …

We present the design and implementation of a small autonomous unmanned aerial vehicle
capable of high‐speed flight through complex natural environments. Using only onboard …

We present an historical overview about the connections between the analysis of risk and
the control of autonomous systems. We offer two main contributions. Our first contribution is …

Many critical tasks in robotics, such as locomotion or manipulation, involve collisions
between a rigid body and the environment or between multiple bodies. Methods based on …

For robotic arms to operate in arbitrary environments, especially near people, it is critical to
certify the safety of their motion planning algorithms. However, there is often a trade-off …