Safety guarantee prior to the deployment of robots can be difficult due to unexpected
disturbances in runtime. This article presents a real-time receding-horizon robust trajectory …

Path planning has long been one of the major research areas in robotics, with probabilistic
roadmap (PRM) and rapidly-exploring random trees (RRT) being two of the most effective …

In 1948, Fritz John proposed a theorem stating that every convex body has a unique
maximal volume inscribed ellipsoid, known as the John ellipsoid. The John ellipsoid has …

Reachable sets for a dynamical system describe collections of system states that can be
reached in finite time, subject to system dynamics. They can be used to guarantee goal …

Optimizing a parameterized zonotope or ellipsoid is a common task in robust state
estimation, fault diagnosis and reachability analysis. Recent studies have unified ellipsoids …

The characteristics of physical constraints and widespread communication of vehicle
platoon system render it vulnerable to physical intrusion or cyber attacks. To enhance the …

We study the convex geometry of the forward reach sets for integrator dynamics in finite
dimensions with bounded control. We derive closed-form expressions for the volume and …

Model predictive control (MPC) is an optimization-based control strategy with broad
industrial adoption. Unfortunately, the required computation time to solve the receding …

This is the first of a two part paper investigating the geometry of the integrator reach sets,
and the applications thereof. In this Part I, assuming box-valued input uncertainties, we …

Set representations are the foundation of various set-based approaches in state estimation,
reachability analysis and fault diagnosis. In this paper, we investigate spectrahedral …