Global regularity of two-dimensional flocking hydrodynamics

We study the systems of Euler equations which arise from agent-based dynamics driven by velocity \emph{alignment}. It is known that smooth solutions of such systems must flock, namely -- the large time behavior of the velocity field approaches a limiting "flocking" velocity. To address the question of global regularity, we derive sharp critical thresholds in the phase space of initial configuration which characterize the global regularity and hence flocking behavior of such \emph{two-dimensional} systems. Specifically, we prove for that a large class of \emph{sub-critical} initial conditions such that the initial divergence is "not too negative" and the initial spectral gap is "not too large", global regularity persists for all time

Enhanced dissipation and blow-up suppression in a chemotaxis-fluid system

In this paper, we investigate a coupled Patlak-Keller-Segel-Navier-Stokes (PKS-NS) system. We show that globally regular solutions with arbitrary large cell populations exist. The primary blowup suppression mechanism is the shear flow mixing induced enhanced dissipation phenomena

Active Simultaneous Localization and Mapping in Unstructured Environment with a Quadrotor

An agent performing Simultaneous Localization and Mapping (SLAM) constructs a map of the environment while estimating its location at the same time. SLAM algorithms primarily focus on finding the best estimate of the location of the agent, and by extension, that of the landmarks in the environment, given observations from sensors. These algorithms do not typically address how an agent should explore an unknown environment to build a map efficiently. This ability for active exploration is important for autonomous robots to work in unknown, unstructured environments such as forests or caves. This paper proposes an active SLAM system that allows an agent to explore its surroundings, using visual-inertial data from an RGBD camera. We formalize this problem as taking actions that maximize the amount of information obtained from the scene. At each time step, a utility function that computes the incremental information gain is used to take actions. We conduct experiments using an Intel RealSense camera mounted on a custom-built quadrotor and show that we can explore indoor environments (while restricting the actions to choosing new viewpoints in SO(3) for practical reasons)