(Georgia Institute of Technology, 2014-06)
Lu, Jun; Diaz-Mercado, Yancy; Egerstedt, Magnus B.; Zhou, Haomin; Chow, Shui-Nee
This paper investigates the problem of finding
shortest paths through 3-dimensional cluttered environments.
In particular, an algorithm is presented that determines the
shortest path between two points in an environment with
obstacles which can be implemented on robots with capabilities
of detecting obstacles in the environment. As knowledge of the
environment is increasing while the vehicle moves around, the
algorithm provides not only the global minimizer – or shortest
path – with increasing probability as time goes by, but also
provides a series of local minimizers. The feasibility of the
algorithm is demonstrated on a quadrotor robot flying in an
environment with obstacles.
(Georgia Institute of Technology, 2010)
Badieirostami, Majid; Adibi, Ali; Zhou, Hao-Min; Chow, Shui-Nee
First, we propose a new stochastic model for a spatially incoherent source in optical phenomena. The model naturally incorporates the incoherent property into the electromagnetic wave equation through a random source term. Then we propose a new numerical method based on Wiener chaos expansion (WCE) and apply it to solve the resulting stochastic wave equation. The main advantage of the WCE method is that it separates random and deterministic effects and allows the random effects to be factored out of the primary partial differential equation (PDE) very effectively. Therefore, the stochastic PDE is reduced to a set of deterministic PDEs for the coefficients of the WCE method which can be solved by conventional numerical algorithms. We solve these secondary deterministic PDEs by a finite-difference time domain (FDTD) method and demonstrate that the numerical computations based on the WCE method are considerably more efficient than the brute-force simulations. Moreover, the WCE approach does not require generation of random numbers and results in less computational errors compared to Monte Carlo simulations.