Date of Award


Degree Name

Electrical and Computer Engineering


College of Engineering and Computer Sciences

Type of Degree


Document Type


First Advisor

Pingping Zhu, PhD, Committee Chairperson

Second Advisor

Sanghoon Lee, PhD

Third Advisor

Mohammed Ferdjallah, PhD


This thesis presents a path planning framework for a very-large-scale robotic (VLSR) system in an known obstacle environment, where the time-varying distributions of agents are applied to represent the multi-agent robotic system (MARS). A novel family of the multivariate skew-normal (MVSN) distributions is proposed based on the Bernoulli random field (BRF) referred to as the Bernoulli-random-field based skew-normal (BRF-SN) distribution. The proposed distributions are applied to model the agents’ distributions in an obstacle-deployed environment, where the obstacle effect is represented by a skew function and separated from the no-obstacle agents’ distributions. First, the obstacle layout is represented by a Hilbert occupancy classification, which can be modeled by a Bernoulli random field and approximated from observation data. Then, we construct the BRF-SN distributions from the approximated BRF and the agents’ no-obstacle distributions, which can be modeled by a parametric distribution, e.g., the multivariate normal distributions or Gaussian mixture distributions. To learn unknown parameters from given samples, an Expectation-Maximization (EM) approach was used to minimize the upper bound of the negative log likelihood (NLL) function. Finally, to implement a time-varying path planning framework, two path-planning method are applied, an artificial potential field (APF) method for the macroscopic distribution trajectory was proposed based on l2 norm function and Cauchy-Schwarz Divergence, also a displacement interpolation (DI) method is applied for the BRF-SN distribution.

This thesis involves no human subjects, surveys, or interviews, proposed framework performance is demonstrated in a simulated virtual environment.

Index Terms – Skew normal mixture model, Bernoulli-random-field based skew-normal, path-planning, multi-agent robotic system, expectation-maximization, artificial potential field.


Interpolation – Displacement.

Multiagent systems.