Date of Award
Electrical and Computer Engineering
College of Engineering and Computer Sciences
Type of Degree
Pingping Zhu, PhD, Committee Chairperson
Sanghoon Lee, PhD
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.
Estephan, Peter, "A path planning framework for multi-agent robotic systems based on multivariate skew-normal distributions" (2023). Theses, Dissertations and Capstones. 1758.