A path planning framework for multi-agent robotic systems based on multivariate skew-normal distributions
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.
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