Available at: https://digitalcommons.calpoly.edu/theses/3419
Date of Award
8-2026
Degree Name
MS in Electrical Engineering
Department/Program
Electrical Engineering
College
College of Engineering
Advisor
Carlos Diaz Alvarenga
Advisor Department
Computer Science
Advisor College
College of Engineering
Abstract
Harmonic potential fields provide provably minimum-free navigation, but any change to the workspace geometry invalidates the field and forces a costly global recomputation, typically restricting them to static environments. This thesis extends the harmonic map framework of Vlantis et al., which maps the free workspace onto a unit disk and uses an atlas of per-region transformations, to dynamic indoor settings. First, we replace their manually annotated room partition with an automatic decomposition based on the Generalized Voronoi Diagram, allowing the atlas to be built from an arbitrary occupancy grid in an automated way. Second, we introduce a localized repair procedure so that when onboard lidar detects a map–to-real world mismatch, only the affected partitions are dissolved, re-partitioned, and re-solved, while all others are preserved. Implemented in ROS2 and evaluated on a simulated TurtleBot4 across 450 dynamic navigation runs, the GVD atlas achieves a 97% success rate. We found that repair cost scales with the size of the change, not the workspace: at 9216 m², the atlas repairs and replans in 0.34 s, a factor of 58× when compared to the global recomputation.