Skip to main content
Open Access Publications from the University of California

UC Davis

UC Davis Previously Published Works bannerUC Davis

Path planning with Pythagorean-hodograph curves for unmanned or autonomous vehicles

  • Author(s): Farouki, RT
  • Giannelli, C
  • Mugnaini, D
  • Sestini, A
  • et al.

Pythagorean-hodograph (PH) curves offer distinct advantages in planning curvilinear paths for unmanned or autonomous air, ground, or underwater vehicles. Although several authors have discussed their use in these contexts, prior studies contain misconceptions about the properties of PH curves or invoke heuristic approximate constructions when exact methods are available. To address these issues, the present study provides a basic introduction to the key properties of PH curves, and describes some exact constructions of particular interest in path planning. These include (a) maintenance of minimum safe separations within vehicle swarms; (b) construction of paths of different shape but identical arc length, ensuring simultaneous arrival of vehicles travelling at a constant speed; (c) determination of the curvature extrema of PH paths, and their modification to satisfy a given curvature bound; and (d) construction of curvature-continuous paths of bounded curvature through fields of polygonal obstacles.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View