Vehicle motion planning using stream functions

Abstract

Borrowing a concept from hydrodynamic analysis, this paper presents stream functions which satisfy Laplace's equation as a local-minima free method for producing potential-field based navigation functions in two dimensions. These functions generate smoother paths (i.e. more suited to aircraft-like vehicles) than previous methods. A method is developed for constructing analytic stream functions to produce arbitrary vehicle behaviors while avoiding obstacles, and an exact solution for the case of a single uniformly moving obstacle is presented. The effects of introducing multiple obstacles are discussed and current work in this direction is detailed. Experimental results generated on the Cornell RoboFlag testbed are presented and discussed, as well as related work applying these methods to path planning for unmanned air vehicles.

Application of transverse functions to control differentially driven wheeled robots using velocity fields

“…1 . (32) From (31) it follows that γ does not depend on ε 1 . Hence, taking into account (32) one concludes that the transversality condition is satisfied for any ε 1 > 0.…”

“…Using trigonometric identities in (31) we have From (31) it follows that γ does not depend on ε 1 . Hence, taking into account (32) Further, we consider selection of parameters ε 2 and ε 3 by analysing function γ. Using trigonometric identities in (31) we have…”

Path Planning for Mobile Robot using 4EGSOR via Nine-Point Laplacian (4EGSOR9L) Iterative Method

“…Then, Sasaki [6] computed harmonic functions using numerical technique to be used for mobile robot navigation. Waydo & Murray [7] used stream functions that are similar to harmonic functions to generate motion planning for a vehicle. Daily & Bevly [8] used harmonic potential field for path planning of high speed vehicles.…”

Path Planning for Indoor Mobile Robot using Half-Sweep SOR via Nine-Point Laplacian (HSSOR9L)

“…The work by Connolly and Gruppen [5] shows that harmonic functions have a number of properties useful in robotic applications. Similarly, Waydo & Murray [6] used stream functions for vehicle motion. More recently, Szulczyński et al [7] employed harmonic functions for real-time obstacle avoidance.…”