Adjustable navigation functions for unknown sphere worlds

Abstract

This paper introduces an algorithm for automatically tuning analytic navigation functions for sphere worlds. The tuning parameter must satisfy a lower bound to ensure collision avoidance and convergence. Until now analytic navigation functions have been manually tuned, although existence of a lower bound had been proved. A theoretical improvement on this lower bound is provided and the method is extended to unbounded manifolds. Then the required formulas are derived and algorithm described. So the lower bound is here evaluated in terms of sphere world centers and radii. Automated tuning enables completely unattended solution of any navigation problem in unknown sphere worlds and a priori known worlds which belong to the sphere world diffeomorphism class.

Navigation Functions for everywhere partially sufficiently curved worlds

“…The form of NF proposed by Koditschek and Rimon (KRNF) require tuning of a parameter k ≥k min to guarantee the desired navigation properties. We extended KRNFs to unknown sphere worlds in [16] and the present work further extends them by proving thatk min exists for more general worlds.…”

“…E-mail: jfilippidis@gmail.com, kkyria@mail.ntua.gr limited sensing range, non-holonomic systems [12] using dipolar NFs, incorporating prioritization [13] and multi-agent connectivity constraints [14], to partially known worlds by applying belt zones [15] and to unknown sphere worlds [16], as well as convex worlds using local diffeomorphisms [17]. Nonetheless, all of them involved either sphere worlds or diffeomorphisms, hence also simply connected obstacles.…”

Set-point Control of Mobile Robot with Obstacle Detection and Avoidance Using Navigation Function - Experimental Verification

“…An algorithm for automatically tuning analytic navigation functions for sphere worlds was presented in [3]. The tuning parameter must satisfy a lower bound to ensure convergence to the desired value.…”

Indoor navigation for mobile robots using predictive fields

“…Navigation functions are attractive solutions for path planning because of their relative ease of formulation, their packaging of various aspects of robot navigation into a single framework, and the fact that they prove convergence to the goal. Thus, they have attracted attention [4], [5], [6], [7] since they were first formulated. Some improvements have been made to the original approach.…”

“…Chen [6] demonstrated that they work with moving obstacles in the workspace. Most recently, Filippidis [4] proposed an algorithm to automatically tune the navigation function gain. In their original formulation, navigation functions did not allow for incorporating an element of uncertainty which is inevitable to obstacles moving in practical environments.…”