Exploratory Navigation Based on Dynamical Boundary Value Problems

Abstract

The paper presents a general framework for concurrent navigation and exploration of unknown environments based on discrete potential fields that guide the robot motion. These potentials are obtained from a class of partial differential equation (PDE) problems called boundary value problems (BVP). The boundaries are generated from sensor readings and therefore they change as the robot moves. This framework corresponds to an extension of our previous work (Prestes, E., Idiart, M. A. P., Engel, P. and Trevisan, M.: Exploration technique using potential fields calculated from relaxation methods, in: IEEE/RSJ International Conference on Intelligent Robots and Systems, 2001, p. 2012; Prestes, E., Engel, P. M., Trevisan, M. and Idiart, M. A.: Exploration method using harmonic functions, Robot. Auton. Syst. 40(1) (2002), 25---42). Here, we propose that a careful choice of the PDE and the boundary conditions can produce efficient exploratory behaviors in sparse and dense environments. Furthermore, we show how to extend the exploratory behavior to produce new ones by changing dynamically the boundary function (the value of the potential at the boundaries) as the exploration takes course. Our framework is validated through a series of experiments with a real robot in office environments.