Dynamic Velocity Field Angle Generation for Obstacle Avoidance in Mobile Robots Using Hydrodynamics Claudia P´ erez-D’Arpino, Wilfredis Medina-Mel´ endez, Leonardo Ferm´ ın, Jos´ e Guzm´an, Gerardo Fern´ andez-L´opez, and Juan Carlos Grieco Simon Bolivar University, Mechatronics Group, ELE-302 Sartenejas 1080-A Miranda, Venezuela {cdarpino,wmedina,lfermin,joseguzman,gfernandez,jcgrieco} @usb.ve Abstract. In this work, a strategy for the generation of the angle ref- erence for a Velocity Field Controller is presented. For an arbitrary tra- jectory given in its parametric form, it is possible to create a desired velocity ﬁeld, that could be modiﬁed if obstacles were detected by an artiﬁcial vision system. Velocity ﬁelds are composed by vectors that can be expressed in polar form, i.e. Vx = | − → V |· cos(α) and Vy = | − → V |· sin(α). In the velocity ﬁeld generation technique proposed, the problem is divided into two separate problems: the calculation of the orientation angle α and the calculation of the linear velocity | − → V |. This paper addresses the calculation of α, using the hydrodynamics theory of an incompressible non-viscous ﬂuid, plus the use of conformal mapping, thus generating a trajectory vector ﬁeld that can evade obstacles. Results obtained show that a smooth and continuous ﬁeld for both open and closed trajectories is achieved. Keywords: Motion and Path Planning, Velocity Field Generation, Hy- drodynamics, Conformal Mapping, Autonomous Navigation. 1 Introduction Velocity ﬁelds consist in specifying a velocity vector to each point of the workspace of a robot, coding a speciﬁed task in terms of velocity. They were in- troduced in [1], and extended in [2] and [3], where authors proposed and tested a Passive Velocity Field Controller for a manipulator. There have been many other velocity ﬁeld controllers developed for wheeled robots and manipulators [4], that focus on the study of the controller itself using time invariant velocity ﬁeld theoretically obtained. However, the problem of generating those references in a dynamic fashion has not been addressed in depth. The work of Li et. al. [5], Yamakita et. al. [6] [7], Dixon et. al. [8] and Medina-Mel´ endez et. al. [9], are important contributions to the velocity ﬁeld generation area, which is still an open problem in robotics, due to its high tasked dependency and the fact that it is not a trivial matter to solve [2]. This work is focused in the develop- ment of an algorithm able to generate velocity ﬁelds for coding desired tasks in environments with uncertain conditions. H. Geﬀner et al. (Eds.): IBERAMIA 2008, LNAI 5290, pp. 372–381, 2008. c  Springer-Verlag Berlin Heidelberg 2008