Dynamic Velocity Field Angle Generation for Obstacle Avoidance in Mobile Robots Using Hydrodynamics

Abstract

In this work, a strategy for the generation of the angle reference for a Velocity Field Controller is presented. For an arbitrary trajectory 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. $V_x=|\overrightarrow{V}|\cdot\cos(\alpha)$ and $V_y=|\overrightarrow{V}|\cdot\sin(\alpha)$. 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 $|\overrightarrow V|$. 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.