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

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. 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.