Systematic Method of Designing and Constructing Velocity Fields for Motion Control

Abstract

Velocity fields for motion control are a kinematic description of the desired trajectories in the Cartesian space whose applications in industrial processes of contouring tasks are promising; however, the lack of a general designing method and the complexity of the controllers designed without concern for the construction of the fields have confined their use to the academic domain. In this paper, the author introduces a systematic method for designing and constructing velocity fields for control that provides a suitable reference in velocity to simplify the structure of the close loop controllers. The method is a three steps procedure where the motion objective in the vector field is described as a main streamline surrounded by an attractive flow to achieve this objective. The main streamline, expressed as a parametric curve, determines the main directional components of the field as a radial-attraction to the curve and a tangential-guide on the curve; directions which are linearly combined to calculate the velocity vectors into a soft and continuous transition of uniform speed to attract and guide the motion as the position gets closer to the curve. It is showed that the method provides a convergent velocity field, either as a static kinematic description of the motion or as a dynamic reference in velocity for a moving particle, and it is tested designing a circular trajectory field, commonly used in control design, and two generic examples of 2D and 3D curves on the Cartesian space.