New approach to visual servo control using terminal constraints

• Published in: Journal of the Franklin Institute Vol. 356; no. 10; pp. 5001 - 5026
• Main Authors: Mehta, S.S., Ton, C., Rysz, M., Kan, Z., Doucette, E.A., Curtis, J.W.
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.07.2019; Elsevier Science Ltd
• Subjects: Cameras; Computer simulation; Control stability; Controllers; Convexity; Direction of arrival; Image acquisition; Optimization; Servocontrol; Simulation; Sliding mode control; Stability analysis; Systems stability; Terminal constraints
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2019.04.026

A large class of visual servo controllers relies on an a priori obtained reference image, captured at the desired position and orientation (i.e., pose) of a camera, to yield control signals to regulate the camera from its current pose to a desired pose. In many applications, accessibility and economics of the operation may prohibit acquisition of such a reference image. This paper introduces a new visual servo control paradigm that enables control of the camera in the absence of reference image using a set of terminal constraints. Specifically, the desired pose is encoded using the angle of obliquity of the optical axis with respect to the object plane and its direction of arrival at the plane. A constrained convex optimization problem is formulated over a conic section defined by the terminal constraints to yield an error system for the control problem. Subsequently, this work introduces continuous terminal sliding mode visual servo controllers to regulate the camera to the desired pose. Lyapunov-based stability analysis guarantees that the origin is a finite-time-stable equilibrium of the system. Numerical simulation results are provided to verify the performance of the proposed visual servo controller.