Path planning approach to visual servoing with feature visibility constraints: A convex optimization based solution

This paper explores the possibility of using convex optimization to address a class of problems in visual servoing. This work is motivated by the recent success of convex optimization methods in solving geometric inference problems in computer vision. We formulate the visual servoing problem with feature visibility constraints as a convex optimization of a function of the camera position i.e. the translation of the camera. First, the path is planned using potential field method that produces unconstrained but straight line path from the initial to the desired camera position. The problem is then converted to a constrained convex optimization problem by introducing the visibility constraints to the minimization problem. The objective of the minimization process is to find for each camera position the closest alternate position from which all features are visible. This algorithm ensures that the solution is optimal. This formulation allows the introduction of more constraints, like joint limits of the arm, into the visual servoing process. The results have been illustrated in a simulation framework.