Path Planning for Visual servoing and Navigation using Convex Optimization

Exploiting visual cues to control systems for robotic applications is a promising idea. Practically, they are usable only if the end result accedes to the restrictions of the specific environment. These restrictions are like the limited field of view of the camera and physical constraints of the workspace of the robot. Hence, there is a need for a general framework that can be used adaptively across various environments. We develop such an algorithmic framework that is flexible to accommodate various kinds of constraints and generate a solution that is optimal in the sense of the considered error measure. We perform a constrained optimization on the error in a convex domain considering all the necessary constraints using convex optimization techniques and further extend it to nonconvex domains. We utilize branch-and-bound algorithm to divide the problem of optimizing over a range of rotations into simpler problems and solve for the optimal rotation. We demonstrate the performance of the algorithm by generating control signals in a simulated framework for visual servoing and in a real-world for robot