A variational approach to trajectory planning in visual servoing

One deficiency of image-based servo is that the induced 3D trajectories are not optimal and sometimes, especially when the displacements to realize is large, these trajectories are not physically valid leading to the failure of the servoing process. In this chapter, we address the problem of generating trajectories of some image features that corresponds to optimal 3D trajectories in order to control efficiently a robotic system using an image-based control strategy. First, a collineation path between given start and end points is obtained and then the trajectories of the image features are derived. Path planning is formulate as a variational problem which allows to consider simultaneously optimality and inequality constraints (visibility). A numerical method is employed for solving the path-planning problem in the variational form. © 2010 Springer-Verlag London.