Visual servoing: a global path-planning approach

This paper considers the problem of realizing visual servoing taking into account constraints such as visibility and workspace constraints while minimizing a cost function such as spanned image area and trajectory length. A new path-planning scheme is proposed by, first, introducing a robust object reconstruction which allows one to obtain feasible image trajectories. Second, the rotation path is parameterized through a particular extension of the Euler parameters in order to obtain an equivalent expression of the rotation matrix as a quadratic function of unconstrained variables, hence largely simplified with respect to standard parameterizations which involve transcendental functions. Then, polynomials of arbitrary degree are used to complete the parametrization and formulate a general optimization where a number of constraints and costs can be considered. The optimal trajectory is followed by tracking the image trajectories with standard IBVS controllers.