When relying on vision-based control techniques, some knowledge about the 3-D structure of the scene is typically needed for a correct execution of the task. This information, however, cannot, in general, be extracted from a single camera image without additional assumptions on the scene. In these cases a Structure from Motion (SfM) estimation process could be exploited for reconstructing this missing 3-D information. However performance of any SfM estimator is known to be highly affected by the trajectory followed by the camera during the estimation process, thus creating a tight coupling between camera motion (needed to, e.g., realize a visual task) and performance/accuracy of the estimated 3-D structure. This talk will discuss a general online trajectory optimization framework that allows maximizing the convergence rate of a SfM estimator by (actively) affecting the camera motion. This active strategy can also be coupled with the concurrent execution of a visual task using appropriate redundancy resolution techniques. The approach naturally lends itself to an instantaneous optimization of the current control inputs driving the system (i.e. the camera linear velocity). Less greedy alternatives, in which an optimized trajectory over a finite time horizon is constantly replanned, will also be discussed.
Finally, we will illustrate a recent extension of the active strategy to the problem of estimating the scale of a quadrotor bearing formation in a decentralized way.