Uncalibrated visual servoing using a biased Newton method for on-line singularity detection and avoidance

While in calibrated settings trajectories can be planned so to avoid singular or poorly observable configurations, in uncalibrated visual servoing in general a priori information about singularities (visual or robotic) may be unavailable. Instead we propose a method where trajectories are corrected online to avoid singular and near singular regions. Mathematically this is achieved using a so called space-biased Newton step in a visual servoing with a Broyden type Jacobian estimation. The bias is applied so to first hand use (any) robot redundancy and thus not compromise the visually specified aspects of the trajectory. The closeness to a singular region is measured online from the estimated visual motor Jacobian. We also illustrate how to apply the bias method for simple visual obstacle avoidance. To show the practical applicability of our method we have applied it to Barrett WAM and PUMA560 manipulators and tested both numerous real trajectories, as well as run exhaustive simulations around critical configurations using a simulation model to confirm empirically that both safe and efficient trajectories are chosen around singular regions.