Gramian-based optimal active sensing control under intermittent measurements

This paper proposes an online optimal perceptionaware strategy meant to maximize the information collected along the trajectory via the available measurements while simultaneously minimizing the negative effects of actuation/process noise. Indeed, in several robotic applications, the actuation/process noise is far from negligible and its negative effects are particularly relevant especially with intermittent measurements (e.g. collected by a vision system with limited Field-Of-View). New metrics are proposed as combinations of the Constructability Gramian, for measuring the amount of information collected via the available sensors, and the Reachability Gramian, for measuring the degrading effects of actuation/process noise. Control inputs that optimize those cost functions are provided. To show the effectiveness of our method, we consider one case study involving a unicycle-like vehicle, subject to Gaussian measurement noise and Gaussian or Brownian actuation noise, that estimates its state using intermittent distances from known environmental markers.