Online optimal active sensing control

This paper deals with the problem of active sensing control for nonlinear differentially flat systems. The objective is to improve the estimation accuracy of an observer by determining the inputs of the system that maximise the amount of information gathered by the outputs over a time horizon. In particular, we use the Observability Gramian (OG) to quantify the richness of the acquired information. First, we define a trajectory for the flat outputs of the system by using B-Spline curves. Then, we exploit an online gradient descent strategy to move the control points of the B-Spline in order to actively maximise the smallest eigenvalue of the OG over the whole planning horizon. While the system travels along its planned (optimized) trajectory, an Extended Kalman Filter (EKF) is used to estimate the system state. In order to keep memory of the past acquired sensory data for online re-planning, the OG is also computed on the past estimated state trajectories. This is then used for an online replanning of the optimal trajectory during the robot motion which is continuously refined by exploiting the state estimation obtained by the EKF. In order to show the effectiveness of our method we consider a simple but significant case of a planar robot with a single range measurement. The simulation results show that, along the optimal path, the EKF converges faster and provides a more accurate estimate than along other possible (non-optimal) paths.