• active
• control
• optimal
• sensing

The goal of my thesis work consists of the implementation of an online active sensing control in the presence of intermittent measurements. The most used metric to improve the estimation level are the condition number/minimum eigenvalue of the Observability/Construictibility Gramian or the trace of the inverse of the Fisher Information matrix. Other approaches impose constraints on the maximum eigenvalue of the position covariance matrix. Works that consider both process and measurement noises model the system either as a partially observable Markov decision process or propose a sensitivity optimization method. In these cases, however, a metric that directly takes into account process noise is not used. Another technique considers maximizing the largest eigenvalue of the a posteriori covariance matrix obtained by solving the Continuous Riccati Equation but this solution is only valid if an Extended Kalman Filter is used as an observer.
My thesis work proposes an active perception strategy meant to increase the estimation performance of a generic filter for nonlinear systems by planning trajectories that maximize the amount of information gathered by onboard sensors under intermittent measurements.
The chosen metric is a combination of the Construictibility and Reachability gramians. The CG quantifies the richness of the acquired information by onboard sensors while the RG quantifies the effects of process noise in degrading the quality of the collected information. This metrics will reduce the estimation uncertainty not only because along the trajectory the gathered information from noisy sensory feedback is maximized, but also because the degrading effects of the process noise on such information are minimized.
To show the effectiveness of the proposed method, I considered the case of a unicycle that has to reach a final pose from an initial pose. Moreover, it exploits the range measurement w.r.t fixed markers provided by the onboard sensor to estimate its pose.
In order to make as limited as possible the estimation uncertainty and limit the negative effects of both measurement and process/actuation noises, I developed several metrics which are different combination of CG and RG. These metrics exploits CG in the situation of complete observability to maximize the amount of acquired information while in situations of partial or non-observability exploits the RG to limit the negative effects of process/actuation noise on the estimation accuracy.
In the first chapter, some important concepts about Observability and reachability are described.
In the second chapter the adopted technique to model intermittent measurement is detailed.
The third chapter described the optimization tool, CasADi, used to implement the optimal control and a preliminary analysis used for the choice of the cost function is reported.
The fourth chapter contains the online optimization. The final cost functions are tested and compared in term of uncertainty in order to show the benefits of the proposed approach.