Constructibility and reachability-based optimal information-aware motion generator

This article introduces a novel framework for addressing an online, information-aware optimal control problem that aims to maximize the informativeness of intermittent noisy sensor data needed for successfully completion of an assigned task while minimizing the detrimental impact of actuation and process noise on the above mentioned information. Central to our approach is the development of new quantitative metrics derived from three fundamental system-theoretic constructs: the constructibility gramian (CG), the reachability gramian (RG), and the cross gramian (XG). The CG captures the quality and quantity of information provided by sensor measurements, the RG measures the information loss due to the influence of noise in the control and system dynamics, and the XG integrates both aspects into a unified representation of information flow within the system. To validate our approach, we conduct an extensive comparative study against two state-of-the-art baseline methods. The evaluation includes simulations of a differential-drive robot tasked with estimating its unknown position using noisy sensor data under varying levels of actuation noise. Our results, supported by statistical analysis, demonstrate that our proposed metrics consistently yield higher information gain and more accurate state estimates. Additionally, we reinforce our findings through real-time experimental tests on a Turtlebot 4 platform, highlighting the practical effectiveness of our method in real-world robotic applications.