• optimal active sensing control strategies
• optimal estimation

Active sensing plays a crucial role in human cognition, as evidenced by historical and contemporary examples. An archetypal manifestation of active sensing is observed in our ancestors' ability to discern patterns among the stars, a skill that underscores the inherent human capability for pattern recognition and environmental interaction. In modern contexts, such as sports, active sensing is exemplified through the sophisticated interplay of our sensory organs with the environment, facilitating the acquisition of essential information. This process is integrally connected to our actions, as our sensory perceptions (visual, auditory, and tactile) are intrinsically influenced by our physical movements.
Therefore, active sensing consists of two primary processes: perception, the processing and interpretation of sensory information to infer environmental and own states, and action, the strategic exploration of the environment to optimize the acquisition of sensory information.

Two primary challenges emerge in attaining the capability of human-like active sensing in robots to improve task execution. The first challenge involves the quantification of sensory information flow, necessitating the development of precise metrics. The second challenge is the effective integration of these metrics into robotic control architectures, a critical step to enhance the ability of robots in task execution. Therefore, this dissertation addresses these challenges by proposing novel metrics and control strategies.

The initial part of this dissertation focuses on identifying information metrics for robotic systems. I introduce and meticulously examine several metrics based on three fundamental constructs: the Constructibility Gramian, the Reachability Gramian, and the Cross Gramian. This comprehensive evaluation compares these measures against existing information metrics, providing deep insights into the delicate balance between acquisition and loss of information during robotic motion.

The second part of this dissertation addresses the embedding of active sensing mechanisms within robotic systems, utilizing various control architectures to enhance task performance. I present two novel task-oriented control strategies. The first strategy integrates active sensing within a Lyapunov-based Model Predictive Control framework. An information metric is optimized while ensuring task convergence through Lyapunov stability principles. The second strategy introduces an active sensing component within a Model Predictive Control framework through a novel Control Barrier Function constraint. This Control Barrier Function allows for the design and execution of tasks according to the quality and quantity of sensory information available to the robot.

The informativeness of sensor data is critical in machine learning applications within robotics, particularly for building training sets for model learning. This highlights the potential of active sensing in enhancing machine learning processes. Consequently, in the final section of my dissertation, I explore an innovative approach for improving model learning by integrating active sensing techniques, proposing a robust framework that leverages active sensing to enhance the efficiency and efficacy of model learning in robotic applications.