Energy-information tradeoffs in motion and sensing for target localization

Recent study in behavioral ecology reveal that certain species trade-off energy and information during various routine activities. This paper explores a similar tradeoff between sensing and motion of mobile agents tasked with target localization. Specifically, the goal is to balance the quality of information collected by sensing agents with the kinetic energy expended by their motion relative to the target. Following common practice, the determinant of the Fisher Information Matrix is chosen to represent the information-quality, while the kinetic energy is quantified by the usual Newton´s laws. We argue that the quality of information has a form reminiscent of potential energy, and with such interpretation, we mimic the basic laws of mechanics by assuming the conservation of the total energy, which is the sum of the potential energy and kinetic energy. In this framework, we formulate an optimal path problem that aims at increasing the information quality while reducing the kinetic energy along the path of the agents. To solve this problem, we apply the calculus of variations, only to discover that the optimal solutions (paths) satisfy the Euler-Lagrange equations that are well known in classical mechanics. This realization suggests that the resulting trajectories may exhibit some well-known phenomena in classical mechanics. Simulation results support this hypothesis.