In autonomous agent systems, memory is an important element to handle agent behaviors appropriately. We present the analysis of memory requirements for robotic tasks including wall following and corridor following. The robotic tasks are simulated with sensor modeling and motor actions in noisy environments. In this paper, control structures are based on finite state machines for memory-based controllers, and we use the evolutionary multiobjective optimization approach with two objectives, behavior performance and memory size. For each task, a quantitative approach to estimate internal states with a different number of sensors is applied and the best controllers are evaluated in several test environments to examine their generalization characteristics and efficiency. Finite state machines with a hierarchy of memory are also compared with feedforward neural networks for the behavior performance.