Hierarchic Entropy: An Information Theoretic Measure of Evolutionary Robotic Behavioral Diversity

This paper investigates the design of information theoretic-based fitness function for embedded evolutionary robotics (ERs). Such fitness relies on the assumption that interesting behaviors result in a high sensorimotor (individual) diversity. The current simple entropy as a diversity metric only considers individuals' differerence but ignores their spatial relationship. The sensorimotor stream can be analyzed to construct a simple directed graph that has unique entry and exit nodes. This paper proposes a hierarchic entropy as a diversity metric by incorporating the simple entropy and the spatial relationship based graph entropy. Maximizing the hierarchic entropy, achieved by on-board evolutionary algorithm, thus defines a self-driven fitness function enforcing the controller visiting diverse sensorimotor states. The proposed algorithm achieves better performance than the published results of other entropy-based methods only relying on simple entropy, without requiring additional computational resources.