Understanding the Navigation of Robot Morphology Spaces with Local Optima Network Analysis

The task of co-optimising the morphology and control system of an embodied robot using evolutionary approaches has received increased attention in recent years, often using a Compositional Pattern Producing Network (CPPN) to encode the morphology. However, a recurring observation is convergence to a local optima within the morphological space. Due to the tight coupling between morphology and control making analysis difficult, there is currently no clear explanation of why this arises. To gain more insight into this, we propose a method that isolates the morphological component by opti-mising a set of objective functions that only relate to aspects of the morphology, independently of any task, environment or control policy. By applying local optima network analysis (LON) with a range of mutation operators, we are able to study the search space induced by a CPPN formulation (i.e. parameter settings and decoding mechanism) and the ability of a search algorithm to navigate this space. We find that using a set of different mutation operators-which is common when evolving neural networks-may not be necessary: a mutation operator which simply adds nodes to the CPPN or changes the attributes (bias, response, and activation function) of existing CPPN nodes provides the best exploration of the search space. Furthermore, we find that the specific formulation of the CPPN used leads to significant bias in the designs produced when designs are randomly generated, which could have implications for a search algorithm.