Quantifying embodiment towards building better robots based on muscle-driven models

In recent years, researchers have investigated different methods to quantify embodiment for a variety of robotic systems including robotic arms, grippers and legged robots. This paper will discuss some of these methods, focusing on their potential contribution to designing robotic systems based on muscle-driven models. We start with the definition of embodiment based on the relational dynamics between the system and its environments by drawing upon the idea of mutual perturbation and structural coupling between the two. We will discuss how such an understanding can provide potential approaches to quantify embodiment. These includes two information-theoretic measures which are particularly suitable for muscle-driven models. The two methods are based on (i) comparing the controller and behaviour complexity and (ii) Conditional Mutual Information, which compares the difference in distribution of the action conditional on the actuated state and purely on its morphological properties. These methods were used on muscle-driven, biologically realistic hopping models to quantify embodiment at different stages of the hopping gait. The results clearly demonstrate the contribution of morphology of the muscle fibers at different points in the hopping cycle. Furthermore, these methods have been used in latter studies to measure the contribution of embodiment across different levels in a hierarchical control system of a neuro-musculoskeletal model and also to quantify the effects of information cost during various actions in a muscle-driven robotic system. We discuss the practical implications as well as limitations and the future work in the application of these quantification methods.