Observability Analysis and Reduced-Order Observer Design for a Super-Coiled Polymer-Driven Robotic Eye

Abstract

With the aid of a robotic eye platform, several ocular motor disorders such as strabismus can be studied by ophthalmologists and biomedical researchers to better under-stand the biomechanisms of the human eye. Our previous work modeled a 2-DOF robotic eye driven by Super-Coiled Polymer (SCP) artificial muscles and presented a Deep Deterministic Policy Gradient (DDPG) learning-based controller. The control policy requires access to the full system states that include the orientation of the robotic eye and temperature changes of the SCPs. While the angular orientations of the robotic eye can be determined using embedded sensors or image-processing of the visual feed, it is quite laborious and expensive to measure the temperatures of the slender SCP muscles without affecting robot dynamics. To address this problem, this paper designs a linear reduced-order state observer based on the linearization of the nonlinear dynamics of the robotic eye. The linearized model is analytically shown to be fully observable along any trajectory within the operation range. To quantify the local observability of the dynamical system, local unobservability indices and local estimation condition numbers are determined along trajectories of the system states. The performance of the designed observer is tested through simulation in both open-loop and closed-loop foveation control of the robotic eye.