In recent years, the design, fabrication, and control of robotic systems inspired by biology has gained renewed attention due to the potential improvements in efficiency, maneuverability, and adaptability with which animals interact with their environments. Motion studies of biological systems such as humans, fish, insects, birds and bats are often used as a basis for robotic system design. Often, these studies are conducted by recording natural motions of the system of interest using a few high-resolution, high-speed cameras. Such equipment enables the use of standard methods for corresponding features and producing three-dimensional reconstructions of motion. These studies are then interpreted by a designer for kinematic, dynamic, and control systems design of a robotic system. This methodology generates impressive robotic systems which imitate their biological counter parts. However, the equipment used to study motion is expensive and designer interpretation of kinematics data requires substantial time and talent, can be difficult to identify correctly, and often yields kinematic inconsistencies between the robot and biology.

To remedy these issues, this dissertation leverages the use of low-cost, low-speed, low-resolution cameras for tracking bat flight and presents a methodology for automatically learning physical geometry which restricts robotic joints to a motion submanifold identified from motion capture data. To this end, we present a spatially recursive state estimator which incorporates inboard state correction for producing accurate state estimates of bat flight. Using these state estimates, we construct a Gaussian process dynamic model (GPDM) of bat flight which is the first nonlinear dimensionality reduction of flapping flight in bats. Additionally, we formulate a novel method for learning robotic joint geometry directly from the experimental observations. To do this, we leverage recent developments in learning theory which derive analytical-empirical potential energy fields for identifying an underlying motion submanifold. We use these energy fields to optimize a compliant structure around a single degree-of-freedom elbow joint and to design rigid structures around spherical joints for an entire bat wing. Validation experiments show that the learned joint geometry restricts the motion of the joints to those observed during experiment.