Computational models of collective motion have yielded many insights about the way that groups of animals or simulated particles may move together and self-organize. Recent literature has compared predictions of models with large datasets of detailed observations of animal behavior, and found that there are important discrepancies, leading researchers to reexamine some of the most widely used assumptions. We introduce FlockOpt, an optimization-based, variable-speed, self-propelled particle model of collective motion that addresses important shortcomings of earlier models. In our model, each particle adjusts its velocity by performing a constrained optimization of a locally-defined objective function, which is computed at each time step over the kinematics of the particle and the relative position of neighboring particles. Our model explains how ordered motion can arise in the absence of an explicitly prescribed alignment term and simulations performed with our model exhibit a wide variety of patterns of motion, including several not possible with popular constant-speed models. Our model predicts that variations in speed and heading of particles are coupled due to costs associated with changes in relative position. We have found that a similar coupling effect may also be present in the flight of groups of gregarious bats. The Mexican Free-tailed bat (Tadarida brasiliensis) is a gregarious bat that forms large maternity colonies, containing hundreds of thousands to millions of individuals, in the southwestern United States in the summer. We have developed a protocol for calibrating cameras used in stereo videography and developed guidelines for data collection. Our field protocol can be deployed in a single afternoon, requiring only short video segments of light, portable calibration objects. These protocols have allowed us to reconstruct the three-dimensional flight trajectories of hundreds of thousands of bats in order to use their flight as a biological study system for our model.