Leonard's background includes feedback control theory, nonlinear dynamics, geometric mechanics, and robotics, where she has made contributions both to theory and to application. She studies and designs complex, dynamical systems comprised of many interacting agents, such as robots, animals, and/or humans that move, sense, and decide together. Her research program emphasizes the development of analytically tractable mathematical models of collective dynamics that provide the systematic means to examine the role of feedback (responsive behavior), network interconnection (who is communicating with whom), heterogeneity (individual differences) in the behavior, learning, and resilience of groups in changing environments.

Leveraging mathematical models, Leonard has studied mechanisms of collective behavior in fish schools, bird flocks, honeybee swarms, and ant colonies, and she has designed rules for distributed robotic vehicles to perform collaborative tasks ranging from search over distributed resource to trash collection in human-populated spaces. She led a large, collaborative, multidisciplinary Adaptive Sampling and Prediction project on the development and demonstration, in Monterey Bay, CA, of an automated and adaptive ocean observing system consisting of a coordinated network of underwater robotic vehicles that move about on their own and carry sensors to collect scientific data about the ocean.