Naomi Ehrich Leonard is the Edwin S. Wilsey Professor of Mechanical and Aerospace Engineering and an associated faculty member of the Program in Applied and Computational Mathematics at Princeton University where she has been since 1994. She is Director of Princeton’s Council on Science and Technology and an affiliated faculty member of the Princeton Neuroscience Institute and Program on Quantitative and Computational Biology.
Leonard is a MacArthur Fellow (2004) and an elected member (2013) of the American Academy of Arts and Sciences. She is a Fellow of the Institute for Electrical and Electronic Engineers (IEEE), the American Society of Mechanical Engineering (ASME), the Society for Industrial and Applied Mathematics (SIAM), and the International Federation of Automatic Control (IFAC). She has also received the Nyquist Lecture Award from the ASME Dynamic Systems and Control Division (2014), the Inaugural Glenn L Martin Medal from the School of Engineering at the University of Maryland (2014), the Inaugural Distinguished Alumni Award from the Electrical and Computer Engineering Deparment at the University of Maryland (2012), the University of California at Santa Barbara Mohammed Dahleh Distinguished Lecture Award (2005), the Automatica Prize Paper Award (1999), the Office of Naval Research Young Investigator Award (1998) and the National Science Foundation CAREER Award (1995). In 2001 she was the Lise Meitner Guest Professor at Lund University, Sweden and in 2007 a Visiting Professor at University of Pisa, Italy. In 2000 she was the Applied Ocean Science and Engineering Visiting Scholar at the Woods Hole Oceanographic Institution (WHOI).
Leonard has delivered public lectures as part of the Princeton University President’s Lecture series and at the Institute for Mathematics and Its Applications (IMA). She has also delivered keynote and plenary lectures at conferences including the IFAC World Congress in 2014, the ASME Dynamic Systems and Control Conference in 2014, the A-Life Conference in 2014, the IFAC Conference on Nonlinear Control Systems (NOLCOS) in 2013, Frontiers in Applied and Computational Mathematics (FACM) in 2011, the American Control Conference (ACC) in 2010, the Canadian Mathematical Society Winter Meeting in 2009, the International Conference on Robot Communication and Coordination (2009), the IEEE International Conference on Robotics and Automation (ICRA) in 2008, the International Symposium on Mathematical Theory of Networks and Systems (MTNS) in 2008, the IFAC Workshop on Navigation, Guidance and Control of Underwater Vehicles in 2008, the SIAM Conference on Control and Its Applications in 2005, the SIAM Conference on Applications of Dynamical Systems in 2003, and the IFAC Nonlinear Control Systems Design Symposium (NOLCOS) in 1998.
Leonard has published well over 140 peer-reviewed articles. She is a member of the Editorial Board of the Princeton University Press, an inaugural senior editor of the IEEE Transactions on Control of Networked Systems. She has served as associate editor for Automatica and SIAM Journal on Control and Optimization. She has co-edited journal special issues, including a special issue in Proceedings of the IEEE in 2012 on “Interaction Dynamics: The Interface of Humans and Smart Machines” and a special issue in Networks and Heterogeneous Media in 2007 on “Modelling and Control of Physical Networks.” She is co-organizer and co-editor of two post-workshop volumes: the First IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control (2000) and the First Block Island Workshop on Cooperative Control (2005). She is co-author of the first book on control using Matlab entitled “Using MATLAB to Analyze and Design Control Systems”, which appeared in 1992 and in second edition in 1995.
Leonard teaches a variety of undergraduate and graduate courses in dynamics and control. She has advised 24 graduate students (MSE and PhD), many of whom have won prestigous fellowships and awards; graduates are now in industry and academia. She has supervised 11 post-doctoral researchers. Former PhD students and post-docs who have gone on to academic positions are now on the faculty at universities that include Virginia Tech, University of Maryland, University of Illinois Urbana-Champaign, University of Toronto, Georgia Institute of Technology, University of Delaware, University of Hawaii, University of Groningen, the Netherlands, University of Southampton, UK, Memorial University of Newfoundland, University of Brussels, Belgium. She has also supervised over 50 undergraduates in their senior thesis work, summer research or lab work, and junior independent work.
Leonard received the B.S.E. degree in mechanical engineering from Princeton University in 1985. From 1985 to 1989, she worked as an engineer in the electric power industry. She received the M.S. and Ph.D. degrees in electrical engineering from the University of Maryland in 1991 and 1994.
Leonard’s main area of research is in the field of nonlinear control and dynamical systems, where she has made contributions both to theory and to application. The field involves designing and analyzing methods for influencing the behavior of complex, dynamical systems using feedback. Feedback refers to adjustments in actions taken by a system in response to measurements of the system’s own state; feedback is critical for performance and robustness in self-regulating engineered systems and, for the very same reasons, feedback is ubiquitous in biological systems at every scale.
In recent years, Leonard has been interested in coordinated control of mobile, multi-agent systems in engineering (robotic teams) and in nature (animal aggregations, human groups). A central goal is to develop rigorous and generalizable methodology to understand collective motion, collective sensing and collective decision making that results from the responsive behavior of individual agents to their environment and their interactions with other agents in the group.
In her master’s work Leonard contributed to control methods for friction compensation in servosystems. In her PhD work she contributed to the control of nonholonomic and underactuated systems (e.g., reorientation of a spacecraft with only two control degrees of freedom); she derived a systematic control methodology based on oscillatory inputs, averaging theory, and geometric methods for left-invariant systems on Lie groups.
At Princeton she developed a body of work, derived from first principles and methods from geometric mechanics, on the modeling, reduction of dynamics, analysis and control of rigid bodies in a fluid with internal or external actuation; she applied this work to autonomous underwater vehicles and marine robotics. This led to seminal work on dynamics and control of buoyancy-driven underwater gliders with actuated internal moving mass. This also led to a collaboration with J. Marsden and A. Bloch and the derivation of the method of controlled Lagrangians for stabilization of underactuated mechanical systems with symmetry. This method restricts to the family of feedback control laws, compatible with available actuation, that yield controlled dynamics derivable from a Lagrangian with kinetic and/or potential energy terms parameterized by the control gains. Energy-based methods can then be used to choose control parameter values that stabilize an otherwise unstable equilibrium point or steady motion.
At about this time Leonard began research into the coordinated control of groups of independent dynamical agents and the development of distributed control methodology for a network of robotic mobile sensors (sensor-equipped autonomous vehicles) that perform better than the sum of its parts in sensing, monitoring, and searching its environment. A central goal was to design adaptive ocean sampling networks for collecting data on ocean properties such as temperature, currents, plankton concentration, for analysis and for assimilation in ocean forecasting models. Methods were derived to yield vehicle network performance despite significant uncertainty and dynamics associated with the coastal ocean. For example, a method based on artificial potentials and virtual bodies was derived (with P. Ogren and E. Fiorelli) to enable a team of vehicles, taking scalar noisy measurements of the environment and moving in a formation, to estimate the gradient of the measured field while also adjusting the shape of the formation to minimize error in the estimate.
This algorithm was successfully demonstrated on a network of autonomous underwater gliders in the month-long, AOSN-II field experiment in Monterey Bay, CA, in August 2003, the first of its kind to integrate, in the field, coordinated glider control with real-time ocean forecasting models; the project was a collaboration with a group of oceanographers and ecologists. Leonard led the Adaptive Sampling and Prediction (ASAP) project which was a MURI project that followed AOSN-II and featured a second major field experiment in Monterey Bay, CA in August 2006. This project focused on sustained, autonomous coordination of the motion of a network of underwater gliders to maximize information in the data collected (equivalently, minimize uncertainty in the prediction of the sampled field). The approach made use of a methodology developed with R. Sepulchre and D. Paley for the systematic derivation of distributed control laws for stabilization of collective motion patterns with limited communication. This method uses a spatial extension of coupled oscillator dynamics and phase and spatial potentials parameterized by synchrony measures and the interconnection graph to yield a large family of stabilizable motion patterns, highly suitable for multi-scale collective sensing problems.
Six Slocum gliders (from WHOI) performed these motion patterns autonomously, serving three ocean forecasting models, for over 24 days continuously in Monterey Bay during August 2006; together with four Spray gliders (from SIO), which moved along optimized trajectories, they provided an unprecedented data set. The Princeton Glider Coordinated Control System (GCCS) software suite was developed to enable the sustained autonomous behavior; it was also used to run virtual pilot experiments in advance of the field experiments for development purposes and to run virtual experiments during the field experiments in forecast flow fields for advance evaluation of sampling plans.
Leonard and her students and colleagues have continued to develop methodologies for autonomous robotic networks to perform collective motion and exploration tasks in an uncertain environment, including for example, networks that can track level sets and generate a contour plot of an unknown, noisy field (with F. Zhang), networks that can perform coverage of a nonuniform field using a method based on cartograms (with F. Lekien), control laws for coordination of rigid body dynamics and systems with otherwise unstable dynamics, and control laws based on dynamics of tensegrity structures.
In parallel with her work on analysis and design of collective behavior in engineered networks, and in collaboration with biologists, Leonard studies collective behavior in animal groups, notably in fish schools and bird flocks where there is no fixed leader, individuals have limitations on sensing and instead rely on social cues from neighbors. She contributes modeling and analytical work to helping to understand how the relatively simple decisions that individuals make in response to their local environment connect to the remarkable behavior observed at the level of the group. She is particularly interested in the role of the interconnection structure on the dynamics of information flow, on the robustness of consensus to uncertainty, and on collective decision making and behavior in groups with heterogeneous information.
Leonard collaborates with cognitive psychologists and neuroscientists to study, model and analyze human decision making and the influence of social feedback on exploration. Models include stochastic differential equations and Markov processes. One central goal is to derive analytically the dynamics and performance of decision making as a function of key parameters that define the individual decision makers and their social interactions. Another central goal is to leverage what is understood about human decision making and the design of robotic behaviors to enable co-robotic systems, notably human-robot decision-making teams that make use of the complementary strengths of humans and programmable machines to jointly address challenging tasks in complex settings.
Leonard is interested in the intersections of art and science and collaborates with choreographer and dance professor S. Marshall on a project called Flock Logic that integrates engineering and dance; they explore from both a scientific and artistic perspective what happens when dancers apply the feedback laws used to model flocking. The artistic goal is to create tools for choreography by leveraging dynamics of multiagent systems with designed feedback and interaction. The engineering goal is to develop insights and design principles for multi-agent systems, such as human crowds, animal groups and mobile robotic networks, by examining the connections between what individual dancers do and what emerges at the level of the group. Together they taught a Princeton Atelier course in Fall 2010 that culminated in two performance events; for more information click here.
Leonard directs the Dynamical Control System Laboratory at Princeton, which features a 21 foot diameter, 8 foot deep, cylindrical freshwater tank for development and testing of underwater single- and multi-vehicle dynamics and control. Four small robotic vehicles can be manually, semi-autonomously or autonomously controlled. A system of overhead cameras connected to image processing and control workstations performs full state estimation for the system and provides a platform for easily implementing control algorithms. An internet-based interface has been developed for human-in-the-loop control of the vehicle network; the human(s) in the loop can be located anywhere there is internet access. A system of cameras connected to a server computer complements this interface by providing real-time streaming video of the tank, thereby enhancing the human operator’s situational awareness. The lab also contains a test-bed on the floor for multi-robot systems as well as a cyber-physical implementation that enables robotic fish to use realtime feedback to control their motion in response to live fish and other environmental features.