For my Ph.D. research, I developed an original, general framework for extracting design principles - relationships between input design parameters and output objectives and constraints that are applicable to many systems - from biological examples using techniques from rigid body dynamics, optimal control, and statistics. I've applied the framework to case studies involving running robots. My long-term goals include generalizing this framework for use in many disciplines, improving the mathematical techniques used in the framework, and automating the principle extraction process with software. By answering high-level, high-impact questions not just for a particular engineering design, but for all designs within a broad class, we can provide engineering designers with the information they need to create complex, high-perfomance systems more efficiently.
During my postdoc at UCLA I've had the opportunity to explore other exciting topics, including control of robotic swarms, ego-action classification of body-worn video using machine learning, and improvements to algorithms including numerical differentiation, removing redundancy from systems of linear equations, and pseudospectral optimal control.
Research
Selected Projects
TELESCOPING JOINTS FOR RUNNING EFFICIENCY Biology uses revolute joints, but engineers have the option of using telscoping joints. There are many potential reasons why engineers might choose one over the other, but is there an inherent effect of their selection on the efficiency of running robots? For hopping or running robots with light legs driven by electric motors, a telescoping knee joint is almost always more efficient than a revolute joint.
FORWARD-BENDING KNEES TO IMPROVE RUNNING EFFICIENCY In biology, we see that bird legs appear to bend in the direction opposite that of humans. While the revolute joint at the middle of a bird's leg is more akin to the human ankle than the knee, the laws of mechanics care little for the word we use to describe the joint, but rather for the relative lengths and mass distributions of leg segments. Which way should robot knees bend? We find that bipedal robots with two-segment legs driven by electric motors are almost always more efficient with a revolute-jointed knee that bends backwards rather than forwards.
TAILS FOR QUADRUPED MANEUVERABILITY Some animals appear to use their tails to improve maneuverability and to perform aerial maneuvers while running. A more common engineering solution to enable rotation is the reaction wheel, which is used to re-orient spacecraft. Which is more effective under the constraints - a long tail with limited travel or a small reaction wheel which can rotate continuously? Using a simple model, we determine how the answer depends on the space available, the mass properties of the machine, and the time available for the maneuver. Specifically, Tails are more effective than reaction wheels for performing rapid roll maneuvers on quadrupedal robots.
ROBOTIC SWARM CONTROL Many tasks for robotic swarms, such as surveillance and crop maintenance, will require that robots be distributed according to some target density function in order for the real work to be performed effectively. In order to keep the robots lightweight and inexpensive, we study simple swarm distribution control laws that require no localization or communication capabilities to implement; all each robot needs to know is the target density at its current position. The idea is simple: choose a random direction, and move with speed inversely proportional to to the square root of the local target density. The consequence is remarkable: the swarm tends toward the target distribution via a process similar to diffusion of heat through a medium.
