• Modeled “side contact” and clumping - The simplest gecko-inspired fiber structure consists of very high aspect ratio cylinders that achieve adhesion by bending over to touch an opposing substrate along their sides under the influence of surface forces. Side contact, inspired by but distinct from the adhesion mode found in geckos, explains the adhesion observed in high aspect ratio arrays of carbon nanotubes, silicon nanowires, and molded polymer fibers. Densely packed, high aspect ratio fibers form large stable clumps, which I have analyzed as a function of fiber geometry, lattice structure and spacing, and material properties.
• Modeled adhesion of fibers tipped with thin membranes - The hairs in the gecko adhesive system have spatula-like tips, and are observed to stick only with these tips while adhering to a surface. Moving beyond the side contact model, we have analyzed membrane tips and studied how changing membrane geometry affects relative performance of shear vs normal adhesion.
• Fabricated synthetic fiber arrays - I prototyped fiber arrays with a range of fiber geometries and from a variety of polymers using commercially available alumina and polycarbonate filters as molds. Collaborating with chemical engineers, we applied self assembled monolayers (SAMs) to lower the surface energy and inhibit clumping. Currently we are developing methods to modify tip geometry.
• Developed adhesion testing apparatus - I designed a custom apparatus for performing probe tests on fiber array adhesives. Performance is characterized in terms of normal and, more recently, shear adhesion. The apparatus uses a spherical glass probe to provide a carefully controlled contact on the order of a few hundred square microns and can resolve forces down to about 1 μN. Appreciable adhesion (0.5 N/cm2) has been achieved on samples made entirely of stiff materials.

My research on synthetic gecko adhesives is a key component of the RiSE (Robotics in Scansorial Environments) project, a multi-university effort to design and build a biologically inspired climbing robot weighing about 2 kg. I have been collaborating with Mark Cutkosky’s lab (ME, Stanford University) to integrate synthetic fiber arrays into the shape deposition manufacturing (SDM) process used to fabricate the feet for the RiSE robot. RHex, a robotic hexapod, is the walking and running predecessor of the RiSE robot. My work on gait adaptation in Dan Koditschek’s lab (formerly EECS at University of Michigan, now ESE chair at University of Pennsylvania), using machine learning techniques to identify leg trajectories that work well with the natural dynamics of the system, increased the speed of RHex up to 2.7 m/s on undisturbed terrain, more than twice its previous top speed. A more sophisticated controller (which employed a piecewise linear homeomorphism) permitted tradeoffs between feedback vs. feedforward and centralized vs. decentralized control of the legs in order to improve performance in the presence of disturbances, such as uneven terrain and obstacles.

On an insect-like size scale, I am working in the Fearing lab on a 50mm long, 3 g crawling robot based on the carbon fiber and polyester flexure construction and piezoelectric bending actuators developed for Micromechanical Flying Insect. This crawling millimeter scale robot (millirobot) is both computation and power autonomous. The feet have integrated fiber arrays to provide directional friction.

To aid in future construction of millirobots, we are designing and building a low-cost (< $1000) microassembly system based on COTS parts, flexure based mechanisms made from moldable polymer (with molds that can be reproduced from an original), and open source software.

• Proposed piecewise linear homeomorphisms (PLH) as a computationally effective, finitely parameterized family of nonlinear changes of coordinates. Other approximation techniques generally require that separate approximations be computed for the forward and inverse maps, whereas piecewise linear homeomorphisms are invertible in closed form, requiring only a single model.
• Designed an algorithm, MINVAR, for computing continuous multidimensional PL approximations to data. MINVAR treats both the domain and codomain vertices of the PL function as parameters, which makes the approximation problem nonconvex, but allows the approximation to fit data with regions of varying curvature with fewer parameters.
• Proved local convergence of the MINVAR algorithm under certain conditions and studied the performance numerically outside of those conditions. • Applied MINVAR to a color systems management problem in collaboration with Xerox Corp. The adaptation of my PL representation and algorithms to color management problem resulted in US Patents 6,714,319 and 6,873,432.