MEAM Seminar Series Summer 2011

The elastic energy for many biopolymer systems is comparable to the thermal energy at room temperature. Therefore, biopolymers and their networks are constantly under thermal fluctuations. From the point of view of thermodynamics, this suggests that entropy is playing a crucial role in determining the mechanical behaviors of these filaments.

In this talk, we will discuss the entropic elasticity of a polymer and polymer network.  A polymer chain under room temperature has higher tendency to be in its curved configurations, instead of in its straight configuration. This is because curved states are overwhelmingly more probable, with higher entropy. The consequence is that one needs to apply forces to “stretch” the polymer in order that it is in the straight configuration. We will talk about how much thermal fluctuations are there in a polymer network and how much force we need to apply to stretch out the fluctuations and to cause deformation [1-3]. We will also discuss the mechanical properties of a polymer network, including its expansion, shear, tension and buckling behaviors, which reveal the non-trivial effects of the thermal fluctuations. We combine structural mechanics and statistical mechanics to tackle these problems theoretically. The network will be viewed as a mechanical structural characterized by a stiffness matrix. Statistical mechanics is built upon this. We will show that thermal fluctuations of a polymer network are governed by (1) thermal energy, and (2) inverse of the stiffness matrix of the structure [1-3].

For applications, thermal fluctuations are useful in several cases. We will show that entropy itself can drive a biopolymer to migrate in a non-uniform nano-channel [4]. The effective entropic driving force is derived based on a random walk model, and the migration and deformation of the polymer in the channel will be discussed. But, thermal fluctuations are not always desirable. For example, to do genome mapping in a nano-channel, one would like the thermal fluctuations to be as small as possible. We will discuss the internal fluctuations of DNA in nano-channels and show a length-dependent transition between de Genne’s and Odjik’s regimes [5]. If there is time, we will briefly discuss how the fluctuating chain theory can be applied to protein forced unfolding problems [6].

References:

(1) T Su and PK Purohit (2010) Thermomechanics of a heterogeneous fluctuating chain. Journal of the Mechanics and Physics of Solids, 58:164-186.

(2) T Su and PK Purohit (2009) Mechanics of heterogeneous fluctuating elastic rods. The Proceedings of the ASME-IDETC conference. (8 pages)

(3) T Su and PK Purohit (2011) Fluctuating elastic filaments under distributed loads.  Accepted to appear in Molecular and Cellular Biomechanics

(4) T Su and PK Purohit (2011) Entropy driven motion of polymers in non-uniform nanochannels. Accepted to appear in Physical Review E.

(5) T Su, SK Das, X Ming, and PK Purohit (2011) Transition between two regimes describing internal fluctuation of DNA in a nanochannel. PLoS One, 6: e16890

(6) T Su and PK Purohit (2009) Mechanics of forced unfolding of proteins. Acta Biomaterialia, 5:1855-1863.

A modular self-reconfigurable robot can change its form to adapt to its environment; however, the module size limits its spatial resolution and dexterity. This talk will present two novel actuation methods to enable module miniaturization:  external actuation and dielectric elastomer actuators. Using the principle of external actuation, modules reconfigure using forces provided by a controlled environment rather than internal actuators. I will present three experimental systems that demonstrate that inertial forces or gravity enable reliable self-reconfiguration with modules as small as 14mm. For the inertia system, we prove that one configuration can reconfigure to any other configuration by arranging modules in groups. I will also present a general stiffness model for analysis of how the configuration affects the structural stiffness. To realize miniature modules with internal actuators, we study dielectric elastomer actuators due to their superior performance at the mesoscale. I will present experimental results of the development and feasibility of dielectric elastomer actuators for miniature modules.

New manufacturing technologies have allowed engineers to fabricate materials with nanometer-scale features such as planar superlattices and quantum dot superlattices.  Inclusions and nanostructures influence the propagation of mechanical waves that transport heat. These waves exist in quantum units of phonons.  The ability to scatter these vibrations, without preventing electron transport, could improve thermoelectric materials which are used to provide compact, high-reliability cooling devices or to convert heat to electrical power.  The formation and the dissipation of hot spots in integrated circuits are also influenced by the details of phonon scattering events.

To simulate phonon-inclusion scattering events I have developed a new computational method using Molecular Dynamics (MD).  It is capable of determining the amount and spatial distribution of vibrational energy scattered by granular nanometer-scale inclusions in anisotropic bulk crystals.  This information is then incorporated into a new Kinetic Monte Carlo model which performs statistical tracking of phonon scattering to calculate a material's thermal conductivity at and beyond the micron scale.  I will also present a straightforward MD-based method to compute optical phonon lifetimes, simulating phonon-phonon collisions in hot spots on computer chips.

I will then discuss the fabrication methods I use to build micron-scale silicon devices for the creation and study of vibrations.  The presentation will show new plate wave devices and the associated MEMS manufacturing procedure.  These devices are made from single crystals using cleanroom lithographic processes originally developed for microelectronics.  The devices function using surface-mounted piezoelectric transducers that generate mechanical waves.  The waves propagate through a thin silicon membrane, scatter off of carefully-etched perforations, and are detected by output transducers. This allows creation and detection of a transient mechanical wave scattering event.  I will discuss laboratory measurements using these sensors, as well as limitations and advantages of this experimental method.

Recent years have a seen a sharp rise in the body of research on unmanned aerial vehicles (UAVs).  UAVs offer many advantages over conventional ground robots as well as large scale aircraft, because they are able to go where ground robots cannot and perform tasks too difficult or dangerous for humans to achieve.  Most UAV research focuses on fixed-wing vehicles, but the field of unmanned rotorcraft has seen
much attention as of late.  Rotorcraft such as quadrotors have the ability to operate indoors, hover in place for surveillance, and still have the advantages of longer flights outdoors.  This makes quadrotors a
very interesting research platform with much potential for applications.

For many years, almost all UAV research has focused on surveillance, mapping, localization, and other areas with no physical interaction with the world.  This work addresses and explores the areas of manipulation and perching with a quadrotor in an effort to increase the utility of UAVs.  To this end, a series of grippers has been designed to give a quadrotor the ability to pick up objects for transportation as well as perch on surfaces to carry out perch-and-stare objectives, or set up radio relays.  The design of the gripper takes inspiration from the area of climbing robots and penetration into surfaces.  Using a fabrication technique called Shape Deposition Manufacturing, the gripper is made with compliant joints, suspension, and embedded claws.  Shape Deposition manufacturing is a form of lost-wax casting that allows for composite parts with embedded components, variable-compliance and multi-material parts to be fabricated together.  A significant feature of the gripper is passive actuation, where penetration into a surface is triggered simply by contact with a surface, allowing the quadrotor to perch without precise timing of an actuator.  In total, this work discusses the design strategy for the penetration-based gripper, the manufacturing process, and the control of the robot to achieve manipulation and perching tasks.

Although the virial stress, which was originally proposed by Clasius (1870) in the context of pressure in gases, is widely adopted in molecular dynamics simulations of fluids and solids, a rigorous and consistent derivation of stress based on atomic coordinates and momenta has proven to be elusive.  In addition, systematic studies to verify the validity of the virial stress through numerical simulations are lacking.  This dissertation addresses those issues.  A rigorous derivation of stress in molecular dynamics (discrete systems) is presented based upon the principle of equivalence virtual work, i.e. the virtual work of applied tractions (and body forces) in the continuum setting and the virtual work of external forces in the atomistic setting, suitably time averaged over time scales associated with thermal vibrations, are equated.  Inertial effects are accounted for through the association of center-of-mass coordinates with continuum material points.  The analysis applies both for the entire system and for sub-domains that include a sufficient number of atoms to approximate a continuum material point. The result is an expression for stress defined by a time average of terms that depend on atomic coordinates and accelerations as well as on the potential functions describing atomic interaction.  Furthermore, if the interval for time averaging is sufficiently long, the stress can be expressed in terms of atomic coordinates and velocities,  thereby eliminating explicit dependence on particle accelerations.  Numerical simulations are presented for Lennard-Jones solids and various loading cases: i) transients and thermal expansion associated with temperature variations and gradients for both free and constrained boundaries, ii) non-uniform stress fields around inclusions, and iii) cantilever beam vibrations which involve both temporal and spatial gradients. Consistent with the theoretical derivation, the atomic-scale expression involving moderate temporal and spatial averages is shown to agree precisely with continuum notions of stress in each simulation.

Quadrotor helicopters are agile crafts with impressive dynamic capabilities. In this presentation I will describe the multiple quadrotor testbed used at the GRASP Lab at the University of Pennsylvania and several projects that have been conducted in this space. I will describe a couple different trajectory generation methods which enable flight through narrow windows, robust perching on vertical surfaces, and dynamically optimal flight through thrown hula hoops. I will also describe a control method for multiple quadrotors rigidly attached to the same payload which enables cooperative transport. Finally, I will present some recent work involving teams of quadrotors autonomously building 3-D structures from simple modular pieces.

Trussed structures are prevalent in everyday life. We use truss construction for the interior structural support of large buildings (Eiffel Tower or power transmission towers) as well as for temporary scaffolding to support workers and materials along the exterior. These structures are usually assembled on-site by human workers. However, there are many instances when construction of these structures is better suited for robots. These situations include environments with extreme temperature, high toxicity (e.g. nuclear incidents) or structurally unsafe areas (e.g. collapsed buildings). In these instances, more automated approaches are needed to build these structures.

In this presentation, I will describe the robotic construction infrastructure used in the GRASP Lab. With the limitations and constraints of this infrastructure, I will develop an algorithm for constructing truss-like cubic structures without holes from simple modular elements. In order to expand the class of cubic structures to those that contain holes, I will introduce another algorithm, which is capable of hole closure. Finally, I will generalized this approach for a larger class of lattice types including tetrahedral lattices.

Search-based techniques have been widely used in robot path planning for finding optimal trajectories in configuration spaces. They have the advantages of being complete, optimal (up to the metric induced by the discretization) and efficient (in low dimensional problems), even in complex environments. Continuous techniques, on the other hand, lending concepts from differential and algebraic geometry and topology, have the ability to exploit specific structures in the original configuration space and help in solving a host of different problems that rarely come under the scope of graph-search based techniques. We propose three new methods that will let us bring these two separate techniques under one umbrella. First, using tools from algebraic topology we synthesize differential forms whose integrals encode  topological information underlying the solution path and lets us impose topological constraints on the planning problems. Second, we show how metric information can be used along with search-based techniques for creating Voronoi tessellations in coverage and exploration problems. In particular, we use entropy as a metric for multi-robot exploration and coverage of unknown or partially known non-convex environments. Finally, in multi-robot constrained planning problems we exploit the product structure in the high dimensional configuration space that let us combine the strengths of graph search methods and gradient descent algorithms in complementary directions and develop a more efficient, scalable algorithm.

A major goal of modern robotics research is to enable systems capable of dealing with the uncertainty and unpredictability of the real world. As humans, we often take for granted the ease and speed with which we accomplish everyday manipulation tasks, such as picking up a wine glass from a table. Neuroscientists have found convincing evidence that both kinesthetic cues (limb position) and haptic information (touch) play critical roles when humans perform these physical tasks. Curiously, haptic sensing still receives comparatively little attention in autonomous robotics.

This talk presents several of the advances we have made in interpreting and using haptic cues to improve robot task performance. Information from a variety of mechanical sensors is carefully integrated to synthesize signals that resemble the haptic sensing channels commonly found in the human hand. By analyzing this information in the context of the manipulation task and the kinesthetic state of the system, we have been able to demonstrate high-performance sensing and acting with autonomous robots such as the Willow Garage PR2.