Andrew H. Miller

Yayun Du, Andrew Miller, M. Khalid Jawed

We explore the locomotion of soft robots in granular medium (GM) resulting from the elastic deformation of slender rods. A low-cost, rapidly fabricable robot inspired by the physiological structure of bacteria is presented. It consists of a rigid head, with a motor and batteries embedded, and multiple elastic rods (our model for flagella) to investigate locomotion in GM. The elastic flagella are rotated at one end by the motor, and they deform due to the drag from GM, propelling the robot. The external drag is determined by the flagellar shape, while the latter changes due to the competition between external loading and elastic forces. In this coupled fluid-structure interaction problem, we observe that increasing the number of flagella can decrease or increase the propulsive speed of the robot, depending on the physical parameters of the system. This nonlinearity in the functional relation between propulsion and the parameters of this simple robot motivates us to fundamentally analyze its mechanics using theory, numerical simulation, and experiments. We present a simple Euler-Bernoulli beam theory-based analytical framework that is capable of qualitatively capturing both cases. Theoretical prediction quantitatively matches experiments when the flagellar deformation is small. To account for the geometrically nonlinear deformation often encountered in soft robots and microbes, we implement a simulation framework that incorporates discrete differential geometry-based simulations of elastic rods, a resistive force theory-based model for drag, and a modified Stokes law for the hydrodynamics of the robot head. Comparison with experimental data indicates that the simulations can quantitatively predict robotic motion. Overall, the theoretical and numerical tools presented in this paper can shed light on the design and control of this class of articulated robots in granular or fluid media.

Sanket Kanjalkar, Ye Zhang, Shreyas Gandlur et al.

In recent years, multiparty computation as a service (MPCaaS) has gained popularity as a way to build distributed privacy-preserving systems. We argue that for many such applications, we should also require that the MPC protocol is publicly auditable, meaning that anyone can check the given computation is carried out correctly -- even if the server nodes carrying out the computation are all corrupt. In a nutshell, the way to make an MPC protocol auditable is to combine an underlying MPC protocol with verifiable computing proof (in particular, a SNARK). Building a general-purpose MPCaaS from existing constructions would require us to perform a costly "trusted setup" every time we wish to run a new or modified application. To address this, we provide the first efficient construction for auditable MPC that has a one-time universal setup. Despite improving the trusted setup, we match the state-of-the-art in asymptotic performance: the server nodes incur a linear computation overhead and constant round communication overhead compared to the underlying MPC, and the audit size and verification are logarithmic in the application circuit size. We also provide an implementation and benchmarks that support our asymptotic analysis in example applications. Furthermore, compared with existing auditable MPC protocols, besides offering a universal setup our construction also has a 3x smaller proof, 3x faster verification time and comparable prover time.

Yayun Du, Andrew Miller, Mohammad Khalid Jawed

A wide range of microorganisms, e.g. bacteria, propel themselves by rotation of soft helical tails, also known as flagella. Due to the small size of these organisms, viscous forces overwhelm inertial effects and the flow is at low Reynolds number. In this fluid-structure problem, a competition between elastic forces and hydrodynamic (viscous) forces leads to a net propulsive force forward. A thorough understanding of this highly coupled fluid-structure interaction problem can not only help us better understand biological propulsion but also help us design bio-inspired functional robots with applications in oil spill cleanup, water quality monitoring, and infrastructure inspection. Here, we introduce arguably the simplest soft robot with a single binary control signal, which is capable of moving along an arbitrary 2D trajectory near air-fluid interface and at the interface between two fluids. The robot exploits the variation in viscosity to move along the prescribed trajectory. Our analysis of this newly introduced soft robot consists of three main components. First, we fabricate this simple robot and use it as an experimental testbed. Second, a discrete differential geometry-based modeling framework is used for simulation of the robot. Upon validation of the simulation tool, the third part of this study employs the simulations to develop a control scheme with a single binary input to make the robot follow any prescribed path.