UCLA Applied Mathematics Laboratory

The Applied Mathematics Laboratory at UCLA was started in May of 2005.

Location 3355/3363 Mathematical Sciences

Phone: 310-206-2430 (X62430)


Lab Director: Andrea Bertozzi (UCLA Math)

Postdocs: Nebo Murisic (UCLA Math), Dirk Peschka (visiting from WIAS Berlin), Martin Short (UCLA Math)

PhD Students: Matthew Mata

Undergraduates: Paul Latterman, Samantha Mersuro, Brian Le, Trystan Koch, Jake Boricious, Edwin Huang, Benjamin Irvine, Max Gonzales

Experimental Collaborators: A. E. Hosoi (MIT MAE), C. J. Kim (UCLA MAE), Emilio Frazzoli (UCLA MAE - now at MIT)

Lab Alumni

Slurry Flow Experiment

We are conducting a slurry flow experiment to produce behavior like in these photos (below) obtained in Peko Hosoi's lab at MIT. To the right is a picture of Chi Wey with the new apparatus. Glass beads of a uniform size are mixed into a less dense viscous fluid. The resulting slurry is poured into a reservoir at the top of an inclined plane. A controlled amount of the slurry is allowed to flow through a gate down the incline. At low inclination angles and concentrations, the particles tend to settle out of the mixture and stick to the surface of the incline, leaving a clear fluid to flow down the slope (left panel). At intermediate angles and concentrations, a well-mixed slurry flows down the slope (middle panel) producing the characteristic fingering pattern seen in visous films. At high inclination angles and particle concentrations (right panel) the beads tend to collect at the front of the film; their presence drastically changes the dynamics of the contact line, supressing fingering and producing a pronounced ridge. We recently published a theory for this mechanism in a paper in Phys. Rev. Lett. 2005. The theory involves shocks in a 2X2 system of conservation laws. The new apparatus will allow us to perform a quantitative comparison between theory and experiment.

Robotic Swarms

During summer 2004, we went to CalTech where we used Richard Murray's Multi-vehicle wireless testbed , which includes the fully autonomous Kelly vehicle shown to the right. That vehicle has an onboard laptop computer, two ducted fans for self-propulsion, and it wears a hat with a bar code on top that is read by an overhead vision tracking system. Information from the vision system is fed back to the vehicle through wireless networking. Many Kellys can communicate on the floor of the testbed through this network.

We developed and tested algorithms for boundary tracking and swarming on that platform. UCLA students Chung Hsieh and Bao Nguyen presented papers at the ACC 2005 conference on this work.

  • Experimental Validation of an Algorithm for Cooperative Boundary Tracking by Chung H. Hsieh, Zhipu Jin, Daniel Marthaler, Bao Q. Nguyen, David J. Tung, Andrea L. Bertozzi, and Richard M. Murray, American Control Conference 2005, June 8-10, Portland OR, pp. 1078-1084
  • Virtual attractive-repulsive potentials for cooperative control of second order dynamic vehicles on the Caltech MVWT by B. Q. Nguyen, Y.-L. Chuang, David J. Tung, C. Hsieh, Z. Jin, L. Shi, D. Marthaler, A. L. Bertozzi, and R. M. Murray, American Control Conference 2005, June 8-10, Portland OR, pp. 1084-1089
  • Link to video clip of Kelly vehicles doing cooperative boundary tracking.

    The MVWT platform inspired us to build our own platform at UCLA. Below we describe our first generation testbed.

    Kevin Leung, Chung Hsieh, and Rick Huang built the vehicles platform. Our testbed arena is a 5X8 area; requiring much smaller vehicles than the CalTech Kellys. We have developed a system using radio controlled cars. The algorithms are programmed off-board and controls are sent to the individual cars using different radio frequencies. We have an overhead vision tracking system modelled on the one at CalTech. Here is a schematic of the vehicles platform.

    On left is a photo of the group and the first generation of vehicles. Left to right - Maria D'Orsogna, Chung Hsieh, Kevin Leung, Yao-Li Chuang, and Rick Huang. On the right is a close up photo of the first generation of vehicles. Here is a videoclip of a demo involving area servicing by three vehicles. In the video, a student uses a stick to flash target images to the overhead cameras. One of the vehicles must then visit that target site. Otherwise the vehicles maintain a holding pattern. This testbed will be used to test cooperative control algorithms for vehicles, including problems involving path planning and dynamic visibility, boundary tracking, and formation control. The mathematics involves stability of large systems of coupled ODEs, geometric curvature dependent path planning, Hamiton Jacobi equations, and level set methods.