Deformation Invariant Multi-View Tracking

By assuming a bound on the total amount of movement between frames, we construct an algebraic descriptor which we can prove is able to track a deforming region (even under lighting changes).

Convex Optimization to Determine the Likelihood of Falling

The compass gait walker (left) has a 4D state space representation which we have plotted in 2D by overlaying the swing leg limit cycle (top right) and stance leg limit cycle (bottom right). We can compute the region of attraction to each portion of the limit cycle (gray) using a single convex program.

Identified Hybrid Dynamical Model of Gait

Each circle represents a distinct dynamical model. Using switched system optimal control, we can automatically identify the control input and the specific dynamical model that is active at any instant of time from kinematic data.

Real-Time Driver Modeling and Intervention

An example of the automated, real-time intervention that we construct when the driver is distracted and the vehicle is in danger. This video was constructed using a personalized driver model that was built after observing an individual in a driving simulator for an hour.

Probability Densities Propagated thru Rigid Body Dynamics

Our numerical methods for advection are able to work on manifolds as illustrated on the sphere at t = 0 (left), t = 5 (middle), and t = 10 (right). This example can serve as a surrogate for understanding the evolution of probability densities under rigid body dynamics.

Virtual Environments for Collaboration and Training

By constructing a real-time, 360 degree reconstruction of people at geographically distributed locations, teleimmersion is a useful tool for teaching exercises and providing rehabilitation. In the picture, two dancers (one that is physically present) are actually collaborating together on a virtual dance performance.

The ROAHM (Robotics and Optimization for the Analysis of Human Motion) Lab seeks to understand and improve human and robot interaction with one another and with the environment. We devise techniques to diagnose unsafe behavior and construct controllers that can then safely intervene or aid in retraining. Our approach can be divided into three categories:

Identification

Sensor analysis and optimization to identify hybrid dynamical models of motion

Analysis

Automated analysis of dynamical models using optimization, robotics, and system theory

Design

Numerical tools to design semi-autonomous control architectures for safe interaction

You can learn more about previous and ongoing research projects here.