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).

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.

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.

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.

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.

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 Movement) 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:

Sensor analysis and optimization to **identify** hybrid dynamical models of motion

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

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

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