### We are currently seeking research engineers, postdocs, undergraduate, and graduate students with a strong interest in human modeling, optimization, or systems theory. If you are interested in any of the following projects, please email Professor Vasudevan.

## Semi-Autonomous Control

### Research Goals

- Devise control architectures within a vehicle that safely share control authority with the driver
- Build a driver model and utilize real-time optimization tools
- Opportunities to collaborate with industry leaders and validate ideas in real world scenarios with the University of Michigan's Transportation Research Institute

### References

- V. Shia, Y. Gao,
**R. Vasudevan**, K. Campbell, T. Lin, F. Borrelli and R. Bajcsy, “Semiautonomous Vehicular Control Using Driver Modeling,”*IEEE Transactions on Intelligent Transportation Systems*, vol. 15, no. 6, pp. 2696-2709, November 2014. [url] **R. Vasudevan**, V. Shia, Y. Gao, R. Cervera-Navarro, R. Bajcsy and F. Borrelli, “Safe semi-autonomous control with enhanced driver modeling,” in*American Control Conference*, pp. 2896-2903, 2012. [pdf]

## Fall Prediction and Prevention

### Research Goals

- Design experimental protocols to perturb human and robot locomotion
- Validate the utility of optimization tools capable of measuring the likelihood of falling
- Develop tools to design and automate therapeutic regimens that mitigate the likelihood of falling
- Opportunities to collaborate with the University of Michigan School of Kinesiology and work on bipedal robotics

### References

- V. Shia,
**R. Vasudevan**, R. Bajcsy and R. Tedrake, “Convex Computation of the Reachable Set for Controlled Polynomial Hybrid Systems,” in*IEEE Conference on Decision and Control*, 2014. [pdf] - A. Majumdar,
**R. Vasudevan**, M. M. Tobenkin and R. Tedrake, “Convex Optimization of Nonlinear Feedback Controllers via Occupation Measures,”*International Journal of Robotics Research*, vol. 33, pp. 1209-1230, August 2014. [url]

## Optimization for Hybrid Systems

### Research Goals

- Formalize and translate diagnostic techniques into computable system properties
- Develop real-time, scalable optimization methods that provably compute useful system properties
- Opportunities to collaborate with the University of Michigan's Department of Mathematics and School of Kinesiology, work on bipedal robotics, and with the University of Michigan's Transportation Research Institute and industry leaders

### References

- S. Burden, H. Gonzalez,
**R. Vasudevan**, R. Bajcsy and S. S. Sastry, “Metrization and Simulation of Controlled Hybrid Systems,”*IEEE Transactions on Automatic Control*, vol. 60, no. 9, September 2015. [preprint] **R. Vasudevan**, H. Gonzalez, R. Bajcsy and S. S. Sastry, “Consistent Approximations for the Optimal Control of Constrained Switched Systems -- Part 1: A Conceptual Algorithm,”*SIAM Journal on Control and Optimization*, vol. 51, no. 6, pp. 4463-4483, 2013. [url]**R. Vasudevan**, H. Gonzalez, R. Bajcsy and S. S. Sastry, “Consistent Approximations for the Optimal Control of Constrained Switched Systems -- Part 2: An Implementable Algorithm,”*SIAM Journal on Control and Optimization*, vol. 51, no. 6, pp. 4484-4503, 2013. [url]