# Optimal Control to Identify Models of Movement from Distributed Sensors

Automated analysis and design for a system (e.g. human, animal, or robotic) becomes tenable when a model is available. Identifying a model of a system interacting with the environment requires addressing two separate, but related problems:

- robust data generation
- efficient model extraction

The state of the art in reliable data generation requires cumbersome sensor placement and careful sensor calibration. Relaxing both of these requirements is critical to mass adoption of any automated system for model generation. By applying techniques from algebraic topology, we have addressed some of these issues and created a more flexible and accessible calibration scheme.

Human and machine interactions with the world are characterized by discontinuous dynamics that arise due to intermittent contact, for instance when a foot is placed on the ground. Hybrid dynamical systems are expressive enough to model such interactions since they describe the coupled interaction between continuous and discrete dynamics. To aid in identifying these hybrid models, we have worked on developing numerical tools for the optimal control of certain classes of hybrid systems and applied them successfully to find models of gait. Current work is looking at improving the quality of these tools with respect to improved convergence properties and scalability.

### References

T. Moore, R. Vasudevan and A. Biewener, “Outrun or outmaneuver: ecological context informs more broadly applicable biomechanical studies,” in *Society for Integrative and Comparative Biology*, 2015.

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]

R. Vasudevan, A. D. Ames and R. Bajcsy, “Persistent Homology for Automatic Determination of Human-Data Based Cost of Bipedal Walking,” *Nonlinear Analysis: Hybrid Systems*, vol. 7, no. 1, pp. 101-115, 2012. [url]

R. Vasudevan, “Hybrid system identification via switched system optimal control for bipedal robotic walking,” in *International Symposium on Robotics Research*, 2011. [pdf]

E. Lobaton, R. Vasudevan, R. Bajcsy and S. S. Sastry, “A Distributed Topological Camera Network Representation for Tracking Applications,” *IEEE Transactions on Image Processing*, vol. 19, no. 10, pp. 2516-2529, 2010. [url]

A. D. Ames, R. Vasudevan and R. Bajcsy, “Human-data based cost of bipedal robotic walking,” in *Hybrid Systems: Computation and Control*, pp. 153-162, 2011. [pdf]