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# Andy Borum

NSF Postdoctoral Associate (Visiting Assistant Professor)

### Departments/Programs

- Mathematics

## Research

Dynamical systems, optimization, mechanics, control, robotics

My research focuses on dynamical systems, optimization, and their applications in mechanics, control, and robotics. Within control theory, I study symmetries in optimal control problems and their effects on sufficient conditions for optimality. I then use these results from optimal control theory to formulate and analyze models of deformable objects. I am particularly interested in the stability properties of thin and constrained elastic structures. Finally, I use these models to derive methods for robotic manipulation of elastic objects, such as deformable cables and thin surfaces.

## Courses

### Spring 2021

## Publications

- When is a helix stable? (with T. Bretl), Phys. Rev. Lett. 125 (2020), 088001.
- Infinitely long isotropic Kirchhoff rods with helical centerlines cannot be stable (with T. Bretl), Phys. Rev. E 120 (2020), 023004.
- Reduction of sufficient conditions for optimal control problems with subgroup symmetry (with T. Bretl), IEEE Trans. Autom. Control 62 (2017), 3209-3224.
- Sufficient conditions for a path-connected set of local solutions to an optimal control problem (with T. Bretl), SIAM J. Appl. Math. 76 (2016), 976-999.
- The free configuration space of a Kirchhoff elastic rod is path-connected (with T. Bretl), IEEE Int. Conf. Robot. Autom. (2015), 2958-2964.