## Gustavo Goretkin

MIT EECS - Draper Laboratory Undergraduate Research and Innovation Scholar

Optimal Motion Planning for Dynamical Systems

2012–2013

Leslie P. Kaelbling

Sample-based motion planners are an effective way to solve difficult motion planning problems and have the property of probabilistic completenessconverging to a solution in the limit with probability one. RRT*, a sample-based algorithm recently developed here at MIT, does even better: it produces optimal trajectories in the limit. However, although RRT* is straightforward to apply to kinematic motion planning problems (where it is possible to control the state of the system directly) dynamical systems (where the state of the system evolves according to a differential equation) are often more challenging. To apply RRT* to these domains, one needs to provide a cost function between states and a way to extend to drive the system from one state toward

another. The effort required to engineer these primitives greatly limits the wide-spread applicability of the algorithm. We are investigating ways to generate this cost function and extension function automatically by applying control theoretic techniques to linear approximations of the dynamics.

Ive worked in the Media Lab, the Biological Engineering Department, and now at CSAIL advancing the state of motion planning

algorithms in the Learning and Intelligent Systems group.