Control Theory seminar | Alex Shum, Optimal Path Planning for Planetary Rovers

MC 5136

Speaker

Alex Shum, University of Waterloo, Waterloo, Ontario

Title

Optimal Path Planning for Planetary Rovers

Abstract

Continuous path planning is a relevant area of research in extraterrestrial exploration, as efficient and safe paths must be found for rovers to traverse their surroundings. The continuous global path planning problem can be formulated as an optimal control problem, where the cost is a function of the environment and properties of the rover. Such a problem can be restated in the form of a static Hamilton-Jacobi-Bellman (HJB) equation. Unfortunately, these equations are difficult to solve analytically, so the solution is often approximated numerically. The environment is discretized and solved on a mesh. The path is not limited to edges of the mesh, but free to travel through the elements of the mesh. In this talk, two algorithms will be discussed. A simpler problem where the cost does not depend on directional weights can be solved with the Fast Marching Method. A more general problem that considers directional weightings can be solved with Ordered Upwind Methods. In both problems, the optimal path is recovered with the use of the solution of the HJB equation. Some extensions to the algorithms will be discussed.