A Topological Approach to Path Planning for a Magnetic Millirobot.

We present a path planning strategy for a magnetic millirobot where the nonlinearities in the external magnetic force field (MFF) are encoded in the graph used for planning. The strategy creates a library of candidate MFFs and characterizes their topologies by identifying the unstable manifolds in the workspace. The path planning problem is then posed as a graph search problem where the computed path consists of a sequence of unstable manifold segments and their associated MFFs. By tracking the robot’s position and sequentially applying the MFFs, the robot navigates along each unstable manifold until it reaches the goal. We discuss the theoretical guarantees of the proposed strategy and experimentally validate the strategy.