A solution to the path planning problem via algebraic geometry and reinforcement learning

In this paper, the path planning problem for an unicycle-like mobile robot is considered. By using some results borrowed from algebraic geometry, a technique is given to determine a dynamical system that is affine in the input and whose trajectories tend to a chosen algebraic set independently of the control input. Since this does not guarantee that the corresponding paths of motion are collision free, an optimal control problem is formulated to enforce this behavior, and its approximate solution is determined via integral reinforcement learning. Finally, it is shown how such results can be used to derive a feedback control law for unicycle-like mobile robots.