A practical path-planning algorithm for a simple car: a Hamilton-Jacobi approach

We consider the problem of optimal path planning of a forward moving simple car with a minimum turning radius (a Dubins´ car), in a known environment possibly containing inpenetrable obstacles. We model this problem in the Hamilton-Jacobi partial differential equation framework, and provide a finite difference numerical method to solve it. Furthermore, we introduce and demonstrate a scheme based on this framework to steer a bidirectional micro-car on a testbed.