  We propose a new algorithm for numerical path tracking in polynomial homotopy
continuation. The algorithm is `robust' in the sense that it is designed to
prevent path jumping and in many cases, it can be used in (only) double
precision arithmetic. It is based on an adaptive stepsize predictor that uses
Pad\'e techniques to detect local difficulties for function approximation and
danger for path jumping. We show the potential of the new path tracking
algorithm through several numerical examples and compare with existing
implementations.
