In this article, we propose two novel experimental design techniques for designing maximally informative experiments to estimate the parameters of nonlinear dynamical vehicle models. The two techniques include a batch design and a sequential design technique that seek to maximize the expected Shannon information gain of the parameter distribution using either an online or offline approach (respectively). We apply and compare the techniques in both simulation and real-world experiments with a wheeled vehicle. In our simulation experiments, both of our proposed designs provide superior Shannon information gains relative to an unoptimized benchmark technique. In our real-world experiments, our sequential design technique achieves superior expected Shannon information gains relative to our batch design technique and the benchmark technique.