  We present a case study applying learning-based distributionally robust model
predictive control to highway motion planning under stochastic uncertainty of
the lane change behavior of surrounding road users. The dynamics of road users
are modelled using Markov jump systems, in which the switching variable
describes the desired lane of the vehicle under consideration and the
continuous state describes the pose and velocity of the vehicles. We assume the
switching probabilities of the underlying Markov chain to be unknown. As the
vehicle is observed and thus, samples from the Markov chain are drawn, the
transition probabilities are estimated along with an ambiguity set which
accounts for misestimations of these probabilities. Correspondingly, a
distributionally robust optimal control problem is formulated over a scenario
tree, and solved in receding horizon. As a result, a motion planning procedure
is obtained which through observation of the target vehicle gradually becomes
less conservative while avoiding overconfidence in estimates obtained from
small sample sizes. We present an extensive numerical case study, comparing the
effects of several different design aspects on the controller performance and
safety.
