  For robot swarms operating on complex missions in an uncertain environment,
it is important that the decision-making algorithm considers both heterogeneity
and uncertainty. This paper presents a stochastic programming framework for the
vehicle routing problem with stochastic travel energy costs and heterogeneous
vehicles and tasks. We represent the heterogeneity as linear constraints,
estimate the uncertain energy cost through Gaussian process regression,
formulate this stochasticity as chance constraints or stochastic recourse
costs, and then solve the stochastic programs using branch and cut algorithms
to minimize the expected energy cost. The performance and practicality are
demonstrated through extensive computational experiments and a practical test
case.
