  In this paper, we consider the problem of minimum-time optimal control for a
dynamical system with initial state uncertainties and propose a sequential
convex programming (SCP) solution framework. We seek to minimize the expected
terminal (mission) time, which is an essential capability for planetary
exploration missions where ground rovers have to carry out scientific tasks
efficiently within the mission timelines in uncertain environments. Our main
contribution is to convert the underlying stochastic optimal control problem
into a deterministic, numerically tractable, optimal control problem. To this
end, the proposed solution framework combines two strategies from previous
methods: i) a partial model predictive control with consensus horizon approach
and ii) a sum-of-norm cost, a temporally strictly increasing weighted-norm,
promoting minimum-time trajectories. Our contribution is to adopt these
formulations into an SCP solution framework and obtain a numerically tractable
stochastic control algorithm. We then demonstrate the resulting control method
in multiple applications: i) a closed-loop linear system as a representative
result (a spacecraft double integrator model), ii) an open-loop linear system
(the same model), and then iii) a nonlinear system (Dubin's car).
