  Safety in the face of uncertainty is a key challenge in robotics. We
introduce a real-time capable framework to generate safe and task-efficient
robot motions for stochastic control problems. We frame this as a
chance-constrained optimisation problem constraining the probability of the
controlled system to violate a safety constraint to be below a set threshold.
To estimate this probability we propose a Monte--Carlo approximation. We
suggest several ways to construct the problem given a fixed number of
uncertainty samples, such that it is a reliable over-approximation of the
original problem, i.e. any solution to the sample-based problem adheres to the
original chance-constraint with high confidence. To solve the resulting
problem, we integrate it into our motion planner VP-STO and name the enhanced
framework Chance-Constrained (CC)-VPSTO. The strengths of our approach lie in
i) its generality, without assumptions on the underlying uncertainty
distribution, system dynamics, cost function, or the form of inequality
constraints; and ii) its applicability to MPC-settings. We demonstrate the
validity and efficiency of our approach on both simulation and real-world robot
experiments.
