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.
View on arXiv