  Safety assurance is critical in the planning and control of robotic systems.
For robots operating in the real world, the safety-critical design often needs
to explicitly address uncertainties and the pre-computed guarantees often rely
on the assumption of the particular distribution of the uncertainty. However,
it is difficult to characterize the actual uncertainty distribution beforehand
and thus the established safety guarantee may be violated due to possible
distribution mismatch. In this paper, we propose a novel safe control framework
that provides a high-probability safety guarantee for stochastic dynamical
systems following unknown distributions of motion noise. Specifically, this
framework adopts adaptive conformal prediction to dynamically quantify the
prediction uncertainty from online observations and combines that with the
probabilistic extension of the control barrier functions (CBFs) to characterize
the uncertainty-aware control constraints. By integrating the constraints in
the model predictive control scheme, it allows robots to adaptively capture the
true prediction uncertainty online in a distribution-free setting and enjoys
formally provable high-probability safety assurance. Simulation results on
multi-robot systems with stochastic single-integrator dynamics and unicycle
dynamics are provided to demonstrate the effectiveness of our framework.
