  Model predictive control (MPC) with control barrier functions (CBF) is a
promising solution to address the moving obstacle collision avoidance (MOCA)
problem. Unlike MPC with distance constraints (MPC-DC), this approach
facilitates early obstacle avoidance without the need to increase prediction
horizons. However, the existing MPC-CBF method is deterministic and fails to
account for perception uncertainties. This paper proposes a generalized MPC-CBF
approach for stochastic scenarios, which maintains the advantages of the
deterministic method for addressing the MOCA problem. Specifically, the
chance-constrained MPC-CBF (CC-MPC-CBF) technique is introduced to ensure that
a user-defined collision avoidance probability is met by utilizing
probabilistic CBFs. However, due to the potential empty intersection between
the reachable set and the safe region confined by CBF constraints, the
CC-MPC-CBF problem can pose challenges in achieving feasibility. To address
this issue, we propose a sequential implementation approach that involves
solving a standard MPC optimization problem followed by a predictive safety
filter optimization, which leads to improved feasibility. Furthermore, we
introduce an iterative convex optimization scheme to further expedite the
resolution of the predictive safety filter, which results in an efficient
approach to tackling the non-convex CC-MPC-CBF problem. We apply our proposed
algorithm to a 2-D integrator system for MOCA, and we showcase its resilience
to obstacle measurement uncertainties and favorable feasibility properties.
