  In this paper, we focus on the problem of shrinking-horizon Model Predictive
Control (MPC) in uncertain dynamic environments. We consider controlling a
deterministic autonomous system that interacts with uncontrollable stochastic
agents during its mission. Employing tools from conformal prediction, existing
works derive high-confidence prediction regions for the unknown agent
trajectories, and integrate these regions in the design of suitable safety
constraints for MPC. Despite guaranteeing probabilistic safety of the
closed-loop trajectories, these constraints do not ensure feasibility of the
respective MPC schemes for the entire duration of the mission. We propose a
shrinking-horizon MPC that guarantees recursive feasibility via a gradual
relaxation of the safety constraints as new prediction regions become available
online. This relaxation enforces the safety constraints to hold over the least
restrictive prediction region from the set of all available prediction regions.
In a comparative case study with the state of the art, we empirically show that
our approach results in tighter prediction regions and verify recursive
feasibility of our MPC scheme.
