  This article proposes a new safety concept: backup plan safety. The backup
plan safety is defined as the ability to complete one of the alternative
missions in the case of primary mission abortion. To incorporate this new
safety concept in control problems, we formulate a feasibility maximization
problem that adopts additional (virtual) input horizons toward the alternative
missions on top of the input horizon toward the primary mission. Cost functions
for the primary and alternative missions construct multiple objectives, and
multi-horizon inputs evaluate them. To address the feasibility maximization
problem, we develop a multi-horizon multi-objective model predictive path
integral control (3M) algorithm. Model predictive path integral control (MPPI)
is a sampling-based scheme that can help the proposed algorithm deal with
nonlinear dynamic systems and achieve computational efficiency by parallel
computation. Simulations of the aerial vehicle and ground vehicle control
problems demonstrate the new concept of backup plan safety and the performance
of the proposed algorithm.
