This article proposes and evaluates a new safety concept called backup plan
safety for path planning of autonomous vehicles under mission uncertainty.
Backup plan safety is defined as the ability to complete an alternative mission
when the primary mission is aborted. To include this new safety concept in
control problems, we formulate a feasibility maximization problem aiming to
maximize the feasibility of the primary and alternative missions. The
feasibility maximization problem is based on multi-objective model predictive
control (MPC), where each objective (cost function) is associated with a
different mission and balanced by a weight vector. Furthermore, the feasibility
maximization problem incorporates additional control input horizons toward the
alternative missions on top of the control input horizon toward the primary
mission, denoted as multi-horizon inputs, to evaluate the cost for each
mission. We develop the backup plan constrained MPC algorithm, which designs
the weight vector that ensures asymptotic stability of the closed-loop system,
and generates the optimal control input by solving the feasibility maximization
problem with computational efficiency. The performance of the proposed
algorithm is validated through simulations of a UAV path planning problem