A Mission Based Fault Reconfiguration Framework for Spacecraft Applications

We present a Markov Decision Process (MDP) framework for computing post-fault reconfiguration policies that are optimal with respect to a discounted cost. Our cost function penalizes states that are unsuitable to achieve the remaining objectives of the given mission. The cost function also penalizes states where the necessary goal achievement actions cannot be executed. We incorporate probabilities of missed detections and false alarms for a given fault condition into our cost to encourage the selection of policies that minimize the likelihood of incorrect reconfiguration. To illustrate the implementation of our proposed framework, we present an example inspired by the Far Ultraviolet Spectroscopic Explorer (FUSE) spacecraft with a mission to collect scientific data from 5 targets. Using this example, we also demonstrate that there is a design tradeoff between safe operation and mission completion. Simulation results are presented to illustrate and manage this tradeoff through the selection of optimization parameters. Nomenclature F = Vector of fault flags (F = {f , f , ..., f }). P = Vector of probabilities of correctness of fault flags (P = {p, p, ..., p}). ) ( i MD P = Probability of missed detection for fault flag i. P(MD) = (1 – p)(1 – f ) ) ( i FA P = Probability of false alarm for fault flag i. P(FA) = (1 – p)f . O = Vector of abstracted sensor observations (O = {o, o, ..., o}). sw = Scalar index of system hardware configuration of the spacecraft. c = Scalar index of active control law for the spacecraft. A = Vector of binary flags indicating active/inactive mission related actions (A = {a, a, ..., a}). B = Vector of binary flags indicating complete/incomplete mission objectives (B = {b, b, ..., b}). S = Set of MDP states (S = {s1, s2, ..., sN}). Where si = {Ai, Bi, Fi, Pi, swi, ci} or si = {Ai, Bi, Fi, Oi, swi, ci}. M = Set of actions for MDP (M = {μ1, μ2, ..., μk}). ) ( i s R = Reward function for state si. ) ( i s V = Value function for state si. ) , | ( i k j s s T μ = Probability of transitioning from state si to sj by executing action μk. γ = discount factor for reward computation. ) ( i s G = Penalty function for reconfiguration under uncertain detection flags. λ β α , , = Positive constant weighting factors. 1 θ = Probability of success of the switching reconfiguration action. 2 θ = Probability of success of the control law reconfiguration action.