Risk analysis for nondeterministic mission planning and sequencing

In this paper, we address the dilemma of planning in the presence of uncertainty - the problem of scheduling events where some events might have nondeterministic durations. Real world planning and scheduling problems are almost always difficult. Planning and scheduling of events with a mixture of deterministic and nondeterministic durations is particularly challenging. The idea of scheduling events into a conflict-free plan becomes obscure and intangible when event durations are not known in advance - there is no guarantee that when the plan is executed, the scheduled events would not violate any pre-defined rules and constraints, and the resource usages would not exceed their maximum allowable limits. This dilemma of not being able to a priori quantify the likelihood of achieving a conflict-free plan in the presence of uncertainty usually results in an overly conservative plan where resources are under utilized. Making use of some standard communication link analysis techniques to characterize communication system performance, to support tradeoffs, and to manage the operational risks associate with the link usage, we instigate a probabilistic description of event durations and introduce the notion of risk in terms of probability that the plan fails to execute successfully, which we denote as Pp. We attempt to define a rational and systematic approach to weight risk against efficiency by iteratively applying constrained optimization algorithms and Monte Carlo simulations to the plan. We also derive a simple upper bound of PF for a given plan, which is independent of the optimization algorithm. This risk management approach allows planners to quantify the risk and efficiency tradeoff in the presence of uncertainty, and help to make forward-looking choices in the development and execution of the plan. Another emphasis of this paper is to demonstrate that the general criteria of optimality and rules and constraints for event planning can be described mathematically in terms of linear and non-linear functions and inequalities. This allows the use of customized and commercial off-the-shelf (COTS) constraint optimization algorithms to generate conflict-free plans. The results described in this paper are applicable to many general planning and scheduling problems. However the emphasis of this work is on mission planning and sequencing of spacecraft events with a mixture of deterministic and nondeterministic durations. Mission planning and sequencing is a critical component for mission operations. It provides a mechanism for scientists and engineers to operate the spacecraft remotely from the ground. It translates the science intents and spacecraft health and safety requests from the users into mission plans and sequences. After a rigorous process validating the plan, the plan will be transmitted to the spacecraft for its execution. Usually mission planning and sequencing and its validation are time consuming and costly operations. We apply the aforementioned methodology for formulating and optimizing both deterministic and nondeterministic sequence events planning. We demonstrate this approach with examples of scheduling science and engineering activities for mission operations.