| الوصف: |
This thesis develops the belief space scheduling framework for scheduling under uncertainty in Stochastic Collection and Replenishment (SCAR) scenarios. SCAR scenarios involve the transportation of a resource such as fuel to agents operating in the field. Key characteristics of this scenario are persistent operation of the agents, and consideration of uncertainty. Belief space scheduling performs optimisation on probability distributions describing the state of the system. It consists of three major components---estimation of the current system state given uncertain sensor readings, prediction of the future state given a schedule of tasks, and optimisation of the schedule of the replenishing agents. The state estimation problem is complicated by a number of constraints that act on the state. A novel extension of the truncated Kalman Filter is developed for soft constraints that have uncertainty described by a Gaussian distribution. This is shown to outperform existing estimation methods, striking a balance between the high uncertainty of methods that ignore the constraints and the overconfidence of methods that ignore the uncertainty of the constraints. To predict the future state of the system, a novel analytical, continuous-time framework is proposed. This framework uses multiple Gaussian approximations to propagate the probability distributions describing the system state into the future. It is compared with a Monte Carlo framework and is shown to provide similar discrimination performance while computing, in most cases, orders of magnitude faster. Finally, several branch and bound tree search methods are developed for the optimisation problem. These methods focus optimisation efforts on earlier tasks within a model predictive control-like framework. Combined with the estimation and prediction methods, these are shown to outperform existing approaches. |