Robust, Goal-directed Plan Execution with Bounded Risk

There is an increasing need for robust optimal plan execution for multi-agent systems in uncertain environments, while guaranteeing an acceptable probability of success. For example, a fleet of unmanned aerial vehicles (UAVs) and autonomous underwater vehicles (AUVs) are required to operate autonomously for an extensive mission duration in an uncertain environment. Previous work introduced the concept of a model-based executive, which increases the level of autonomy, elevating the level at which systems are commanded. This thesis develops model-based executives that reason explicitly from a stochastic plant model to find the optimal course of action, while ensuring that the probability of failure is within a user-specified risk bound. This thesis presents two robust mode-based executives: probabilistic Sulu or p-Sulu, and distributed probabilistic Sulu or dp-Sulu. The objective for p-Sulu and dp-Sulu is to allow users to command continuous, stochastic multi-agent systems in a manner that is both intuitive and safe. The user specifies the desired evolution of the plant state, as well as the acceptable probabilities of failure, as a temporal plan on states called a chanceconstrained qualitative state plan (CCQSP). An example of a CCQSP statement is "go to A through B within 30 minutes, with less than 0.001% probability of failure." p-Sulu and dp-Sulu take a CCQSP, a continuous plant model with stochastic uncertainty, and an objective function as inputs, and outputs an optimal continuous control sequence, as well as an optimal discrete schedule. The difference between p-Sulu and dp-Sulu is that p-Sulu plans in a centralized manner while dp-Sulu plans in a distributed manner. dp-Sulu enables robust CCQSP execution for multi-agent systems. We solve the problem based on the key concept of risk allocation, which achieves tractability by allocating the specified risk to individual constraints and mapping the result into an equivalent deterministic constrained optimization problem. Risk allocation also enables a distributed plan execution for multi-agent systems by distributing the risk among agents to decompose the optimization problem. Building upon the risk allocation approach, we develop our first CCQSP executive, p-Sulu, in four spirals. First, we develop the Convex Risk Allocation (CRA) algorithm, which can solve a CCQSP planning problem with a convex state space and a fixed schedule, highlighting the capability of optimally allocating risk to individual constraints. Second, we develop the Non-convex Iterative Risk Allocation (NIRA) algorithm, which can handle non-convex state space. Third, we build upon NIRA a full-horizon CCQSP planner, p-Sulu FH, which can optimize not only the control sequence but also the schedule. Fourth, we develop p-Sulu, which enables the real-time execution of CCQSPs by employing the receding horizon approach. Our second CCQSP executive, dp-Sulu, is developed in two spirals. First, we develop the Market-based Iterative Risk Allocation (MIRA) algorithm, which can control a multiagent system in a distributed manner by optimally distributing risk among agents through the market-based method called tatonnement. Second and finally, we integrate the capability of MIRA into p-Sulu to build the robust model-based executive, dp-Sulu, which can execute CCQSPs on multi-agent systems in a distributed manner. Our simulation results demonstrate that our executives can efficiently execute CCQSP planning problems with significantly reduced suboptimality compared to prior art. Thesis Supervisor: Prof. Brian C. Williams