Robust Metric Hybrid Planning in Stochastic Nonlinear Domains Using Mathematical Optimization

Abstract

The deployment of automated planning in safety critical systems has resulted in the need for the development of robust automated planners that can (i) accurately model complex systems under uncertainty, and (ii) provide formal guarantees on the model they act on. In this paper, we introduce a robust automated planner that can represent such stochastic systems with metric specifications and constrained continuous-time nonlinear dynamics over mixed (i.e., real and discrete valued) concurrent action spaces. The planner uses inverse transform sampling to model uncertainty, and has the capability of performing bi-objective optimization to first enforce the constraints of the problem as best as possible, and second optimize the metric of interest. Theoretically, we show that the planner terminates in finite time and provides formal guarantees on its solution. Experimentally, we demonstrate the capability of the planner to robustly control four complex physical systems under uncertainty.