Generative multi-robot task and motion planning over long horizons

The state of the art practice in robotics planning is to script behaviors manually, where each behavior is typically precomputed in advance. However, in order for robots to be able to act robustly and adapt to novel situations, they need to be able to plan sequences of behaviors and activities autonomously. Since the conditions and effects of these behaviors are tightly coupled through time, state and control variables, many problems require that the tasks of activity planning and trajectory optimization are considered together. There are two key issues underlying effective hybrid activity and trajectory planning: the sufficiently accurate modeling of robot dynamics and the capability of planning over long horizons. Hybrid activity and trajectory planners that employ mixed integer programming within a discrete time formulation are able to accurately model complex dynamics for robot vehicles, but are often restricted to relatively short horizons. On the other hand, current hybrid activity planners that employ continuous time formulations can handle longer horizons but they only allow actions to have continuous effects with constant rate of change, and restrict the allowed state constraints to linear inequalities. This greatly limits the expressivity of the problems that these approaches can solve. In this work we present Scotty, a planning system for hybrid activity and trajectory planning problems. Unlike other continuous time planners, Scotty can solve a broad class of expressive robotic planning problems by supporting convex quadratic constraints on state variables and control variables that are jointly constrained and that affect multiple state variables simultaneously. In order to efficiently generate practical plans for coordinated mobile robots over long horizons, our approach employs recent methods in convex optimization combined with methods for planning with relaxed planning graphs and heuristic forward search. The contributions of this thesis are threefold. First, we introduce a convex, goaldirected scheduling and trajectory planning problem. To solve this problem, we present the ScottyConvexPath planner, which reformulates the problem as a Second Order Cone Program (SOCP). Our formulation allows us to efficiently compute robot