Motion planning in dynamic environments with bounded time temporal logic specifications

In this paper, we consider the problem of robotic motion planning that satisfies some bounded time high level specifications. Although temporal logic can efficiently express high level specifications such as coverage, obstacle avoidance, temporal ordering of tasks etc., it fails to address problems with explicit timing constraints. The inherent limitations of Linear Temporal Logic (LTL) to address problems with explicit timing constraints have been overcome by translating the planning problem from the workspace of the robot to a higher dimensional space called spacetime where the existing LTL semantics and grammar are sufficient to mathematically formulate the bounded time high level specifications. A discrete path will be generated, that will meet the specifications with all timing constraints and, at the same time, it will optimize some cost function. A continuous trajectory satisfying the continuous dynamics of the robot will be generated from the discrete path using proper control laws.