Exact Smooth Reformulations for Trajectory Optimization Under Signal Temporal Logic Specifications

Abstract-- We study motion planning under Signal T emporal Logic (STL), a useful formalism for specifying spatial-temporal requirements. We pose STL synthesis as a trajectory optimization problem leveraging the STL robustness semantics. T o obtain a differentiable problem without approximation error, we introduce an exact reformulation of the max and min operators. The resulting method is exact, smooth, and sound. Temporal logics are formal specification languages used to describe complex desired behaviors of autonomous systems.