Exact Smooth Reformulations for Trajectory Optimization Under Signal Temporal Logic Specifications

TL;DR

This paper introduces an exact, smooth reformulation of STL trajectory optimization that eliminates approximation errors, enabling precise and differentiable motion planning under complex temporal specifications.

Contribution

It presents a novel exact reformulation of max and min operators in STL, ensuring smoothness and accuracy in trajectory optimization without approximation errors.

Findings

The method is exact, smooth, and sound.

Numerical simulations validate practical effectiveness.

Improves precision in STL-based motion planning.

Abstract

We study motion planning under Signal Temporal Logic (STL), a useful formalism for specifying spatial-temporal requirements. We pose STL synthesis as a trajectory optimization problem leveraging the STL robustness semantics. To 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. We validate it in numerical simulations, demonstrating its practical performance.