Optimal Planning and Control under Signal Temporal Logic Specifications

TL;DR

This paper presents a novel sampling-based planning and control method for nonlinear systems to satisfy complex Signal Temporal Logic specifications, combining local task decomposition, waypoint synthesis, and optimization.

Contribution

It introduces a local-to-global synthesis approach that effectively handles STL specifications for nonlinear systems through safe corridors and satisfaction sets.

Findings

Successfully decomposes STL tasks into local tasks

Generates position trajectories satisfying STL constraints

Demonstrates effectiveness through numerical examples and comparisons

Abstract

This paper addresses the planning and control problem for nonlinear systems under Signal Temporal Logic (STL) specifications. We first decompose an STL task into finite local tasks. A sampling-based method generates sequences of local waypoints to satisfy all local tasks, from which the corresponding satisfaction pair sets are derived. Following a local-to-global strategy, all sequences of local waypoints are synthesized into a global one, based on which a safe corridor is then constructed. Leveraging the safe corridor and the satisfaction pair sets, an optimization problem is formulated and solved to derive a position trajectory that satisfies the STL task. Finally, numerical examples and comparative results are presented to demonstrate the efficacy of the proposed approach.