Continuous-Time Control Synthesis for Multiple Quadrotors under Signal Temporal Logic Specifications

TL;DR

This paper presents a two-stage control framework for multiple quadrotors that ensures continuous-time satisfaction of STL specifications in constrained environments, combining geometric control, Lyapunov analysis, and mixed-integer convex programming.

Contribution

It introduces a novel integrated control and planning approach that guarantees STL task satisfaction with improved transient performance and reduced conservativeness.

Findings

Optimized gains reduce oscillations and improve transient response.

The framework guarantees STL task satisfaction in constrained environments.

Numerical simulations validate the effectiveness of the proposed method.

Abstract

Continuous-time control of multiple quadrotors in constrained environments under signal temporal logic (STL) specifications is critical due to their nonlinear dynamics, safety constraints, and the requirement to ensure continuous-time satisfaction of the specifications. To ensure such control, a two-stage framework is proposed to address this challenge. First, based on geometric control, a Lyapunov-based analysis of the rotational tracking dynamics is performed to facilitate multidimensional gain design. In addition, tracking-error bounds for subsequent STL robustness analysis are derived. Second, using the tracking-error bounds, a mixed-integer convex programming (MICP)-based planning framework with a backward-recursive scheme is developed. The framework is used to generate reference trajectories that satisfy multi-agent STL tasks while meeting the trajectory requirements imposed by geometric control. Numerical simulations demonstrate that, compared with uniform gains, the optimized multidimensional gains yield less conservative time-varying bounds, mitigate oscillations, and improve transient performance, while the proposed framework ensures the satisfaction of multi-agent STL tasks in constrained environments with provable tracking guarantees.