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

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.