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

-- Ensuring continuous-time control of multiple quadrotors in constrained environments under signal temporal logic (STL) specifications is challenging due to nonlinear dynamics, safety constraints, and disturbances. This letter proposes a two-stage framework to address this challenge. First, exponentially decaying tracking error bounds are derived with multidimensional geometric control gains obtained via differential evolution. These bounds are less conservative, while the resulting tracking errors exhibit smaller oscillations and improved transient performance. Second, leveraging the time-varying bounds, a mixed-integer convex programming (MICP) formulation generates piecewise Bézier reference trajectories that satisfy STL and velocity limits, while ensuring inter-agent safety through convex-hull properties. Simulation results demonstrate that the proposed approach enables formally verifiable multi-agent coordination in constrained environments, with provable tracking guarantees under bounded disturbances. I. INTRODUCTION As drone technology progresses, quadrotors are increasingly required to execute complex tasks in confined environments--particularly narrow passages and strict terminal zones [1]. In this context, signal temporal logic (STL) offers a formal language to define tasks over continuous signals with explicit time semantics.