Abstract
This paper focuses on optimization-based control of multi-aircraft systems that have several mission objectives. Signal Temporal Logic (STL) is used to express the mission specifications that combine temporal and logical constraints. A methodology is presented to construct an optimization problem in the form of Mixed-Integer Linear Programming (MILP) by using the differential flatness property of a nonlinear dynamical system and STL specifications to generate feasible trajectories. Contrary to general implementations of Temporal Logic to discrete-time systems, the proposed method deals with continuous-time systems. It can be used to find optimal control strategies to achieve the assigned tasks for nonlinear dynamical systems without discretizing the system dynamics. As an illustration, we present an air traffic control example. The nonlinear dynamical model for the aircraft is represented as a partially differentially flat system, and the presented method is applied to manage approach control and to solve the arrival sequencing problem. The method is also applied with a quadrotor fleet to show that the method can be used with different multi-agent systems.
Highlights
Mission planning and control of multi-aircraft systems involve several temporal and logical constraints
The Linear Temporal Logic (LTL) specifications are represented as mixed-integer linear constraints to generate optimal control strategy for a discretetime system via Mixed-Integer Programming (MIP)
The desired behavior of a group of agents is specified with variants of Temporal Logic (TL) in the studies [7]–[9] that evaluate the problem in a grid-based environment using discrete abstractions of the system dynamics
Summary
Mission planning and control of multi-aircraft systems involve several temporal and logical constraints. Başpınar et al.: Mission Planning and Control of Multi-Aircraft Systems With STL Specifications in continuous-time It is a sampling-based method without guarantees and it is hard to apply this approach to multi-agent systems. The desired behavior of a group of agents is specified with variants of TL in the studies [7]–[9] that evaluate the problem in a grid-based environment using discrete abstractions of the system dynamics It is common practice in many studies to use discrete abstractions when dealing with temporal logic for multi-agent systems. One of the contributions of this study is that the proposed method generates feasible trajectories in continuous-time that satisfy the tasks described via STL, without discretizing the system dynamics.
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