Drive-by-Logic: Trajectory Generation for Nonholonomic Ground Robots with Signal Temporal Logic Objectives

Autonomous mobile robots are actively applied to execute complex tasks, such as package delivery, autonomous taxiing, and search-and-rescue. Signal Temporal Logic (STL) offers a powerful formalism for such complex tasks. However, designing plans (trajectories) that satisfy tasks formalized by STL grammar, particularly for nonholonomic systems such as a car-like robot or a fixed-wing aircraft, is a challenging problem. This paper proposes a method to generate trajectories for a multi-robot system with car-like robots to perform complex tasks specified with STL grammar. The proposed method solves a nonlinear program (NLP) to construct trajectories with several constant curvature curves that satisfy the specification. In doing so, it also guarantees the kinematic feasibility of the solution trajectories. Extensive simulation studies show that the proposed method finds satisfying solutions <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$4 \times$</tex> faster than a model predictive control baseline. Additionally, it is able to construct trajectories for complex STL specifications that the baseline fails to satisfy.