  Temporal logic is a concise way of specifying complex tasks. But motion
planning to achieve temporal logic specifications is difficult, and existing
methods struggle to scale to complex specifications and high-dimensional system
dynamics. In this paper, we cast Linear Temporal Logic (LTL) motion planning as
a shortest path problem in a Graph of Convex Sets (GCS) and solve it with
convex optimization. This approach brings together the best of modern
optimization-based temporal logic planners and older automata-theoretic
methods, addressing the limitations of each: we avoid clipping and passthrough
by representing paths with continuous Bezier curves; computational complexity
is polynomial (not exponential) in the number of sample points; global
optimality can be certified (though it is not guaranteed); soundness and
probabilistic completeness are guaranteed under mild assumptions; and most
importantly, the method scales to complex specifications and high-dimensional
systems, including a 30-DoF humanoid. Open-source code is available at
https://github.com/vincekurtz/ltl_gcs.
