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This paper proposes a new highly scalable and asymptotically optimal controlsynthesis algorithm from linear temporal logic specifications, called$\text{STyLuS}^{*}$ for large-Scale optimal Temporal Logic Synthesis, that isdesigned to solve complex temporal planning problems in large-scale multi-robotsystems. Existing planning approaches with temporal logic specifications relyon graph search techniques applied to a product automaton constructed among therobots. In our previous work, we have proposed a more tractable sampling-basedalgorithm that builds incrementally trees that approximate the state-space andtransitions of the synchronous product automaton and does not requiresophisticated graph search techniques. Here, we extend our previous work byintroducing bias in the sampling process which is guided by transitions in theB$\ddot{\text{u}}$chi automaton that belong to the shortest path to theaccepting states. This allows us to synthesize optimal motion plans fromproduct automata with hundreds of orders of magnitude more states than thosethat existing optimal control synthesis methods or off-the-shelf model checkerscan manipulate. We show that $\text{STyLuS}^{*}$ is probabilistically completeand asymptotically optimal and has exponential convergence rate. This is thefirst time that convergence rate results are provided for sampling-basedoptimal control synthesis methods. We provide simulation results that show that$\text{STyLuS}^{*}$ can synthesize optimal motion plans for very largemulti-robot systems which is impossible using state-of-the-art methods.

STyLuS*: A Temporal Logic Optimal Control Synthesis Algorithm for Large-Scale Multi-Robot Systems