We present a mathematical programming-based method for optimal control of nonlinear systems subject to temporal logic task specifications. We specify tasks using a fragment of linear temporal logic (LTL) that allows both finite-and infinite-horizon properties to be specified, including tasks such as surveillance, periodic motion, repeated assembly, and environmental monitoring. Our method directly encodes an LTL formula as mixed-integer linear constraints on the system variables, avoiding the computationally expensive process of creating a finite abstraction. Our approach is efficient; for common tasks our formulation uses significantly fewer binary variables than related approaches and gives the tightest possible convex relaxation. We apply our method on piecewise affine systems and certain classes of differentially flat systems. In numerical experiments, we solve temporal logic motion planning tasks for high-dimensional (10+ continuous state) systems.
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