Graph-Based Convexification of Nested Signal Temporal Logic Constraints for Trajectory Optimization

Optimizing high-level mission planning constraints is traditionally solved in exponential time and requires to split the problem into several ones, making the connections between them a convoluted task. This paper aims at generalizing recent works on the convexification of Signal Temporal Logic (STL) constraints converting them into linear approximations. Graphs are employed to build general linguistic semantics based on key words (such as Not, And, Or, Eventually, Always), and super-operators (e.g., Until, Implies, If and Only If) based on already defined ones. Numerical validations demonstrate the performance of the proposed approach on two practical use-cases of satellite optimal guidance using a modified Successive Convexification scheme.