Successive Convexification for Optimal Control with Signal Temporal Logic Specifications

Abstract

As the scope and complexity of modern cyber-physical systems increase, newer and more challenging mission requirements will be imposed on the optimal control of the underlying unmanned systems. This paper proposes a solution to handle complex temporal requirements formalized in Signal Temporal Logic (STL) specifications within the Successive Convexification (SCvx) algorithmic framework. This SCvx-STL solution method consists of four steps: 1) Express the STL specifications using their robust semantics as state constraints. 2) Introduce new auxiliary state variables to transform these state constraints as system dynamics, by exploiting the recursively defined structure of robust STL semantics. 3) Smooth the resulting system dynamics with polynomial smooth min-and maxfunctions. 4) Convexify and solve the resulting optimal control problem with the SCvx algorithm, which enjoys guaranteed convergence and polynomial time subproblem solving capability. Our approach retains the expressiveness of encoding mission requirements with STL semantics, while avoiding the usage of combinatorial optimization techniques such as Mixed-integer programming. Numerical results are shown to demonstrate its effectiveness. CCS CONCEPTS• Mathematics of computing → Nonconvex optimization; • Theory of computation → Modal and temporal logics; • Computer systems organization → Robotic autonomy.

Lexicographic Mixed-Integer Motion Planning with STL Constraints

“…Although sampling-based motion planning approaches are available for STL (e.g., see [24], [25]), they are often limited to fragments of STL and only exhibit asymptotic optimality. Optimization-based methods, such as mixed-integer approaches [26]- [28] and gradient-based approaches [29]- [31], are commonly used for motion planning with STL constraints. Mixed-integer methods usually lack scalability, while gradient-based methods often require smoothing the STL constraints, altering the underlying problem.…”