Optimization with Temporal and Logical Specifications via Generalized Mean-based Smooth Robustness Measures
arxiv(2024)
Abstract
This paper introduces a generalized mean-based C^1-smooth robustness measure
over discrete-time signals (D-GMSR) for signal temporal logic (STL)
specifications. In conjunction with its C1-smoothness, D-GMSR is proven to be
both sound and complete. Furthermore, it demonstrates favorable gradient
properties and addresses locality and masking problems, which are critical for
numerical optimization. The C^1-smoothness of the proposed formulations enables
the implementation of robust and efficient numerical optimization algorithms to
solve problems with STL specifications while preserving their theoretical
guarantees. The practical utility of the proposed robustness measure is
demonstrated on two real-world trajectory optimization problems: i) quadrotor
flight, and ii) autonomous rocket landing. A sequential convex programming
(SCP) framework, incorporating a convergence-guaranteed optimization algorithm
(the prox-linear method) is used to solve inherently non-convex trajectory
optimization problems with STL specifications. The implementation is available
at https://github.com/UW-ACL/D-GMSR
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