A Smooth Robustness Measure of Signal Temporal Logic for Symbolic Control

Gilpin, Yann; Kurtz, Vince; Lin, Hai

doi:10.1109/lcsys.2020.3001875

Cited by 64 publications

(66 citation statements)

References 18 publications

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“…This means that for STL specifications written in Postive Normal Form (PNF) [4], if the resulting smooth robustnessρ ϕ is positive, then the signal must satisfy the specification. For further details on this approach, we refer the interested reader to [7]. By replacing ρ ϕ with the smooth approximationρ ϕ , the optimization (3) becomes smooth, and can be solved with gradient-based techniques like SQP.…”

Section: Signal Temporal Logicmentioning

confidence: 99%

“…Smoothness is relatively easy to address: we simply use a smooth approximation of the robustness [7],ρ ϕ . As noted in Section II,ρ ϕ < ρ ϕ for ϕ in PNF, and as k i → ∞,ρ ϕ → ρ ϕ .…”

Section: Differential Dynamic Programming For Signal Temporal Logicmentioning

confidence: 99%

“…So the complexity of our approach is roughly linear in the STL time bound T . (a) SQP approach [7]. Optimization time 22.4s (b) Our approach (DDP).…”

Section: Differential Dynamic Programming For Signal Temporal Logicmentioning

confidence: 99%

“…The scenario shown in Figure 3 represents something of a benchmark problem in the STL planning literature [2], [6], [7]. A robot must visit one of two intermediate targets (blue) and avoid collisions with an obstacle (red) before reaching a goal region (green).…”

Section: A Mobile Robot Motion Planningmentioning

confidence: 99%

“…(15) Again, we compare our proposed approach with a baseline smooth optimization method [7] which uses SQP. Both resulting trajectories, shown in Figure 3, satisfy the specification, but our approach finds a satisfying solution faster (2.2s vs 16.6s).…”

Section: A Mobile Robot Motion Planningmentioning

confidence: 99%

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Trajectory Optimization for High-Dimensional Nonlinear Systems Under STL Specifications

Kurtz

Lin

2021

IEEE Control Syst. Lett.

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Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis problemgenerating a trajectory that satisfies a given specification-can be formulated as a trajectory optimization problem. Unfortunately, the associated cost function is nonsmooth and non-convex. As a result, existing synthesis methods scale poorly to high-dimensional nonlinear systems. In this letter, we present a new trajectory optimization approach for STL synthesis based on Differential Dynamic Programming (DDP). It is well known that DDP scales well to extremely high-dimensional nonlinear systems like robotic quadrupeds and humanoids: we show that these advantages can be harnessed for STL synthesis. We prove the soundness of our proposed approach, demonstrate order-of-magnitude speed improvements over the state-of-the-art on several benchmark problems, and demonstrate the scalability of our approach to the full nonlinear dynamics of a 7 degree-of-freedom robot arm.

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Section: Signal Temporal Logicmentioning

confidence: 99%

Section: Differential Dynamic Programming For Signal Temporal Logicmentioning

confidence: 99%

“…So the complexity of our approach is roughly linear in the STL time bound T . (a) SQP approach [7]. Optimization time 22.4s (b) Our approach (DDP).…”

Section: Differential Dynamic Programming For Signal Temporal Logicmentioning

confidence: 99%

Section: A Mobile Robot Motion Planningmentioning

confidence: 99%

Section: A Mobile Robot Motion Planningmentioning

confidence: 99%

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Trajectory Optimization for High-Dimensional Nonlinear Systems Under STL Specifications

Kurtz

Lin

2021

IEEE Control Syst. Lett.

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Verification-guided Programmatic Controller Synthesis

Wang

Zhu

2023

Lecture Notes in Computer Science

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We present a verification-based learning framework VEL that synthesizes safe programmatic controllers for environments with continuous state and action spaces. The key idea is the integration of program reasoning techniques into controller training loops. VEL performs abstraction-based program verification to reason about a programmatic controller and its environment as a closed-loop system. Based on a novel verification-guided synthesis loop for training, VEL minimizes the amount of safety violation in the proof space of the system, which approximates the worst-case safety loss, using gradient-descent style optimization. Experimental results demonstrate the substantial benefits of leveraging verification feedback for synthesizing provably correct controllers.

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