可微三值时序逻辑语义与多项式代理网络
Differentiable Ternary Temporal Logic Semantics with Polynomial Surrogate Networks
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中文总结 AI 辅助
本文提出一种三值时序逻辑的概率松弛方法，通过多项式代理网络实现可微的值与梯度计算，并用于机器人控制综合，在两个操纵器任务中验证了其有效性。
中文摘要 AI 辅助
时序逻辑为设计者提供了一种形式化推理工具，用于指定自主系统的复杂时空行为和任务。针对根据时序逻辑规范进行控制综合，已有许多技术，涵盖包括机器人学在内的多种系统。然而，绝大多数实现仅限于布尔时序逻辑。布尔时序逻辑没有内在机制来量化弃权（不执行），其判定要么是确定的 \textit{True}，要么是确定的 \textit{False}。最近的研究表明，三值逻辑是推理机器人行为的一种有效形式体系，能够自然地用 \textit{Unknown} 文字对不确定性进行分类。三值时序逻辑仍处于起步阶段，现有工作仅限于线性系统的综合和监控。本文提出了一种三值时序逻辑的概率松弛方法，允许通过同一网络进行值和梯度计算，同时在实际数据上保留精确判定。松弛后的网络可用作基于梯度的控制综合中的目标函数，适用于离线和在线机器人控制应用。我们通过两个机器人操纵器任务展示了我们框架的实用性，一个离线任务和一个在线任务，涉及中间检查和子任务排序，以展示我们方法在正确和及时执行方面的优势。
英文摘要
Temporal logic provides designers a formal reasoning tool for specifying complex spatio-temporal behaviors and tasks for autonomous systems. Many techniques exist for control synthesis according to temporal logic specifications, spanning a large variety of systems, including robotics. However, the vast majority of implementations are limited to Boolean temporal logics. Boolean temporal logic does not have an innate mechanism for quantifying abstention, rather verdicts are either definitively \textit{True} or \textit{False}. Recent work demonstrates that ternary logic is a capable formalism for reasoning about robotic behaviors, with the natural ability to classify uncertainty with the \textit{Unknown} literal. Ternary temporal logic is still in its infancy, with work limited to synthesis for linear systems and monitoring. This work proposes a probabilistic relaxation of ternary temporal logic that allows for value and gradient computation through the same network while retaining exact verdicts on actual data. The relaxed network can be used as an objective in gradient-based control synthesis for both offline and online robotic control applications. We demonstrate the utility of our framework with two robotic manipulator tasks, one offline and one online, involving intermediate checking and sequencing of subtasks to demonstrate the benefit of our approach in terms of correct and timely execution.
发表机构
- Institute for Systems Research, University of Maryland（马里兰大学系统研究所）
机构由 AI 辅助整理，请以论文原文为准。
