This article presents a neurosymbolic framework to solve motion planning problems for mobile robots involving temporal goals. The temporal goals are described using temporal logic formulas, such as bounded linear temporal logic (LTL) and co-safe LTL to capture complex tasks. The proposed framework trains neural network (NN)-based planners that enjoy strong correctness guarantees when applying to unseen tasks, i.e., the exact task (including workspace, temporal logic formula, and errors in the dynamical models of the robot) is not available during the training of NNs. Our approach to achieving theoretical guarantees and computational efficiency is based on two insights. First, we incorporate a symbolic model into the training of NNs such that the resulting NN-based planner inherits the interpretability and correctness guarantees of the symbolic model. Moreover, the symbolic model serves as a discrete “memory,” which is necessary for satisfying temporal logic formulas. Second, we train a library of NNs offline and combine a subset of the trained NNs into a single NN-based planner at runtime when a task is revealed. In particular, we develop a novel constrained NN training procedure, named formal NN training, to enforce that each NN in the library represents a “symbol” in the symbolic model. As a result, our neurosymbolic framework enjoys the scalability and flexibility benefits of machine learning and inherits the provable guarantees from control-theoretic and formal-methods techniques. We demonstrate the effectiveness of our framework in both simulations and on an actual robotic vehicle and show that our framework can generalize to unseen tasks where state-of-the-art meta-reinforcement learning techniques fail.

中文翻译：

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线性时序逻辑任务的神经符号运动和任务规划

本文提出了一个神经符号框架来解决涉及时间目标的移动机器人的运动规划问题。时间目标是使用时间逻辑公式来描述的，例如有界线性时间逻辑（LTL）和共同安全LTL来捕获复杂的任务。所提出的框架训练基于神经网络（NN）的规划器，这些规划器在应用于未见过的任务时享有强大的正确性保证，即在执行过程中无法获得确切的任务（包括工作空间、时序逻辑公式和机器人动态模型中的错误）。 NN 的训练。我们实现理论保证和计算效率的方法基于两个见解。首先，我们将符号模型纳入神经网络的训练中，使得基于神经网络的规划器继承了符号模型的可解释性和正确性保证。此外，符号模型充当离散的“存储器”，这是满足时序逻辑公式所必需的。其次，我们离线训练一个神经网络库，并在任务揭示时在运行时将训练过的神经网络的子集合并到一个基于神经网络的规划器中。特别是，我们开发了一种新颖的约束神经网络训练程序，称为正式神经网络训练，以强制库中的每个神经网络代表符号模型中的一个“符号”。因此，我们的神经符号框架享有机器学习的可扩展性和灵活性优势，并继承了控制理论和形式方法技术的可证明保证。我们在模拟和实际机器人车辆上展示了我们的框架的有效性，并表明我们的框架可以推广到最先进的元强化学习技术失败的看不见的任务。