Dealing with planning problems with both logical relations and numeric changes in real-world dynamic environments is challenging. Existing numeric planning systems for the problem often discretize numeric variables or impose convex constraints on numeric variables, which harms the performance when solving problems. In this paper, we propose a novel algorithm framework to solve numeric planning problems mixed with logical relations and numeric changes based on gradient descent. We cast the numeric planning with logical relations and numeric changes as an optimization problem. Specifically, we extend syntax to allow parameters of action models to be either objects or real-valued numbers, which enhances the ability to model real-world numeric effects. Based on the extended modeling language, we propose a gradient-based framework to simultaneously optimize numeric parameters and compute appropriate actions to form candidate plans. The gradient-based framework is composed of an algorithmic heuristic module based on propositional operations to select actions and generate constraints for gradient descent, an algorithmic transition module to update states to next ones, and a loss module to compute loss. We repeatedly minimize loss by updating numeric parameters and compute candidate plans until it converges into a valid plan for the planning problem. In the empirical study, we exhibit that our algorithm framework is both effective and efficient in solving planning problems mixed with logical relations and numeric changes, especially when the problems contain obstacles and non-linear numeric effects.

在现实世界的动态环境中处理逻辑关系和数值变化的规划问题是具有挑战性的。针对该问题的现有数值规划系统经常将数值变量离散化或对数值变量施加凸约束，这会损害求解问题时的性能。在本文中，我们提出了一种新的算法框架来解决混合了基于梯度下降的逻辑关系和数值变化的数值规划问题。我们将具有逻辑关系和数字变化的数字规划视为优化问题。具体来说，我们扩展了语法以允许动作模型的参数是对象或实数值，这增强了对真实世界数值效果进行建模的能力。基于扩展的建模语言，我们提出了一个基于梯度的框架，以同时优化数值参数并计算适当的动作以形成候选计划。基于梯度的框架由一个基于命题运算的算法启发式模块组成，用于选择动作并生成梯度下降的约束，一个用于将状态更新到下一个状态的算法转换模块，以及一个用于计算损失的损失模块。我们通过更新数字参数和计算候选计划反复最小化损失，直到它收敛到规划问题的有效计划。在实证研究中，我们展示了我们的算法框架在解决混合了逻辑关系和数值变化的规划问题方面既有效又高效，尤其是当问题包含障碍物和非线性数值效应时。