Task and Motion Planning (TAMP) integrates high-level task planning and low-level motion planning to equip robots with the autonomy to effectively reason over long-horizon, dynamic tasks. Optimization-based TAMP focuses on hybrid optimization approaches that define goal conditions via objective functions and are capable of handling open-ended goals, robotic dynamics, and physical interaction between the robot and the environment. Therefore, optimization-based TAMP is particularly suited to solve highly complex, contact-rich locomotion and manipulation problems. This survey provides a comprehensive review on optimization-based TAMP, covering (i) planning domain representations, including action description languages and temporal logic, (ii) individual solution strategies for components of TAMP, including AI planning and trajectory optimization (TO), and (iii) the dynamic interplay between logic-based task planning and model-based TO. A particular focus of this survey is to highlight the algorithm structures to efficiently solve TAMP, especially hierarchical and distributed approaches. Additionally, the survey emphasizes the synergy between the classical methods and contemporary learning-based innovations such as large language models. Furthermore, the future research directions for TAMP is discussed in this survey, highlighting both algorithmic and application-specific challenges.

翻译：任务与运动规划（TAMP）通过整合高层任务规划与底层运动规划，赋予机器人自主处理长时程动态任务的能力。基于优化的TAMP聚焦于混合优化方法，该方法通过目标函数定义任务条件，能够处理开放目标、机器人动力学以及机器人与环境间的物理交互。因此，基于优化的TAMP特别适用于解决高度复杂、接触频繁的运动与操作问题。本综述系统回顾了基于优化的TAMP研究，涵盖：（i）规划领域表示方法，包括动作描述语言与时序逻辑；（ii）TAMP各组成部分的独立求解策略，包括人工智能规划与轨迹优化；（iii）基于逻辑的任务规划与基于模型的轨迹优化之间的动态交互机制。本文重点剖析了高效求解TAMP的算法结构，特别是分层式与分布式方法。同时，综述着重探讨了经典方法与当代学习型创新（如大语言模型）的融合路径。最后，本文讨论了TAMP的未来研究方向，着重分析了算法层面与应用层面的核心挑战。