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）将高层级任务规划与低层级运动规划相结合，使机器人具备有效推理长期动态任务的自主能力。基于优化的TAMP专注于通过目标函数定义目标条件、能够处理开放式目标、机器人动力学及机器人与环境物理交互的混合优化方法。因此，基于优化的TAMP特别适用于解决高度复杂、富含接触的移动与操作问题。本综述对基于优化的TAMP进行了全面回顾，涵盖以下内容：（i）规划领域表示（包括动作描述语言与时序逻辑），（ii）TAMP各组件的个体求解策略（包括AI规划与轨迹优化），以及（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相互作用。本综述特别聚焦于高效求解TAMP的算法结构，尤其是层次化与分布式方法。此外，本综述强调经典方法与当代基于学习的创新技术（如大语言模型）之间的协同作用。同时，本文还探讨了TAMP的未来研究方向，揭示了算法层面与应用层面面临的挑战。