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.

任务和运动规划（TAMP）综述了基于优化的TAMP的规划领域表示、解决方法以及逻辑规划和模型优化之间的相互作用等内容，并强调高效解决TAMP的算法结构，包括分层和分布式方法，并突出了经典方法与当代大语言模型等学习创新之间的协同性，并讨论了TAMP的未来研究方向和应用挑战。

基于优化的任务和动作规划综述：从经典到学习方法