Embodied Robot Manipulation in the Era of Foundation Models: Planning and Learning Perspectives

Recent advances in vision, language, and multimodal learning have significantly accelerated progress in robotic foundation models, with robotic manipulation remaining one of the most challenging embodied tasks. Its difficulty lies in integrating perception, semantic understanding, task reasoning, physically grounded action generation, and reliable execution. This survey examines robotic manipulation from an algorithmic perspective and organizes recent learning-based approaches through a unified abstraction of high-level planning and low-level action modeling. At the high level, we extend the classical notion of task planning to include reasoning over language, code, affordances, geometric constraints, and 3D representations. At the low level, we present a learning-paradigm-oriented taxonomy of learning-based action models, covering input modeling, latent learning, and policy learning. Within this abstraction, foundation models contribute either by generating structured planning artifacts that are instantiated as constraints or latent inputs for downstream action generation, or by directly modeling executable actions and trajectories. Finally, we summarize open challenges and future directions related to scalability, generalization, data efficiency, multimodal physical interaction, and safety. Together, this survey provides a structured view of the design space and emerging trends in foundation models for robotic manipulation.