Embodied systems can update policies, world models, skills, and executable programs from deployment experience, allowing one interaction to benefit later tasks. When a system also revises and reuses its data-acquisition, feedback, or learning procedures, experience changes the process that produces capability, introducing recursive self-improvement. This paper surveys research in physical AI through the connection between persistent capability and its improvement process. We first explain the functional distinction between learner updates and improvers, then compare policy learning, imagined experience, memory and skill accumulation, and executable harnesses. These approaches connect to revisions of curricula, rewards, and research programs in different ways. Contact validity, recovery, retention, and resource costs determine whether the resulting gains accumulate during continued deployment. An L0-L3 rubric distinguishes task-local adaptation, persistent capability gain, inherited process revision, and verified improver gain. Representative benchmarks and within-study contrasts relate these distinctions to existing results. We further propose common-data and interactive comparisons that evaluate reference and revised improvers from shared learner starts, separating the use of experience from its acquisition. This perspective connects the diverse methods, physical operating conditions, and evaluation evidence, underpinning embodied RSI. A comprehensive list of studies in this survey is available at https://github.com/nkd-lkz/physical-ai-rsi-survey.

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