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.
Vision-Language-Action (VLA) models remain brittle in long-horizon, contact-rich manipulation because success-only imitation provides little supervision for execution drift, while failed rollouts are often discarded. We introduce RePO-VLA, a recovery-driven policy optimization framework that assigns distinct roles to success, recovery, and failure trajectories. RePO-VLA first applies Recovery-Aware Initialization (RAI), slicing each corrective suffix into a new episode so corrective actions depend on the current adverse state rather than the preceding failure. It then learns a Progress-Aware Semantic Value Function (PAS-VF), aligning spatiotemporal trajectory features with instructions and successful references. The resulting labels salvage useful failure prefixes via reliability decay, while low-value labels mark drift and terminal breakdowns, teaching differences among nominal, failed, and corrective actions. The data engine turns adverse states into planner-generated or human-collected corrective rollouts, teaching recovery to the success manifold. Value-Conditioned Refinement (VCR) trains the policy to prefer high-progress actions. At deployment, a fixed high-value token biases actions toward the learned success manifold without online failure detectors or heuristic retries. We introduce the Failure-Recovery Benchmark (FRBench), with standardized error injection and recovery-focused evaluation. Across simulated and real-world bimanual tasks, RePO-VLA improves robustness, raising adversarial success from 20% to 75% on average and up to 80% in scaled real-world trials. Code and video results are available at https://1018weijia.github.io/RePO-VLA-Web/.