Medical automation and robotics are transforming medical care delivery in that they render accuracy, efficacy, and real-time decision-making. However, the superior systems are founded on safe, clear, and effective data-sharing systems. The blockchain technology has been proven to provide decentralized, immutable and traceable data control and this is highly relevant to healthcare robotics. Nonetheless, traditional blockchain architecture, particularly the one that uses energy-intensive consensus mechanisms like Proof of Work is unsustainable. The chapter discusses blockchain-based energy-saving techniques that can be employed as the basis of sustainable medical automation and robots. It examines the concept of blockchain, energy consumption patterns, and the limitations of conventional architectures. Consensus models and mechanisms, other potential models of consensus, such as Proof of Stake, PBFT and PoA, hybrid blockchain models and Layer-2 solutions that are less energy-consuming and yet provide the security and scalability are mentioned in the discussion. The aim of smart contracts in robotic process automation is also analyzed. The healthcare system will be able to achieve a safe, low-latency and sustainable robot operation through the application of energy-efficient blockchain solutions and support improved patient outcomes and environmental responsibility. The chapter also ends with future research directions and practical implications for actual world deployment.