<p>This paper addresses the consensus problem in multi-agent systems (MASs) with input saturation and unknown disturbances. The study introduces energy-efficient consensus control protocols that, unlike existing methods, work under more relaxed assumptions: only bounded disturbances are required, without exact bounds or dynamic models. This feature makes the approach less conservative and more practical for real applications. Our approach only assumes bounded disturbances, without needing exact bounds or dynamics, so the controller does not rely on worst-case designs and achieves lower energy consumption. The proposed protocols ensure state consensus in systems with actuator saturation and actuator velocity disturbances, as well as systems with input saturation and state disturbances. Simulation studies demonstrate that the proposed control laws achieve consensus while keeping the control effort significantly lower than existing methods. Simulation results further show that the proposed controllers reduce total power from 497.23 to 138.99 in the first case and from 256.31 to 7.91 in the second case, while achieving comparable or better consensus accuracy.</p>