The pneumatic artificial muscle (PAM) is a kind of flexible actuators used to simulate the characteristics of human muscles. Robots actuated by PAMs possess compliance and safety, which can achieve satisfactory man–machine interaction control. Nevertheless, such robots actuated by PAMs tend to have lots of control problems due to the inherent characteristics, such as hysteresis, creep, high nonlinearities, and so on, which is not conducive to accurate modeling and motion control. Moreover, most existing control methods do not consider constraining overshoots, etc.; however, based on safety requirements and actual physical constraints, systems with unconstrained overshoots may have potential risks. In this article, a new energy-based nonlinear control method is proposed for 2-link PAM-actuated robots to realize accurate positioning control. For this purpose, first, the dynamic model of 2-link PAM-actuated robots is presented. Further, a new energy storage function is constructed. Additionally, the overshoots and the terms coupled with control inputs are also constrained reasonably, which can reduce the unnecessary energy loss while improving the system safety. To the best of our knowledge, the proposed method is the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">first</i> nonlinear control approach for 2-link PAM-actuated robots which is designed and analyzed based upon the original nonlinear dynamics <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">without</i> any linearization to provide high-performance positioning control with constrained overshoots and eliminated residual oscillations simultaneously. By rigorous analysis, the asymptotic stability of the system is proven. To validate the effectiveness of the proposed method, a series of hardware experimental results are presented based on a self-built 2-link PAM-actuated robot.