The pneumatic artificial muscle 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 have lots of control problems due to the inherent characteristics, such as hysteresis, creep, high nonlinearities, and so on. 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. A new energy-based nonlinear control method is proposed for 2-link PAM-actuated robots to realize accurate positioning control. First, the dynamic model of 2-link PAM-actuated robots is presented. Further, a new energy storage function is constructed. The overshoots and the terms coupled with control inputs are constrained, which can reduce the unnecessary energy loss while improving the system safety. To our knowledge, the proposed method is the first nonlinear control approach for 2-link PAM-actuated robots, designed and analyzed based upon the original nonlinear dynamics without any linearization, to provide high-performance positioning control with constrained overshoots and eliminated residual oscillations simultaneously. By rigorous analysis, asymptotic stability of the system is proven. Hardware experimental results are presented.