Tendon–sheath artificial muscle (TSAM) is a type of artificial muscle, which is widely used in robotic flexible endoscopies. The characteristics of the tendon force/position transmission were studied recently, but the control issue of the TSAM <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> twist <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> is still barely concerned. In this article, an effective robust control scheme is proposed for the TSAM <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> twist <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> , which achieves satisfactory tracking performance. First, a rigorous model was developed for the TSAM <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> twist <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"/> with consideration of parameters uncertainty and actuator input constraints, moreover, the disturbance of the discontinuous friction (Coulomb friction) was analyzed. Next, by applying some signal operation methods, a nonlinear robust controller was designed. In addition, the stability of the control strategy was proven theoretically by utilizing Lyapunov-based theory. Finally, a series of hardware experiments were conducted on a robotic flexible ureteroscope test-bed. The feasibility of the proposed model, the effectiveness and robustness of the designed control method were extensively validated.