The human shoulder, with its glenohumeral joint, tendons, ligaments, and muscles, allows for the execution of complex tasks with precision and efficiency. However, current robotic shoulder designs lack the compliance and compactness inherent in their biological counterparts. A major limitation of these designs is their reliance on external sensors like rotary encoders, which restrict mechanical joint design and introduce bulk to the system. To address this constraint, we present a bio-inspired antagonistic robotic shoulder with two degrees of freedom powered by self-sensing hydraulically amplified self-healing electrostatic actuators. Our artificial muscle design decouples the high-voltage electrostatic actuation from the pair of low-voltage self-sensing electrodes. This approach allows for proprioceptive feedback control of trajectories in the task space while eliminating the necessity for any additional sensors. We assess the platform's efficacy by comparing it to a feedback control based on position data provided by a motion capture system. The study demonstrates closed-loop controllable robotic manipulators based on an inherent self-sensing capability of electrohydraulic actuators. The proposed architecture can serve as a basis for complex musculoskeletal joint arrangements.