Hybrid pneumatic–electric actuators (HPEAs) are redundant actuators that combine the large force, low bandwidth characteristics of pneumatic actuators with the large bandwidth, small force characteristics of electric actuators. It has been shown that HPEAs can provide both accurate position control and high inherent safety, due to their low mechanical impedance, making them a suitable choice for driving the joints of assistive, collaborative, and service robots. If these characteristics are mathematically modeled, input allocation techniques can improve the HPEA’s performance by distributing the required input (force or torque) between the redundant actuators in accordance with each actuator’s advantages and limitations. In this paper, after developing a model for a HPEA-driven system, three novel model-predictive control (MPC) approaches are designed that solve the position tracking and input allocation problem using convex optimization. MPC is utilized since the input allocation can be embedded within the motion controller design as a single optimization problem. A fourth approach based on conventional linear controllers is included as a comparison benchmark. The first MPC approach uses a model that includes the dynamics of the payload and pneumatics; and performs the motion control using a single loop. The latter methods simplify the MPC law by separating the position and pressure controllers. Although the linear controller was the most computationally efficient, it was inferior to the MPC-based controllers in position tracking and force allocation performance. The third MPC-based controller design demonstrated the best position tracking with RMSE of 46%, 20%, and 55% smaller than the other three approaches. It also demonstrated sufficient speed for real-time operation.