This paper investigates an optimal control strategy for the dynamic locomotion of a simplified planar compliant half-circular legged monopod model. We first present a novel planar leg model which incorporates rolling kinematics and a new compliance model, motivated by the use of similar leg designs on existing platforms. Two locomotion tasks, moving at a prescribed horizontal velocity and a one-shot jump to maximum possible height or length, are then investigated within this model. The designs of two high-level optimal controllers for these tasks are then described to investigate the performance and stability of resulting behaviors, based on the optimization of trajectory parameters for a closed-loop low-level Proportional-Derivative controller at the hip. Our results show that with these optimized parameters the robot can achieve stable locomotion at a desired horizontal velocity and can successfully jump over and across a specified height and length. Finally, the composition of objective functions capturing multiple criteria is also investigated for the one-shot jump task. (C) 2014 Elsevier Ltd. All rights reserved.