We are proposing and testing two model-free approaches for locomotion control of a light-weight, compliant, quadruped robot: open loop central pattern generators (CPG), and open and closed- loop dynamical movement primitives (DMP). We are presenting two different knee joint controllers, based on the hypothesis that the passive- compliant leg design might require less control effort for the knee joint control. CPG-control parameters are optimized applying extensive optimization runs using PSO, resulting trot gaits are evaluated for speed and robustness. One derived gait is selected as learning input for a gait controller based on DMP. We design the DMP-based trot gait controller both for open and closed-loop control. For the latter we are feeding back gyroscope and touch sensor signals to modulate the core phase pattern. Found CPG based trot gaits are up to 90cm/sec fast (more than 3 BL/sec). The joint controller assisting the passive compliant knee joint shows gaits with higher speed, and larger hip amplitude. Closed- loop DMP based gaits let the robot handle frontal and sideways slopes, step-downs, and random pushes to the robot’s COM more robustly.