in terms of speed, joint motion ranges, required torques and impacts. Humanoid locomotion also involves changing contacts with the environment, which have to be properly chosen. Stability control of humanoid locomotion is one of the biggest problems, since bio-inspired bipedal walking cannot be performed in a statically stable way, but must be dynamically stable. The precise definition of dynamic stability of human walking is still unknown, and up to now, many humanoid robots still apply the well-known Zero Moment Point (ZMP) criterion [1] instead, which is very convenient to use, but results in more conservative gaits. Motion generation for humanoid robots can be divided into two main categories: motion remapping and model-based generation. In the first case, walking motions from humans are recorded via motion capturing systems, then they can be transferred to the robot by taking into account robot specific constraints such as physical constraints and stability criteria. The recorded motions can be first processed as motion primitives and then concatenated to generate complex motions, such as achieved on the robot HRP-2 (Humanoid Robotics Projects, Kawada) [2], or directly transferred to the robot by means of reduced models and adjustments of end effector positions, as achieved on the JAXON and CHIDORI robots [3]. In the case of model-based motion generation, the most common method is to use reduced models together with the ZMP criterion. Reduced models are for example the Linear Inverted Pendulum (LIPM) [4] or the table cart [5], which allowed many robots to achieve stable walking, such as on HRP-2 [6], by means of Nonlinear Model Predictive Control (NMPC), on the compliant humanoid robot CoMan [7] and iCub [8]. In all these cases, the whole-body posture is computed by means of inverse kinematics matching the desired end effector positions computed with the dynamics of the reduced models. The main reason for which reduced models are still widely used is because they allow for fast online control. However, it is known that due to the many assumptions that are introduced due to the use of such models, the whole-body dynamics of the robot is not well exploited, and the motions often appear over-constrained and not very natural. Another, more bio-inspired way of motion generation is to use optimization, or to be more precise, optimal control, based on whole-body models of the robots. Optimality is often considered to be a guiding principle of nature, and movements that are performed frequently such as everyday motions or trained motions tend to be optimal with respect to some optimality criterion. By the use of mathematical optimization in the generation of motions for humanoid robots, this biological optimization process is mimicked. The optimization criteria used can be either biologically inspired (by analyzing the optimality criteria of humans or other biological systems, e.g., by inverse optimal control [9]), or technically motivated. In addition, optimization helps to solve the feasibility and the redundancy issues of walking. It generates motions that are feasible with respect to all constraints that can be formulated in a detailed whole-body model of the robot and of the motion task. From all redundant solutions of a particular task, it selects the one that is optimal with respect to the chosen optimization criterion. In addition, optimization techniques can be used to kinematically adjust humanoid motions to recorded human motions, taking the different geometry into account (see, e.g., [10]). See [11] for a general overview of optimization in the context of humanoids. Optimal control has previously been used to generate challenging motions using whole-body models for robots such as HRP-2 [12; 13; 14; 15; 16; 17; 18]. In an approach that is situated between whole-body optimization and motion generation by reduced models, optimization of template models has been used for generating walking motion of humanoid robots in challenging scenarios [19].