Controlling the robot with a permanently-updated optimal trajectory, also known as model predictive control, is the Holy Grail of whole-body motion generation. Before obtaining it, several challenges should be faced: computation cost, non-linear local minima, algorithm stability, etc. In this paper, we address the problem of applying the updated optimal control in real-time on the physical robot. In particular, we focus on the problems raised by the delays due to computation and by the differences between the real robot and the simulated model. Based on the optimal-control solver MuJoCo, we implemented a complete model-predictive controller and we applied it in real-time on the physical HRP-2 robot. It is the first time that such a whole-body model predictive controller is applied in real-time on a complex dynamic robot. Aside from the technical contributions cited above, the main contribution of this paper is to report the experimental results of this première implementation.

In this paper, we present a system that enables humanoid robots to imitate complex whole-body motions of humans in real time. In our approach, we use a compact human model and consider the positions of the end-effectors as well as the center of mass as the most important aspects to imitate. Our system actively balances the center of mass over the support polygon to avoid falls of the robot, which would occur when using direct imitation. For every point in time, our approach generates a statically stable pose. Hereby, we do not constrain the configurations to be in double support. Instead, we allow for changes of the support mode according to the motions to imitate. To achieve safe imitation, we use retargeting of the robot's feet if necessary and find statically stable configurations by inverse kinematics. We present experiments using human data captured with an Xsens MVN motion capture system. The results show that a Nao humanoid is able to reliably imitate complex whole-body motions in real time, which also include extended periods of time in single support mode, in which the robot has to balance on one foot.

We present a system that enables a humanoid robot to imitate complex whole-body motions of humans in real time. For recording the human motions, any sensor system capable of inferring the joint angle trajectories can be used. In our work, we capture the human data with an Xsens MVN motion capture system consisting of inertial sensors attached to the body. Our framework converts the human joint angles to the robot's joint angles in real time. Here, we use a mapping between the human's and the robot's joints to ensure feasibility of the motion. The focus of our system lies in ensuring static stability when the motions are executed which is a challenging task, depending on the complexity of the movements. To avoid falls of the robot that might occur when using direct imitation of the joint angle trajectories due to the different weight distribution, we developed an approach that actively balances the center of mass over the support polygon of the robot's feet. At every point in time, our approach ensures that the robot is in a statically stable configuration, i.e., that the ground projection of the center of mass lies within the convex hull of the foot contact points. To achieve this, we apply inverse kinematics given valid foot positions that satisfy the stability criterion and generate the corresponding leg joint angles. In more detail, our system first finds valid positions for the robot's feet by determining a target plane and its orientation, so that the feet can be placed planar and the robot's center of mass is over the support polygon. The new positions of the feet are chosen as the projection on the target plane. Afterwards, the corresponding leg joint angles are calculated via inverse kinematics. To determine whether the configuration is in the double support modus, and if not, which foot is the stance foot, we evaluate the position of the center of mass relative to the feet.