Learning movement primitives from optimal and dynamically feasible trajectories for humanoid walking

We present a new approach for humanoid gait generation based on movement primitives learned from optimal and dynamically feasible motion trajectories. As testing platform we consider the humanoid robot HRP-2, so far only in simulation. Training data is generated by solving a set of optimal control problems for a minimum-torque optimality criterion and five different step lengths. As the dynamic robot model with all its kinematic and dynamic constraints is considered in the optimal control problem formulation, the resulting motion trajectories are not only optimal but also dynamically feasible. For the learning process we consider the joint angle trajectories of all actuated joints, the ZMP trajectory and the pelvis trajectory, which are sufficient quantities to control the robot. From the training data we learn morphable movement primitives based on Gaussian processes and principal component analysis. We show that five morphable primitives are sufficient to generate steps with 24 different lengths, which are close enough to both dynamical feasibility and optimality to be useful for fast on-line movement generation.