A novel approach for the generation of complex humanoid walking sequences based on a combination of optimal control and learning of movement primitives - Clever, Debora; Harant, Monika; Koch, Kai Henning; Mombaur, Katja; Endres, Dominik (Robotics and autonomous systems, 2016)
We combine optimal control and movement primitive learning in a novel way for the fast generation of humanoid walking movements and demonstrate our approach at the example of the humanoid robot HRP-2 with 36 degrees of freedom. The present framework allows for an efficient computation of long walking sequences consisting of feasible steps of different kind: starting steps from a static posture, cyclic steps or steps with varying step lengths, and stopping motions back to a static posture. Together with appropriate sensors and high level decision strategies this approach provides an excellent basis for an adaptive walking generation on challenging terrain. Our framework comprises a movement primitive model learned from a small number of example steps that are dynamically feasible and minimize an integral mean of squared torques. These training steps are computed by solving three different kinds of optimal control problems that are restricted by the whole-body dynamics of the robot and the gait cycle. The movement primitive model decomposes the joint angles, pelvis orientation and ZMP trajectories in the example data into a small number of primitives, which effectively deals with the redundancy inherent in highly articulated motion. New steps can be composed by weighted combinations of these primitives. The mappings from step parameters to weights are learned with a Gaussian process approach, the contiguity of subsequent steps is promoted by conditioning the beginning of a new step on the end of the current one. Each step can be generated in less than a second, because the expensive optimal control computations, which take several hours per step, are shifted to the precomputational off-line phase. We validate our approach in the virtual robot simulation environment OpenHRP and study the effects of different kernels and different numbers of primitives. We show that the robot can execute long walking sequences with varying step lengths without falling, and hence that feasibility is transferred from optimized to generated motions. Furthermore, we demonstrate that the generated motions are close to torque optimality on the interior parts of the steps but have higher torques than their optimized counterparts on the steps boundaries. Having passed the validation in the robot simulator, we plan to tackle the transfer of this approach to the real platform HRP-2 as a next step.