Design of optimized soft soles for humanoid robots

We describe a methodology to design foot soles for a humanoid robot given walking gait parameters (i.e. given center-of-mass and zero-moment-point trajectories). In order to obtain an optimized compliant sole, we devised a shape optimization framework which takes - among other inputs, an initial rough (simplified) shape of the sole and refines it through successive optimization steps under additional constraints and a cost function. The shape is optimized based on the simulation of the sole deformation during an entire walking step, taking time dependent input of the walking pattern generator into account. Our shape optimization framework is able to minimize the impact of the foot with the ground during the heel-strike phase and to limit foot rotation in case of perturbations. Indeed, low foot rotation enforces a vertical posture and secures the balance of the humanoid robot. Moreover, weight restriction (formulated as a constraint on the sole volume) is added to our optimization problem.