Quintic Spline Collocation for Real-Time Biped Walking-Pattern Generation with variable Torso Height

This paper presents our newest findings in planning a dynamically and kinematically feasible center of mass motion for bipedal walking robots. We use a simplified robot model to incorporate multi-body dynamics and kinematic limits, while still being able to meet hard real-time requirements. The vertical center of mass motion is obtained through interpolation of a quintic spline whose control points are projected onto the kinematically feasible region. Subsequently, the horizontal motion is computed from multi-body dynamics which we approximate by solving an overdetermined boundary value problem via spline collocation based on quintic polynomials. The proposed algorithm is an improvement of our previous method, which used a parametric torso height optimization for vertical and cubic spline collocation for horizontal components. The novel center of mass motion improves stability, especially for stepping up and down platforms. Moreover, the new method leads to a less complex overall algorithm since it removes the necessity of manually tuned parameters and strongly simplifies the incorporation of boundary values. Lastly, the new approach is more efficient, which leads to a significantly reduced total runtime. The proposed method is validated through successfully conducted simulations and experiments on our humanoid robot platform, LoLA.