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

Abstract

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.

Learning the Noise of Failure: Intelligent System Tests for Robots

“…For details we refer the reader to [12], [13]. The simulation software also includes instances of the Walking Pattern Generator (WPG) [14] and the Stabilization and Inverse Kinematics (SIK) [15] modules to control the humanoid in its virtual environment. For a typical simulation run, highlevel commands are sent to the WPG module to have the robot execute a certain movement (e.g.…”

Fast Approximation of Over-Determined Second-Order Linear Boundary Value Problems by Cubic and Quintic Spline Collocation

“…. The proposed algorithm is used within the walking pattern generation framework of LOLA, see [13] for details. The robot is 1.8 m tall and weights about 60 kg.…”

“…Explaining the technical details of the walking pattern generation framework of LOLA goes beyond the scope of this paper. Instead, the interested reader is referred to [13], in which the application of the proposed algorithm is presented. The publication [13] comes with an accompanying video, see [14], which visualizes the sequential steps of the walking pattern generation pipeline of LOLA.…”

“…Instead, the interested reader is referred to [13], in which the application of the proposed algorithm is presented. The publication [13] comes with an accompanying video, see [14], which visualizes the sequential steps of the walking pattern generation pipeline of LOLA. The simulations and experiments presented in the video show the successful application of our algorithm.…”

“…Lastly, we point out that although (62) describes a very simple system, we also successfully applied the proposed algorithm to the much more complex walking-pattern generation system of our humanoid robot LOLA, cf. [13]. However, the properties and characteristics of the proposed method can be better investigated and explained by means of a less complex test system.…”