Modeling and Numerical Analysis of Kangaroo Lower Body based on Constrained Dynamics of Hybrid Serial-Parallel Floating-Base Systems

TL;DR

The paper addresses the challenge of accurately modeling Kangaroo’s lower body, a biped with serial-parallel hybrid leg chains, using constrained dynamics for floating-base systems. It develops a general constrained multi-body framework, including passive-to-actuated mappings and a three-step inverse dynamics approach with a QP for contact forces, extended to $SE(3)$ floating-base representations. The study analyzes the Kangaroo lower body, detailing non-linear transmissions and compares inertia metrics against TALOS using the equivalent Cartesian inertia matrix $oldsymbol{ abla}$ and the Centroidal Angular Momentum Matrix (CAMM), showing clear improvements for Kangaroo. Validated through numerical simulations and preliminary real-world experiments, the work also provides software tools (Closed Linkage Library) to support modeling and control of series-parallel hybrid chains, enabling advances toward agile and resilient locomotion in humanoid robots.

Abstract

This paper presents the modeling and numerical analysis of the Kangaroo lower body prototype, a novel bipedal humanoid robot developed and manufactured by PAL Robotics. Kangaroo features high-power linear electric actuators combined with unique serial-parallel hybrid chains, which allow for the positioning of all the leg actuators near the base of the robot in order to improve the overall mass distribution. To model and analyze such complex nonlinear mechanisms, we employ a constrained formulation that is extended to account for floating-base systems in contact with the environment. A comparison is made to demonstrate the significant improvements achieved with TALOS, another humanoid bipedal robot designed by PAL Robotics, in terms of equivalent Cartesian inertia at the feet and centroidal angular momentum. Finally, the paper includes numerical experiments conducted through simulation and preliminary tests performed on the actual Kangaroo platform.

Figures (23)

• Figure 1: Humanoid bipedal robots designed and produced by PAL Robotics since 2004.
• Figure 2: 1DOF RRPR closed mechanism.
• Figure 3: 2DOFs U-2RRPU differential mechanism.
• Figure 4: Prototype of the lower body of the Kangaroo robot.
• Figure 5: Normalized manipulability of the left leg. Position shown at the top, orientation at the bottom. View from the front on the left, and rear view on the right.