Angular momentum analysis on Karate roundhouse kicks: a longitudinal case study
Authors: Jan C. L. Lau, Christian Mele, Jonathan Feng-Shun Lin, Katja Mombaur
Organizations: BioRobotics Lab, Optimization and Biomechanics for Human-Centred Robotics (HCR), Institute for Anthropomatics and Robotics (IAR), Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany · Canada Excellence Research Chair in Human-Centred Robotics and Machine Intelligence, Systems Design & Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, N2L3G1, Ontario, Canada
Human gait in reality extends beyond straight-line walking, with some situations even requiring drastic back-and-forth rotations. A smooth and stable execution may seem intuitive, but the underlying mechanics remains unknown. The Karate roundhouse kick may be an extreme case of exhibiting dynamic back-and-forth rotations, but investigating the angular momentum (AM) management can potentially inform stability analysis in dynamic human motions and smoother gait in robots and exoskeletons. This paper introduces two new AM-based measures and analyzes AM-related variables to study the target-less retractable back-leg Karate roundhouse kick. The purpose is to understand the underlying AM management, analyze the differences between stable and unstable kicks, and investigate how these variables and measures change over time with improvement. A one-year longitudinal study was conducted with the first author as a Karate student, and a Karate instructor was also recruited for one session as an expert, whose data is used for comparison. Results show that unstable kicks have higher peak total AM before Strike and smaller braking peak after Strike. The proposed AM-based measures are able to identify the cause of some unstable kicks, though no clear distinction could be made between stable and unstable kicks since kicks can be unstable for different reasons. Nonetheless, the proposed measures can be applied as performance measures to analyze other types of dynamic motions. To incorporate them as stability criteria, however, it is recommended to also consider their coordination with time, kinematics, and center of pressure.
Figures & tables
Figure 1 : Sequential illustration of the Karate right back-leg roundhouse kick, with indication of start and end instances of all phases. This figure demonstrates the setup with force plates but without motion capture markers. The darker red line represents the Strike instance. Informed consent was obtained to publish the images above in an online open access publication.
Figure 2 : Top : Summary of stable, marginally stable, and unstable kicks across all student sessions and expert’s single session. Middle : Breakdown of instability occurrence in unstable kicks. Bottom : Mean (star) and standard deviation of all kick durations in all sessions.
Figure 3 : Top : Kick leg AMz w.r.t. COM in stable kicks of all sessions. Bottom : Kick leg AMz w.r.t. COM in unstable kicks of all sessions. Values are normalized to body mass and height squared. Mean and standard deviation are represented by solid line and shaded region respectively. Dotted trajectory means there is only one kick in the session. The darker vertical line represents the Strike instance.
Figure 4 : Top : AMRCz w.r.t. COM in stable kicks of all sessions. Bottom : AMRCz w.r.t. COM in unstable kicks of all sessions. Values are normalized to body mass and height squared. Positive means counterclockwise rotation, and negative means clockwise rotation. Mean and standard deviation are represented by solid line and shaded region respectively. Dotted trajectory means there is only one kick in the session. The darker vertical line represents the Strike instance.
Figure 5 : Top : Total AM magnitude w.r.t. COM in stable kicks of all sessions. Bottom : Total AM magnitude w.r.t. COM in unstable kicks of all sessions. Mean and standard deviation are represented by solid line and shaded region respectively. Dotted trajectory means there is only one kick in the session. The darker vertical line represents the Strike instance.
Figure 6 : Inclination angle, inclination velocity, and COM path with total AM vector in example stable and unstable kicks.
Figure 7 : Top : Kick leg AMA in stable kicks of all sessions. Middle : Kick leg AMA in unstable kicks of all sessions. Mean and standard deviation are represented by solid line and shaded region respectively. Dotted trajectory means there is only one kick in the session. Bottom : An example from a stable kick illustrating the total AM magnitude (solid line) and breakdown of body part AMAs (shaded regions). The darker vertical line represents the Strike instance.
Figure 8 : Top : Kick leg AMO in stable kicks of all sessions. Bottom : Kick leg AMO in unstable. kicks of all sessions. Values are normalized to body mass and height squared. Mean and standard deviation are represented by solid line and shaded region respectively. Dotted trajectory means there is only one kick in the session. The darker vertical line represents the Strike instance.
In this paper, we explore the impulsive dynamics common to single-joint, two-link models of walking and brachiating gaits with respect to slope and switching time. In particular, we investigate how the stability of a gait and bifurcations encountered within a family of gaits change under time-based and state-based switching of the impulsive dynamics.
Alan Estrada Flores, Nelson Rosa
Illinois Institute of Technology, Chicago IL 60616, USA
Recent humanoid soccer systems make motion tracking the substrate and derive locomotion from it, typically by steering a motion-reference anchor toward the ball. This yields strong shooting results, but locomotion is trained only on the narrow, deterministic command distribution ball approach induces, never evaluated as a capability in its own right. We invert the stack: a general, command-conditioned locomotion policy is trained first as the substrate, and N motion-guided kicking skills are added on top as task-gated layers, so the reachable gait space is set by the locomotion curriculum rather than any reference clip. Because every skill starts from and returns to this same commandable state, locomotion also becomes a composition hub (O(N) transitions rather than O(N^2)), and post-strike stabilisation is handed back to the trained controller rather than scripted per clip. We instantiate this on a 29-DoF Unitree G1 with seven retargeted kicking skills spanning 259.5 degrees of nominal aim direction, including lateral, rearward and weak-foot strikes a single forward-facing reference cannot express, and report shooting accuracy alongside command-tracking, terrain and push-recovery results with the full skill library attached, an axis prior humanoid soccer systems do not report. The library is validated on hardware across forward, lateral, rearward and commanded approaches.
Abu Hanif Muhammad Syarubany, Jaehyun Jang, Hwanhee Kim +3
School of Electrical Engineering, KAIST, Daejeon, Republic of Korea
Learning diverse locomotion skills for humanoid robots in a unified reinforcement learning framework remains challenging due to the conflicting requirements of stability and dynamic expressiveness across different gaits. We present a multi-gait learning approach that enables a humanoid robot to master five distinct gaits -- walking, goose-stepping, running, stair climbing, and jumping -- using a consistent policy structure, action space, and reward formulation. The key contribution is a selective Adversarial Motion Prior (AMP) strategy: AMP is applied to periodic, stability-critical gaits (walking, goose-stepping, stair climbing) where it accelerates convergence and suppresses erratic behavior, while being deliberately omitted for highly dynamic gaits (running, jumping) where its regularization would over-constrain the motion. Policies are trained via PPO with domain randomization in simulation and deployed on a physical 12-DOF humanoid robot through zero-shot sim-to-real transfer. Quantitative comparisons demonstrate that selective AMP outperforms a uniform AMP policy across all five gaits, achieving faster convergence, lower tracking error, and higher success rates on stability-focused gaits without sacrificing the agility required for dynamic ones.
Yuanye Wu, Keyi Wang, Linqi Ye +1
School of Future Technology, Shanghai University, Shanghai, 200444, China · National and Local Co-Built Humanoid Robotics Innovation Center, 201203 Shanghai, China