We introduce an analytic method for generating a parametric and constraint-aware kick for humanoid robots. The kick is split into four phases with trajectories stemming from equations of motion with constant acceleration. To make the motion execution physically feasible, the kick duration alters the step frequency. The generated kicks seamlessly integrate within a ZMP-based gait, benefitting from the stability provided by the built-in controls. The whole approach has been evaluated in simulation and on a real NimbRo-OP2X humanoid robot.

The RoboCup Humanoid League holds annual soccer robot world championships towards the long-term objective of winning against the FIFA world champions by 2050. The participating teams continuously improve their systems. This paper presents the upgrades to our humanoid soccer system, leading our team NimbRo to win the Soccer Tournament in the Humanoid AdultSize League at RoboCup 2023 in Bordeaux, France. The mentioned upgrades consist of: an updated model architecture for visual perception, extended fused angles feedback mechanisms and an additional COM-ZMP controller for walking robustness, and parametric in-walk kicks through waveforms.

Beating the human world champions by 2050 is an ambitious goal of the Humanoid League that provides a strong incentive for RoboCup teams to further improve and develop their systems. In this paper, we present upgrades of our system which enabled our team NimbRo to win the Soccer Tournament, the Drop-in Games, and the Technical Challenges in the Humanoid AdultSize League of RoboCup 2022. Strong performance in these competitions resulted in the Best Humanoid award in the Humanoid League. The mentioned upgrades include: hardware upgrade of the vision module, balanced walking with Capture Steps, and the introduction of phase-based in-walk kicks.