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Maximum Impulse Approach to Soccer Kicking for Humanoid Robots

Grzegorz Ficht, Sven Behnke

TL;DR

This work addresses robust in-walk kicking for humanoid robots by maximizing impulse rather than solely shaping trajectories. It introduces a maximum-impulse method that splits the kick into four phases (Prepare, Swing, Continue, Return) using constant-acceleration trajectories and timing derived from $t_{sw}$ and $\alpha_k$, with $\alpha_k = \tau_h / I_l$ where $I_l$ comes from a five-mass centroidal model. The approach is integrated into a ZMP-based gait and respects hip torque and leg inertia constraints, achieving larger ball momentum and improved kicking distance, demonstrated in MuJoCo simulations and on real hardware (NimbRo-OP2X). The results show robustness to timing disturbances and match or exceed prior waveform-based methods, with extensions suggested to lateral-plane kicks for omnidirectional capability.

Abstract

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.

Maximum Impulse Approach to Soccer Kicking for Humanoid Robots

TL;DR

This work addresses robust in-walk kicking for humanoid robots by maximizing impulse rather than solely shaping trajectories. It introduces a maximum-impulse method that splits the kick into four phases (Prepare, Swing, Continue, Return) using constant-acceleration trajectories and timing derived from and , with where comes from a five-mass centroidal model. The approach is integrated into a ZMP-based gait and respects hip torque and leg inertia constraints, achieving larger ball momentum and improved kicking distance, demonstrated in MuJoCo simulations and on real hardware (NimbRo-OP2X). The results show robustness to timing disturbances and match or exceed prior waveform-based methods, with extensions suggested to lateral-plane kicks for omnidirectional capability.

Abstract

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.

Paper Structure

This paper contains 9 sections, 10 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Approach
  3. Swing Phase
  4. Prepare Phase
  5. Continue Phase
  6. Return Phase
  7. In-walk Application
  8. Experimental Results
  9. Conclusions

Figures (3)

  • Figure 1: Proposed maximum-impulse approach to kicking, consisting of four phases: a) preparation, b) swing, c) extension and d) return. Throughout the kick, the robot remains in-gait.
  • Figure 2: NimbRo-OP2X kicking with the presented approach. From a walking state, the calculated swing motion builds up the leg velocity. At impact, the ball is visibly propelled into the air and travels the full 5.5m field in our lab, stopping at the goal. After kicking, the robot continues walking despite the timing and impact disturbances to the gait.
  • Figure 3: Generated and measured () leg motion trajectories during an experiment, with phases separated and denoted by their first letter.