Tight Spiral

What a tight spiral is

At release, the ball's spin axis, its nose, and its velocity must line up. I score each throw with two metrics.

Spin efficiency

100% means all of the spin is about the ball's long axis.

Nose angle

0° means the nose points exactly along the velocity.

Why it's hard

• Coupled momentum, fast. The robot has to reach the required coupled momentum with high-DoF motion in about half a second.
• A brief, underactuated release. The release lasts under 100 ms while the ball rolls partly across the fingers, leaving it effectively underactuated.
• Joints at their limits. In the final 50 ms of one throw, waist pitch was torque-saturated 90.9% of the time, and shoulder pitch and elbow were saturated 54.5% of the time.

How it works

1. 1

   Legs

   A whole-body controller (GR00T) keeps the robot balanced. An extended Kalman filter estimates pelvis motion from contacts, leg kinematics, and the IMU.

2. 2

   Throw phase

   Trajectory optimization (Crocoddyl + Pinocchio) runs offline on a 10-DoF waist-and-arm model over 0.6 s, and the robot tracks the result. Target launch elevation: 35°.

3. 3

   Follow-through

   Model predictive control drives the wrist and the fingers still in contact, with a 15-step horizon of 4 ms steps. One online solve took about 500 ms, so I run it as an offline lookup table. It penalizes off-axis spin, nose misalignment, and fingers pushing into the ball.

4. 4

   Release

   The thumb opens at the end of the throw while the other fingers stay in contact. Follow-through lasted 78.5 ms on average over 61 trials.

Results

• 93.6%
  Peak spin efficiency
• 16.4°
  Best nose-angle error0.286 rad
• 5.35 m/s
  Peak release speed
• 14.5 rad/s
  Peak spin rate

Ablation Without follow-through, average spin efficiency fell from 67.1% to 60.9% and average nose angle rose from 18.9° to 34.7°.

Setup

Robot

Unitree G1, 29 DoF

Hand

Dex3-1, 7 DoF, three fingers, with a 3D-printed extended thumbnail

Ball

Mini football: 0.252 kg, 21.6 cm long, 12.7 cm wide, 12 psi

Tracking

OptiTrack, six PrimeX 22 cameras at 360 Hz, ≤0.15 mm accuracy

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