Predicting where the birdie lands

What the prediction has to do

The stereo vision system outputs a stream of 3D positions: where the birdie is right now, at each frame. The prediction system takes this stream of coordinates and predicts where and when the birdie will land.

It does this by fusing each position measurement into a running state estimate that tracks both position and velocity. The prediction module then forward-simulates the trajectory under realistic aerodynamic drag to produce a predicted landing location and time-to-arrival. This output is what the robot will use in Year 2 to move to the correct court position before the birdie arrives.

Shuttlecock aerodynamics

A shuttlecock experiences significant drag due to its feathered skirt, so a constant-acceleration model is insufficient. The shuttlecock can instead be modelled as being subject to two primary forces: drag and gravity. Drag force depends on velocity, so deceleration is most pronounced at high speeds and decreases as the birdie slows.

Grouping the constants into a single term α = ρC_d A / 2m (units: m⁻¹) gives the drag acceleration α|v|v. Decomposing the net force into its Cartesian components yields a system of three coupled ordinary differential equations. Knowing the position and velocity at a given moment lets us solve them and calculate the entire trajectory of the birdie, both past and future flight path. We used α = 0.215 m⁻¹, fitted to ground-truth Vicon data from a published shuttlecock dataset, rather than fitting against our own data, as live trajectory capture was not completed.

The Extended Kalman Filter

The raw stereo vision measurements are inherently noisy due to sensor limitations and environmental factors. An EKF combines the physics model above with each new measurement to produce a cleaner state estimate.

The EKF tracks the 6D state [x, y, z, vx, vy, vz] of the birdie. Each frame, the filter runs two steps: prediction, where the dynamics model propagates the state forward, and update, where the triangulated 3D position is fused with the prediction via the Kalman gain. The Kalman gain weights the measurement against the model prediction based on their relative uncertainty.

Measurement noise is set to σ = 2 cm for X/Y and σ = 5 cm for Z, based on physical reasoning and tuned against the published dataset. They have not yet been validated against live camera data.

Tracking and landing prediction

The tracker manages the EKF lifecycle through three states. In SEARCHING, the system waits for two consecutive detections to estimate an initial velocity before initializing the EKF. In TRACKING, each frame runs a predict-update cycle, and if no detection is found, the filter coasts for up to 30 frames to handle brief occlusions. Beyond this window, the tracker transitions to LOST and resets for the next birdie.

Once the EKF state converges, a Runge-Kutta 4th-order integrator forward-simulates the trajectory using the same aerodynamics model until the birdie reaches a target intercept height, returning the predicted landing position and time-to-arrival. RK4 is used rather than the EKF’s 2nd-order integration because small errors compound over a 1 to 3 second prediction horizon.

Testing without a live detector

Without a working live detection pipeline, validating the EKF and landing predictor required an alternative approach. The replay tool feeds ground-truth Vicon trajectories through the full tracker stack and reports per-frame EKF error and landing prediction convergence, allowing iterative tuning of noise parameters and α without live cameras.

To validate the physics and EKF before live testing, random Gaussian noise was injected into the dataset and fed into the EKF to simulate noisy camera measurements. The output of our prediction algorithm was then compared against the clean, ground-truth data.

The EKF converges quickly and is robust to measurement noise. It locks onto the true trajectory in under 0.25 seconds, and once locked, the filter achieves a steady-state mean positional error of less than 10 cm for the remainder of the flight. Validated against 247 Vicon ground-truth trajectories, the system achieves 3.6 cm mean tracking error, which is sufficient for interception.