Tracking the Trajectory of an Ballistic Projectile with Cameras and Prediction of Landing position by Multilayer Percept

1. Tracking the Trajectory of an Ballistic Projectile with Cameras and Prediction of Landing position by Multilayer Perceptron By Kin-chung Wong

2. Motivation • A badminton-playing robot?

3. What needs to be done • Look at the shuttlecock • Estimate the trajectory • Go near the trajectory • Hit the shuttlecock For now, • Restrict the motion to 2-D (a vertical plane) • Assume the robot simply “catches” the shuttlecock at ground level

4. Objective • Need an algorithm to convert visual information to trajectory estimation • Uses MLP and polynomial approximation • Test different configurations of camera

5. The watered-down Model • The trajectory of the shuttlecock (replaced by a “projectile” in the project) derived fromF = mg + bv • That is, force = weight + air resistance • Simulation by evaluating ODE • Uses 4° Runge-Kutta method – similar to Euler’s method but more accurate

6. Scenario #1:Configuration • One camera located in the middle, pointing upward • One camera located in the far right, pointing left • Launch position, velocity are random • No wind

7. Scenario #1: Result MLP 3-5-2 3rd order Polynomial V(a, b, c) = [1 a b c ab bc ca a2 b2 c2a2b a2c b2a b2c c2a c2ba3 b3 c3 abc] Least-square fit

8. Scenario #1: Comment • 3rd order polynomial is more accurate due to simplicity of the simulation model • However, a rare input data in test set #2 can cause polynomial to fail! • A single case (projectile thrown almost upward rather than forward) causes 5000% error, which in turn causes overall error SD to shoot up • MLP does not have this problem

9. Scenario #2: Configuration • Two cameras near the center • Launch position, velocity unknown • No wind

10. Scenario #2: Result 4-8-2 MLP 3rd order polynomial 4 input variables Again, 3rd order polynomial is better!

11. Conclusion • Due to simplicity of the simulation model, 3rd order polynomial performs better than MLP • However, MLP output is more stable than high-order polynomial fitting • Future work: Train an MLP to recognize the safety zone of a given polynomial approximation