fit_trajectory
Fit polynomial equations to trajectory data for smoothing noisy measurements or deriving motion equations, supporting linear, quadratic, or cubic fits to model constant acceleration or other motion patterns.
Instructions
Fit polynomial to trajectory data.
Useful for smoothing noisy data or finding trajectory equations.
Default fit_type="quadratic" fits parabolic trajectory (constant acceleration).
Args:
times: Time values in seconds (or JSON string)
positions: Position vectors [[x,y,z], ...] in meters (or JSON string)
fit_type: Polynomial type - "linear", "quadratic", or "cubic" (default "quadratic")
Returns:
Dict containing:
- coefficients_x: Polynomial coefficients for x(t)
- coefficients_y: Polynomial coefficients for y(t)
- coefficients_z: Polynomial coefficients for z(t)
- r_squared: R² goodness of fit (0-1)
- predicted_positions: Fitted positions [[x,y,z], ...]
Example - Projectile motion:
result = await fit_trajectory(
times=[0, 1, 2, 3],
positions=[[0,0,0], [10,15,0], [20,20,0], [30,15,0]],
fit_type="quadratic"
)
# Fits x(t) = c0 + c1*t + c2*t²Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
| times | Yes | ||
| positions | Yes | ||
| fit_type | No | quadratic |