Camera Perspective causes Position offset

[haecto]

Problem

The robot position currently estimated from the camera exhibits a systematic error.
The main cause is the camera perspective and the viewing angle towards the robot or the marker.

The robot moves in the plane z = 0, while the detected position originates from a marker observation located above this plane. As a result, the estimated position is shifted depending on the camera viewing angle. The larger the lateral offset or the steeper the viewing angle, the larger the resulting position error.

Observed Behavior

• The position estimated by the camera system does not exactly match the actual robot position in the ground plane.
• The error is systematic rather than random.
• The detected point appears further outward than the actual robot position (when the camera is mounted above the center of the field and looking straight downward).
• The error depends on the camera perspective.
• The error becomes more pronounced with increasing distance from the image center or when the marker is observed under a steeper viewing angle.

Expected Behavior

The position computed from the camera should correspond to the actual 2D position of the robot in the ground plane, independent of the camera viewing angle.

Suspected Cause

The current position estimation does not sufficiently account for the projection geometry of the camera.

In particular, the following aspects are not compensated:

• the observed marker is not located at ground level,
• the camera observes the scene from an angled perspective,
• the detected marker position is therefore not identical to the robot's ground contact point.

This leads to a perspective-induced systematic position offset.

Impact

• Distortion of the absolute position measurement
• Reduced quality of the camera measurement as EKF input
• Systematic deviations in trajectory comparison and validation
• Possible degradation of sensor fusion performance due to biased measurements

Possible Solution

1. Dynamic estimation of the camera pose
   Determine the camera position and orientation in the world coordinate system dynamically from visible reference markers.

2. Dynamic estimation of the marker height
   Estimate the vertical offset of the ArUco marker relative to the ground plane.

3. Geometric reprojection onto the ground plane
   Use the estimated camera pose and marker height to project the observed marker position back onto the ground plane (z = 0) in order to compute the actual robot position.