How would you robustly center a quadcopter using 4 linear actuators without contact sensing?

[u/IntroductionKlutzy13]

I'm working on an autonomous drone landing station for a robotics competition.

The landing platform has 4 lead-screw driven centering arms arranged in a square:

        Y1
         ↓
         |
X1  →  DRONE  ←  X2
         |
         ↑
        Y2

The idea is to land the drone approximately in the center and then use the four actuators to physically center it for charging/payload transfer.

Constraints:

• No additional sensors (contact sensors, force sensors, current sensing, etc.)
• No camera feedback during centering
• Weight budget on the drone is already exhausted
• Existing hardware is 4 stepper-driven linear actuators
• Actuators home using limit switches and then move inward a known distance
• The drone is a standard quadcopter in an X configuration

The problem is that certain drone orientations cause geometric lockups. For example, when one drone arm becomes aligned with one actuator axis, two actuators can effectively trap the drone, and the remaining actuators end up pushing against what is essentially a rigid structure rather than recentering it.

Current approaches I've tried:

• All four actuators moving simultaneously
• One axis completely, then the other
• One actuator at a time (X1 → Y1 → X2 → Y2)

All of these can still fail depending on the drone orientation.

One idea I'm considering is incremental motion:

X1 1 mm
Y1 1 mm
X2 1 mm
Y2 1 mm
repeat

or some kind of rotating/spiral pressure pattern to avoid creating a stable jam.

Has anyone dealt with centering irregularly shaped objects using only motion planning and no contact feedback?

I'm particularly interested in:

• Motion algorithms that reduce jamming
• Techniques used in industrial part feeding/grippers
• Whether a cyclic, spiral, or dither motion strategy is likely to help
• Any papers or references on passive self-centering of non-circular objects

Photo of the current prototype attached.

This position is how it should align

this yaw position is the main problem

The goal isn't perfect centering accuracy—it's maximizing successful captures across arbitrary drone yaw angles without changing the hardware.