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Besiege Notes on Automation Block Stabilization #3 --- Hover Car Implementation

Lemonade-1, with a 3-sensor tracker based 3-controller system for hovering


This series of articles document how my approximated automation-block PID controller works and how I implement them on self-stabilizing machines.

Hinged Thruster Configuration for Hovering Machines

The P-controller output was introduced as an opposed hinged thruster pair previously. The force generated by the pair is cancelled at neutral angle. But a pair is not needed when there are multiple controller units in one machine. I can have side-way forces of opposing units cancelling each other. like the example below on the right, the front and back controller units for a pair, their hinged thrusters cancel each other's. Hence, I can cut down the block count, save space as well because there are fewer moving parts.

1-sensor PD controller unit with a hinged thruster pair and D thruster pair; hover system with 4 controllers

A note for the initial angle of hinged thrusters. I have to make sure the range covers the upside-down situation, which needs the controllers to pull the machine towards the surface.
In the picture below, the 1-sensor tracker uses a reversed sensor and on a 20° x0.4 RTC steering hinge, the hinged thruster is on a 40° x0.8 RTC steering hinge.
Since it is a one-sensor setup, it starts at the extreme of the angle range. In this case it is an inverted sensor that tilts down until it finds the ground, and the thruster tilts down at twice the speed and through twice the angle range. The further the ground is the lower the thrust.
But to make the machine hover upside-down, it won't pull the machine to the ceiling if the force only reduces to 0, gravity will win. The thruster must tilt across to the other side to pull the machine downwards. Therefore, I have the thruster starts at 20° up, so as the sensor tilts down over 10°, the thruster tilts to -20°, pulling the machine down.

The initial angle of hinged thrusters is set to half of the range of the RTC steering hinge to cover upside-down situations


Sensor Placement

With trackers, the sensors are not detecting the ground right beneath them but all the way at the end of the sensor beams. When the sensors are placed intuitively at for corners sprawling outwards, there'll be a great blind spot under the machine. The machine will get caught by the rough terrains.
Using a crossed sensor placement can eliminate the blind spot underneath allows the machine to go through uneven surfaces and even flip over edges like a cockroach.

Spread sensor placement and crossed sensor placement
Crossed sensor placement has no blind spot underneath

In hover car application, since the car is mostly driving forwards and backwards, I swap the front and rear sensors to create a crossed placement. The X-shape crossed placement still has a small blind spot between the front and rear "wheels". There are more types of crossed placement as the image below shows. I've yet to test out the mixed crossed placement which has the most space beneath covered theoretically.

Diagonal crossed placement and mixed crossed placement

1-Sensor & 3-Sensor Comparisons

Earlier in the end of the first article of this series I explained that the dead zone of 2-sensor controllers can greatly impact the stability. The dead zone can be reduced easily by narrowing the angle difference between the two sensors, but then the tracker starts to oscillate exactly like a 1-sensor system because the hinge moves past the dead zone before the sensor detects it. Therefore 2-sensor controllers are ruled out in this comparison.

the first three use 1-sensor controllers, the last three use 3-sensor controllers and overflow flying blocks

1-sensor controllers have faster response, lower block count and emulation key count. The downside is the machine will constantly bobbing up and down due to the term D oscillation. Whether or not using RTC thrusters for term D will improve the issue is yet to be tested.
3-sensor controllers hover more smoothly, but it comes with a price of slower response due to the dead zone, higher block count and emulation key count (3x more keys), and complexity. Also 3-sensor controllers have to rely on overflow flying blocks or water cannons, or they will bob in low frequency.

Active Angular Dampers & Gimbal Lock

Active dampers are very effective in a low block count. When a machine needs to be dampened but there's little space inside for an effective gyro, active damper is a really good solution that offers greater damping power that can be tuned. Especially when it's a car that is longer rotating in one dimension, and it has greater angular inertia in one axis over another. Tweaking the reaction wheel speeds and tracker speeds will get you a perfectly dampened machine.

Active damper, a D controller with 2-anglometer angle tracker and a reaction wheel

However the gimbal lock is present in active dampers. For hover cars, when the machine goes upside down, the tracker will have to rotate 180° to be back on track with the upright angle. This leads to rolling or pitching instability for the duration of time where the angle tracker is catching up, which is not ideal for hover cars that's designed to drive on walls and ceilings.

Roll gimbal lock causes the machine to roll after pitching over 90° 
Pitch gimbal lock causes the machine to pitch after rolling over 90° 

There is no simple way to solve the issue*, so I made a compromise in my ORC-43 Buan. I installed an active damper only for pitch. Because the sensor coverage is bigger fore-aft, the greater stability prevents the machine to go out of control. Also, pitch is aligned with the car's moving direction, it is less likely to encounter a pitch gimbal lock.
On the other hand, roll gimbal lock will leads to greater problems. The machine will suddenly roll every time it does a loop, and roll is less stable than pitch. So I decided to remove the active damper for roll.
When the hover car is not designed for 3-D maneuvers, it is safe to install active dampers for pitch, roll and yaw.

The series ends here. When there are developments in the future, I might continue writing,

*Now we have angular speed mode on speedometer, it is solved.
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