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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 a opposed hinged thruster pair. The the force generated by a hinged thruster pair is cancelled at neutral. When having multiple controller units in a machine, the side-way force can be cancelled by one of the hinged thrusters in another unit. Thus the block count can be cut down and the implementation of the mechanism is easier as there are less moving parts to install.

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

A note for the initial angle of hinged thrusters. The Initial angle of hinged thrusters determines the output range.
In the configuration shown in the pic below, the 1-sensor tracker uses a reversed sensor and a 20° x0.4 RTC steering hinge. And the hinged thruster uses a 40° x0.8 RTC steering hinge. The controller would be at minimum tracker angle since it uses a reversed sensor, so the initial thruster angle is set to the maximum 20° which is half of the range of the thruster hinge.
For a tracker with a non-reverse sensor, the initial thruster angle would be -20° and the sensor should be pointing further 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 pointing outward, 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 cockroaches.

Spread sensor placement and crossed sensor placement
Crossed sensor placement has no blind spot underneath
In the 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 front-rear crossed placement still has a small blind spot between the "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 and behaves exactly like a 1-sensor system. 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 has 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 the complexity of making them. Also 3-sensor controllers have to rely on overflow flying blocks or water cannons, or they will bobbing up and down 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 a 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 in one dimension, i.e having 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 the car rolling or pitching instability over a period of time, which is not ideal for hover cars that's designed to climb to the 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 are 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 along the car's axis, the 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. Plus the roll is less stable than pitch and people love to do loops. 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,
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