8
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What is $\alpha \sin(\theta) + \beta \frac{d \theta}{d t}$ in the inverted pendulum problem?
The function $f$ comes from the equation of motion for the inverted pendulum problem (inverted pendulum alone, not including the motion of the wheeled platform). If you consider your figure but ignore ...
- 1,377
6
votes
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Relation between pole placement and marginal stability?
You are most likely running into problems with the maximum time step in your simulation. This phenomenon is known as stiffness, where your equations of motion are highly sensitive to the size of the ...
- 1,377
5
votes
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Humanoid balancing
Keep in mind that the ZMP is a simplification. In practice with walking robots the support polygon is constantly changing so it can be tough to keep the ZMP inside.
Pregenerated (offline) ...
- 4,355
5
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Why is it so hard to walk?
I'm not sure I agree that bipedal walking is so much harder that airplane control. It depends on how you look at it.
Many robots can walk (bipedal walking) and many airplanes are difficult to control ...
- 4,355
5
votes
For what step disturbance value the system will become unstable?
The stability is a property of the linear systems themselves, hence there is no meaning in considering stability as regarded with the input disturbance $T_d$.
To verify if the closed-loop system $C/...
- 3,985
4
votes
Fixed Wing UAV: Do inherently unstable systems desire to be stable for all cases when a closed loop control is implemented on them?
Not all fixed wing aircraft are inherently instable. That feature greatly depends on the center pressure and gravity center designed position. Passenger aircrafts are quite stable, and fight planes ...
- 470
4
votes
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How do I decide the size of the time steps between sensing and control actuation?
Regarding point 1, yes you are understanding the problem correctly.
Regarding points 1 and 2, I believe what you are looking for is the Nyquist-Shannon sampling theory. This theory says that your ...
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4
votes
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PID Control: Integral error does not converge to zero
I don't think this is related to integral windup at all.
I noticed that the I-error does not converge to zero
That's a good thing, because it means your integral term is not useless.
The integral ...
- 1,425
4
votes
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Inverted pendulum controller
Without going into the details of the underlying equations of motion, I could argue that the D part is needed to damp out the oscillations of the pole while reaching for the (unstable) equilibrium ...
- 3,985
3
votes
Helicopter Stabilization Algorithm
Stabilization of a helicopter and a quadrotor are similar tasks - have a reference signal, compare that to feedback, then act on the difference.
A quad rotor has four motors, and the helicopter ...
- 15.9k
3
votes
How to use quaternions to feed a PID quadcopter stabilization loop?
This paper, Full Quaternion Based Attitude Control for a Quadrotor by
Emil Fresk and George Nikolakopoulos, demonstrates what you are trying to achieve.
Abstract— The aim of this article is to ...
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3
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Deciding length of quadcopter arms
For the most part, it will increase the gain of the controller.
doesn't affect lift capabilities.
Adding weight to something that flies always decreases lift capabilities. However, this influence ...
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3
votes
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Can we show converenge for a variant of inverse dynamics controller?
This answer is inspired by Ryszard Szwarc's answer in: https://math.stackexchange.com/questions/4509062/how-to-show-that-the-matrix-0-i-m-1k-p-m-1k-d-has-eigenvalues.
The dynamics of the system is in ...
- 55
3
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Can we show converenge for a variant of inverse dynamics controller?
This would be too long for a comment, so I will add some work as an answer:
The proof of $A(\mathbf{q})$ being invertible is not perfect. First, add some structure to the $K_p$ and $K_d$ matrices. ...
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2
votes
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PID quaternion contoller
You are using one PID controller to try to drive a quaternion? A quaternion by definition represents three degrees of freedom, roll pitch yaw, and a PID controller is Single Input, Single Output (SISO)...
- 15.9k
2
votes
Quadcopter stability vs (PID error signal lag and sample time)
A PID can provide great control, but it's a very unsophisticated technique -- it only understands error and correction. The longer you wait between measurements, the larger your error will be each ...
- 11k
2
votes
Humanoid balancing
They are two main approachs for humanoid robot walking. Practically it depends on the physical capabilities of your robot and what you want to achieve.
If your robot is able to sustain strong impact ...
2
votes
Accepted
Quadcopter PID Controller: Derivative on Measurement / Removing the Derivative Kick
All PID controllers act on an error signal, so you definitely should stick with your first implementation. The derivative term in the PID controller wants to "see" how the error is changing - if the ...
- 15.9k
2
votes
Accepted
Quadcopter PID Control: Is it possible to stabilize a quadcopter considering only angle measurements?
It is possible to stabilize a quadcopter using only angle measurements in a single loop pid. However it is easier to stabilize a quadcopter using a cascaded PID controller. Yes you are tuning more ...
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votes
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Fixed Wing UAV: Do inherently unstable systems desire to be stable for all cases when a closed loop control is implemented on them?
I'm going to ignore your section on aircraft and attempt to answer the (vague) question,
Do inherently unstable systems desire to be stable for all cases when a closed loop control is implemented ...
- 15.9k
2
votes
Accepted
Quadcopter PID Tuning for Altitude Hold/Position Hold along Z axis
Currently I am performing my research on that, and in my case I decided to tune all the PIDs. Angles of the quadrotor tend to zero, while altitude controller tend to the objective height. That's ...
- 470
2
votes
Accepted
Quadcopter PID: Controller is Saturating
I feel like I make the same comments every time you ask a question about your controller:
How are you tuning the gains?
I think your slack line is interfering with your results.
Your quadcopter is ...
- 15.9k
2
votes
Accepted
PID Gains: Drop in control loop rate, need to retune?
All three constants should be able to stay the same assuming that you calculate the derivative and integral using the actual time step size.
The only effect of a lower sampling rate should be a ...
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2
votes
Using Quaternions to feed a quadcopter PID stabilizing controller to avoid Gimbal lock
you should not be seeing a singularity. For the standard roll, pitch, and yaw Euler angles, which are defined by a 3-2-1 rotation from level to the vehicle attitude, there is only a singularity at ...
- 1,843
1
vote
Accepted
Comparison of Balance Bot design
The "Balance Bot" robot you describe is widely known as the "inverted pendulum on a cart". For static balancing (keeping the body upright), it is generally desired to have as much as possible time to ...
- 562
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vote
Why is it so hard to walk?
A bipedal robot is essentially unstable - a little knock will cause it to fall over.
A commercial aircraft is essentially stable - a little gust of wind might move it off course, but it will keep ...
- 521
1
vote
Locking the yaw direction of a laser pointer
My guess would be it is going to be fine if you make sure that the stepper reacts fast enough. Hand motions are naturally jerk (and acceleration) limited, so your reaction will also be -- unless you ...
- 729
1
vote
Accepted
Quadcopter: X-Y Velocity PID Controller
Your setup as is will certainly not work. Roll and Pitch do not map to X and Y one-to-one. You will need to use linear algebra to convert demanded XY (see this stack overflow question on how) into ...
- 336
1
vote
Accepted
Quadcopter refuses to fly when the Yaw PID component is added
disclaimer: This is more of a longer comment than an answer. I'm not sure what the problem is. There is a lot going on here (thankfully a lot of information is provided, too) and my attention shifted ...
- 1,425
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