8
This is a standard dynamics problem. Let's use this figure I drew:
Some definitions:
$$
\begin{align}
m & \mbox{, the mass of the vehicle in kg.} \\
\mu_{\mbox{rolling}} & \mbox{, the rolling friction coefficient of your tires.} \\
\theta & \mbox{, the incline of the plane in radians.}\\
g & \mbox{, the gravitational constant, 9.81 } m/s^2 \...
7
In that context, SE means "Special Euclidean" group, e.g. SE(3)* which is shorthand for "the special Euclidean group of rigid body displacements in three-dimensions".
*Planning Algorithms, Steven M LaValle 2012-04-20
4
I can't think of a reason why a velocity model (based on control commands)
would be superior to an odometry model (which uses the actual wheel speeds).
The lecture notes from Freiburg on motion models imply the same:
Odometry-based models are used when systems are equipped with wheel
encoders.
Velocity-based models have to be applied when no ...
4
Scott-Russell type mechanism. For weeks I was trying to come up with a solution for that exact problem for a engineering project mine. Look it up.
4
It is a mathematical concept call the "Special Euclidean" group. Roughly, it is a combination of a rotation and translation. You'll also frequently see SO3, which is the special orthogonal group which means rotations.
4
Many articles reference algorithms such as A*, PRM or RRT based planners to motion planning algorithms which seems unreasonable since it is still necessary to parametrize found path with time.I wonder, why?
First of all, RRT, for example, can be used to plan trajectories directly. When the robot in question has $n$ DOFs, such a planning problem happens in a ...
4
The author expects a background that includes a course in physics or mechanics where this equation is taught. When that is the case, this equation gives you instantaneous velocity of a particle (point) moving on a circular path.
The $\times$ in $\dot{p} = \omega \times p$ is the cross product. (This may already be obvious to you, it's hard to tell from the ...
4
The S-Curve profile can have several divisions along the time axis
7 divisions as per this image. This example has a constant positive jerk zone, a constant acceleration zone, a constant negative jerk zone, a zero acceleration zone and then the vice-versa. This is the S-Curve in its most general form
5 divisions if there exists no constant acceleration ...
3
There are several traps you might have stepped into, but it is difficult to tell without more information. The first issues that came to my mind:
The equations you wrote down are for sampling from the velocity motion model. But then you write about the Kalman Gain approaching singularity, which only makes sense of you apply a Gaussian filter (EKF or UKF). ...
3
All theory aside, circumferences and actual distances travelled will vary with your wheel geometry since your wheels aren't perfectly tangential to their direction of travel while turning. While Ian gives some good math I think I would run tests and assign a pseudo-circumference.
I think I would just measure what the odometers read for a full 360 turn-...
3
I agree that the motion models in Probabilistic Robotics are badly suited for omnidirectional robots. I always interpreted the models presented there as examples only that should enable you to devise a custom model for your own robot.
First of all you need to model and solve the forward kinematics for this kind of omnidirectional drive. I guess you already ...
3
You need the transformation from the car to the IMU.
You can get this by recording the IMU published attitude with the car in known orientations.
You should be able to construct the IMU to car transformation by grabbing the IMU orientation while the car is flat, pitched up a bit (30 deg would should enough), and rolled (again, 30 deg should be enough).
...
3
$SE(3)$ is the representation for both translation and rotation in 3D space, whereas $SO(3)$ is only the representation for rotations. $\mathbb{R}^3$ is for translations in 3D space.
If you only consider 2-dimentional space, then you can simply change 3 to 2, i.e., $SE(2)$, $SO(2)$, $\mathbb{R}^2$.
I wouldn't worry too much about it. You can just consider ...
3
To come up with a mathematical expression of the position reference $x\left(t\right)$ as a function of time $t$, we can inspect the profile of the acceleration $a\left(t\right)$. It is piece-wise linear and defined as follows:
$
a\left(t\right)=\begin{cases} \Delta \cdot t, & t \in \left[0,0.025\right] \\
2000 - \Delta \cdot \left(t-0....
3
I think this is not really difficult trigonometry. Suppose we want the robot to move in a forward direction? We need to use the two front motors. (I tried to sketch this out in the pictures, I will now explain all this scribble). Due to the fact that the motors are not at right angles to the axis we need, therefore, we need to feed the motors a little higher ...
2
I think you have two problems; first, on the mathematical side, the models aren't matching your geometry, so the assumptions about error accumulation are wrong, as you've ascertained. I suspect that's fixable.
The second problem is harder and is related to the messy physics of omnidirectional robots (at least for 120-degree and Mecanum) - they generally ...
2
I found a paper (Learning probabilistic motion models for mobile robots) which examines the constraints of the motion models introduced by Thrun and presents a more general model.
Abstract:
Machine learning methods are often applied to the problem of learning a map from a robot's sensor data, but they are rarely applied to the problem of learning a robot'...
2
This should have probably been a comment to @RobertEnglish answer ... but comments don't seem to allow pictures
Bavel gears. Plastic ones should be rather inexpensive.
2
The majority of the noise you're hearing is not from the motor itself but from gearing, which both servo motors and drills have a lot of. However, if you don't have a gearbox then when power is cut the torque exherted by the motor will become zero and your arm will fall. I would reccomend a standard brushed DC motor with an encoder for precise control, ...
2
It's called a slip ring.
http://en.wikipedia.org/wiki/Slip_ring
The Wikipedia page has several alternate names for it.
Be careful when using these devices, a cheap or damaged one with poor brushes will destroy a high-speed digital signal (and even worse, it will get damaged after you build a working prototype.)
2
Assuming you need only to eject the drawer automatically and can close it back manually, I would suggest using compressed spring which would push out the drawer if there is no resistance.
A hook or similar mechanism holds the spring when the drawer is pushed back in.
This mechanism would save you use of motors, and thus you won't use electricity. The ...
2
I guess you want to find a cubic polynomial for the end effector. You have 3 coordinates for your points A and B, from your question is not clear if they are $x,y,z$ or $x,y,\theta$. Anyway, I'll show here the procedure for $x$, and you can repeat it for the other two coordinates.
Given the cubic parametric form $x = a_0+a_1 t + a_2 t^2 + a_3 t^3$ ($*$), ...
2
Through my reading of this book "Probabilistic Robotics" chapter 5 pp. 120,121. It seems what you thought is right. And this is the reason the authors mentioned.
Many commercial mobile robots (e.g. differential drive, synchro drive)
are actuated by independent transnational and rotational velocities,
or are best thought of being actuated in this way. ...
2
My solution is to use the following model with disturbance only at acceleration and curvature.
$$
\begin{bmatrix}
x_{k+1} \\
y_{k+1} \\
\theta_{k+1} \\
v_{k+1} \\
a_{k+1} \\
\kappa_{k+1} \\
\end{bmatrix} =
f_k(\vec{x}_k,u_k,\vec{\omega}_k,\Delta t) =
\begin{bmatrix}
x_k + v_k \Delta t \cos \theta_k \\
...
2
The model you have given is called the unicycle model and is widely used n robotics. In general the model is given by
\begin{eqnarray}
\dot{x} &= v\cos \theta \\
\dot{y} &= v\sin \theta \\
\dot{\theta} &= \omega
\end{eqnarray}
where $v = 1/2(v_1+v_2)$ and $\omega = 1/b(v_2-v_1)$ are the controls of the robot.
The method that you have mentioned ...
2
From my side I can provide two remarks.
First the human have elastic actuators (muscles) with a lots of sensors for balance. Whereas robots have mostly rigid actuators with a few dampers here and there to avoid breaking the motors on collision, and then they have far less sensing capabilities to maintain balance. So the two are not really comparable.
Another ...
2
In this paper rotation matrices are used to describe the orientation of the quadrotor. This is chosen because each orientation as a single representation (contrary to quaternions) and gimbal lock is not possible (contrary to any Euler angle convention).
In the proposed controller, ones want to know how close the actual rotational velocities from the desired ...
2
First note that
$p(0)$ travels along an arc of the circle of radius $r = \Vert p \Vert \sin(\phi)$ centered at a point on the axis of $\omega$; and
the velocity $\dot{p}$ is perpendicular to the arc of the circle; and
(from the definition) $\omega = \dot{\theta} u$, where $u$ is a unit vector perpendicular to the plane of rotation.
Now we try to relate $\...
2
If I understand your question correctly, it seems to me that you are looking for a DC torque motor (brushed or brushless) with a suitable sensor attached to the load or to the output shaft. The sensor measures whatever it is what you want to control, you need a processor to implement the control system algorithms, and a power amplifier to deliver electrical ...
2
There's two parts.
The wheel you're remembering is a castor wheel that's designed to stick at straight forward when the car is going forward, and will turn to about 20 degrees when the car goes backwards. There used to be some really cheap remote-control cars that just had a button that did that (so, no response to hitting a wall).
If you took that ...
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