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6

Given that an homogeneous transformation $T \in SE\left(3\right)$ can be expressed as $$ T= \left( \begin{matrix} \mathbf{R} & \mathbf{p} \\ 0 & 1\end{matrix} \right), $$ where $\mathbf{R} \in \mathbb{R}^{3 \times 3}$ is symmetric and $\mathbf{p} \in \mathbb{R}^{3 \times 1}$, then we seek for the inverse $T^{-1}$, such that: $$ T^{-1}=\left( \begin{...


6

OK, I'm working from the 1st edition of the book, so section 4.2.4 of my edition starts on page 75, but the text appears otherwise to be the same. Initially, the book re-writes the equations of motion of the robot, given earlier as Eq. 4.2: $ \dot x = \nu cos \theta $ $ \dot y = \nu sin \theta $ $ \dot \theta = \frac {\nu} {L} tan \gamma $ in matrix ...


4

Thanks for the question and great derivation by @sempaiscuba. I first learnt about this kind of controller from the book by Siegwart etal. but the source is Exponential Stabilization of a Wheeled Mobile Robot Via Discontinuous Control, A. Astolfi, Journal of Dynamic Systems, Measurement, and Control, March 19999, Vol 121, pp. 121-126. Yes, there is an ...


4

I have read the book, and found it unnecessarily obtuse. Unfortunately, the code snippets will not be very helpful, since they will probably look exactly like the equations, while using a matrix library like Eigen, OpenCV, boost, or just Matlab. To get a good understanding of a Kalman Filter, you should start with a review of multi-variate Gaussian random ...


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The two links that I found most useful were Kalman Filter for Undergrads1 and Kalman Filter for Dummies. They're not high on the theory though. and Student Dave's Kalman Filter Tutorial. The last one has matlab code that you can play with and is easy to follow.


3

This is my go-to book for all things manipulation. But it covers some other topics as well. Robotics: Modelling, Planning and Control by Bruno Siciliano, Lorenzo Sciavicco, Luigi Villani, Giuseppe Oriolo.


3

If you are looking for a source to get an intuitive feeling for what the Kalman Filter is actually doing I would suggest going through lesson 2 of Udacity's Artificial Intelligence for Robotics course found here: https://www.udacity.com/course/cs373. The course is free and it has video lectures and simple code examples. The explanation given is a little ...


2

I've been collecting books on Kalman filtering and target tracking for some years now. Most approachable book I've found: Gelb's Applied Optimal Estimation. It is widely considered a classic in the field. It is also relatively inexpensive. Second place goes to Brookner's Tracking and Kalman Filtering Made Easy. It is aimed primarily at radar processing. ...


2

Once you have a real intuition for the Kalman equations you will easily be able to translate the equations / models into code. I highly recommend working (by hand) the examples in the Lecture Subject MI63: Kalman Filter Tank Filling - Kalman Filter Applications. The examples highlight how the system model can greatly affect the output of the Kalman filter ...


1

Making advanced projects with PID control is easy. At first, a uav-testbed is needed. This consists of two UAVs at the same time. The left UAV is controlled by the human operator with a joystick. And the right UAV is controlled by the pid-tracking controller. The idea is, that the pid-controller follows the human-demonstration in realtime and reduces the ...


1

I can see two parts to this question! You need to learn the math needed to develop such control systems in an advance manner. Look for Author: Norman S. Nice - Control Systems Engineering. Sixth Edition I found this PDF online and was used in my course. the programming skills needed to convert this math into a usable system. Warning - Controlling a ...


1

There are many tutorials and forums to help in learning ROS. It can work on a Raspberry Pi, so you don't need an expensive computer to run Linux. ROS includes (or is associated with) Gazebo, a robot simulator. With ROS you get a lot of things involving movement that are easy to use. You also get drivers for many common sensors. You get SLAM and a few kinds ...


1

You could look at three books. A Mathematical Introduction to Robotic Manipulation - S.Sastry, X.Li and R.Murray provides a theoretical foundation to the kinematics, dynamics and control aspects of robotic manipulators. The only downside to this book is that it lacks in algorithmic content like that available in Probabilistic Robotics - Sebastian Thrun ...


1

I think I would solve this as I believe you did, where I find a rotation matrix $E$, a translation vector $\overrightarrow {dr}$, and I locate point P in frame B by adding it to the origin of frame B; $\overrightarrow P_{B} = \overrightarrow P + F_B$. Recall that you are "unrotating" from frame B to frame A, so you need to transpose the rotation matrix. ...


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I'm biased (since I have TA'd his course twice), but I think Prof. Marin Kobilarov's derivation of the KF/EKF is far superior to Thrun's. I have read almost every book on KF/EKFs mentioned in previous answers, and I think Marin's lecture notes are excellent for the theoretical aspects of optimal state estimation. Thrun's presentation is far from the worst, ...


1

The Kalman Filter is based on some assumptions - a linear process with independent normally distributed noise. Noise over time is independent. Each measurement is also independent. The Wikipedia article (http://en.wikipedia.org/wiki/Kalman_filter) is quite complete in information on this. This article should be enough to allow you to implement the Kalman ...


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