Questions tagged [robotics]

"Robotics is the branch of mechanical engineering, electrical engineering and computer science that deals with the design, construction, operation, and application of robots, as well as computer systems for their control, sensory feedback, and information processing."

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23 views

Controlling Surface Plane with 3 Servos

I am working on a project and essentially, I have this device made, which has 3 servos connected to a surface via a 2 bar linkage. Given a surface normal, I am trying to position the surface ...
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27 views

Why we can assume the constantness of the variables in solving differential equations?

This belongs to the derivation of the exponential map of $SO(3)$. In solving the ordinary differential equation, the author states that $\omega$ can be assumed as a constant. I don't know why it's ...
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21 views

How many constraints the 2D rigid body transformation matrix provide?

The 2D rigid body transformation matrix I'm concerned with is in homogeneous representation, hence the form: \begin{bmatrix} \textbf{R} & \textbf{t} \\ 0^T & 1 \end{bmatrix} I know the ...
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24 views

Help! Lyapunov proof for calculated torque control with friction term for robot

I want to prove asymptotic stability for a Calculated torque control with friction compensation. I was told to find "an already proved" system but I have had no luck while searching for books and ...
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18 views

How can I achieve S curve profile

I want to plan robot's motion according to S curve profile.I am following the bellow mention article,which contain basics related to S curve motion profiles in robotic platforms. https://www.pmdcorp....
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28 views

Moore Penrose inverse of the end-point map

We consider the end-point map $\mathcal{E}$ of a nonlinear control system: $$ \dot{x}(t) = f(t,x(t), u(t)), \quad x\in \mathbb{R}^n,\ u\in \mathcal{U}\subset L^{2}([0,T], \mathbb{R}^m) $$ starting ...
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30 views

How to use Minkowski Sum on convex hulls of obstacle in robotics?

Let's say I have a convex obstacle given by the vertices in their convex hull. Specifically, the obstacle is given by points {(1,0), (2,0), (2,2)}. In addition, I have a robot which is just a unit ...
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22 views

Proving $\omega \times (-\omega \times q) = q$ with $||\omega|| = 1$ using matrix representation of cross product

Define the matrix representation of the cross product as the following: Define $so(n)$ : And finally define the following Lemma: (Source: Page 26 and 28 of A Mathematical Introduction to Robotic ...
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17 views

camera calibration problem - computer vision

I am new to computer vision and I have a problem which may not require a complex algorithm, however im not sure if I have enough data to ignore this. problem statement: I have a 6-joint robot arm and ...
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21 views

Lagrange equations of motion of very unstable robot

I'm trying to control a robot and I have somewhere bug and I can't found it. I would be grateful if is there anybody who would check my equations. The robot diagram can be found here 1. I would like ...
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38 views

Converting two magnitudes (of joysticks) to one single vector with direction

I'm working on a driver system for a robot and I intend to use a dual joystick "tank drive" system. Each joystick controls one half of the drive system - left stick controls left wheels, right stick ...
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Given a spherical 6-bar linkage with 3 angular actuators, can I find the *analytical* solution of the inverse kinematics problem?

Description: Scheme of the problem This is like a spherical 4-bar linkage, but with 6 bars. Everything's on a sphere. P1 and P6 are static, while ther rest is mobile. Parameters: r is the sphere ...
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22 views

How to compute the orientation error between two 3D coordinate frames?

For my master thesis in robotics I have to compute the orientation error between two coordinate frames, called E and H. Their orientation is expressed through rotation matrices (3x3) with respect to a ...
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15 views

I need to estimate how narrow a passage is for a point surrounded by obstacles.

I find the nearest obstacle from a given point. For the obstacle on the opposite side which along the perpendicular between the given point and the obstacle in the first case, how do I find this point?...
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Mathematical Description of Space of Points Reachable by Robot Hand

Consider a planar robot consisting of n rigid segments of length $l_i, 1 < i < n$, that are connected by revolute joints. The hand or tool is attached, by means of a freely orientable joint, to ...
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Inverse Kinematics. Struggling to rearrange to get general equations for the two angles $\theta_2$ and $\theta_3$.

I have successfully done the forward kinematics of a Robot and have obtained the following relevant equations for the position of the end-effector / tool: $$\begin{aligned} P_x &= 200 \cos⁡ (\...
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12 views

How to express the kinetic energy of the robot and its derivative?

The figure below describes a robot moving in a vertical plane $(x, y)$ with two degrees of freedom: one vertical translation of length $q_1$ and one rotation of angle $q_2$ measured with respect to ...
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46 views

Convert from unit vector to rotation angles

In CAD model, the orientation can be represented by a unit vector $(i,j,k)$ where $i^2+j^2+k^2=1$. In robot arm, the orientation can be represented by rotation angles $(rx,ry,rz)$ where each variable ...
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18 views

Calculation of vector components through spherical angles and serial chains

Continuing the topic: Set of vectors describing two interconnected pyramids in Euclidean space I found an article that can help solve my problem. Forward kinematics of spherical parallel ...
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14 views

Submodularity of objective function

I am reading a paper on information gathering by autonomous robot and it discusses submodularity of objective function as follows: The submodularity of the objective function arises from the ...
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37 views

Understanding an abstract notion of “frame” for Klein geometries

The Wikipedia page for "Moving frame" introduces the following abstract notion of a "frame" for a Klein geometry: Formally, a frame on a homogeneous space $G/H$ consists of a point in the ...
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72 views

Explicit calculation of condition number of a square matrix

According to Wikipedia, the condition number is defined as follows: Assume the linear system of equation $$Ax = b.$$ Let $e$ be the error in b, then the error of the solution $A^{-1}b$ is $A^{-1}e$. ...
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42 views

Is the differential drive wheeled mobile robot underactuated or not?

I have read about underactuated robotic but I still need to know about differential drive wheeled mobile robot with ordinary wheels, is it underactuated or not? In many articles there is written in ...
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Synthesizing variables using KKT on Lagrange multipliers

I'm working on a presentation that's due to next week. My topic is a scientific paper on: 'An Optimal Task Allocation Strategy for Heterogeneous Multi-Robot Systems'. There's a Proposition + Proof in ...
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32 views

Coordinates of Point with change of Reference Frame

I am reading Probabilistic Robotics (Fox, Thrun, Burgard). I am having trouble with the following passage: The key idea is to first project the end points of a sensor scan $z^t$ into the global ...
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34 views

Coordinate of the third angle in a right angle triangle

I am designing a robotic arm and am stuck. The scenario is like this: The end effector or the point where the gripper is at point C with a displacement d from the arm. I want to know the coordinate ...
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14 views

How do nonholonomic constraints affect on generalized coordinates?

I have read that the nonholonomic constraints in robotic system (for example) work such as generalized coordinates cannot take independent values. Does that mean generalized coordinates will take ...
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32 views

Is it possible to control a robotic system with two or more generalized coordinates by one actuator?

I have robotic system that has one actuator as control input. In the dynamic modeling (Lagrange dynamic) of this system and if I choose one coordinate as generalized coordinate the dynamic will be ...
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57 views

Given $R\in SO(3)$ and $w\in \mathbb R^3$, prove the following identity

Given $R\in SO(3)$ and $w\in \mathbb R^3$, and $a \times b= \hat a b$ prove the following identity: $$R {\hat w} R^T=\widehat{(Rw)}$$ It's from the textbook A Mathematical Introduction to Robotic ...
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129 views

What is the difference between Lie group sim3 and 3d affine transformation?

I am confused between 3D rigid affine (with scale, without shear) transformation and Lie group's sim(3) matrix. 3D affine should be $[sR|t; 0 1]$ \begin{matrix} s\cdot r_{11} & s\cdot r_{12} &...
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164 views

Converting from Euler angles to quaternion for covariance estimate

I am working on a graph optimization problem (g2o for SLAM) to optimize poses of a robot. The optimizer expects a 6x6 information matrix for the robot poses $[x, y, z, q_x, q_y, q_z, q_w]$. Here the ...
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62 views

Reading a mathametical notation

I am reading a paper on task allocation ...
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4answers
227 views

Calculate max velocity given time, distance and acceleration

Supposing I have a linear axis with linear acceleration/deceleration. I would like it to move to its target location and arrive after a specific amount of time. How can I calculate the maximum ...
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599 views

Derivative of a Rotation Matrix with changing rotation axis

Just to introduce the background of this question: As many of you know a Rotation Matrix can transform a point $^{B}\textrm{p}$ described in a rotated Coordinate Frame {B} into the point $^{A}\textrm{...
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44 views

How to interpret smoothing equation?

Sorry guys. This may be a basic question. I am doing a course on Robotics. I came across this equation for smoothing: Here, u -> control action, delta -> pose, z -> sensor measurement, l -> landmark ...
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62 views

Where does this formular for rotating a vector in 3D space around another 3D vector comes from?

I found this formular: $\mathbf{R}_{\vec{n}}(\alpha)\vec{x}=\vec{n}(\vec{n}\cdot\vec{x})+\cos(\alpha)(\vec{n}\times\vec{x})\times\vec{n}+\sin(\alpha)(\vec{n}\times\vec{x})$ here: https://de.wikipedia....
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18 views

second order diffrential equations to state space

i derived this Ordinary Difrential Equations of Motion of a self balancing robot using lagrange mechanics the next step is to convert them to state space representaion where with foure state variables ...
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102 views

Angular error (in Euler angles) through quaternions

I found this formula in some notes but I would like to have a reference (book, paper, etc.) to understand where it comes from. I know that it works only for small angles. $ \begin{bmatrix} \phi_e\\ \...
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111 views

Mapping [nonlinear] sensor input to sensor output, and vice-versa

I am hoping someone can refer me to a text reference, forum, or other online resource describing the following question. I thought this forum might be a good place to start, but apologies if I was ...
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88 views

How to extract the screw axis vector and the angle from the exponential coordinates?

Given the 6-dimensional vector of the exponential coordinates of the homogeneous transformation: $S\theta$, where $S$ is the screw axis consisting of the pair $(\omega, v)$ and both of them are $3$ ...
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28 views

Calculating wheel velocities for differentail drive.

I really want to know how to determine formulas for velocity in a differential drive? I found these formulas that work for me: $$v_r = \frac{(2 \cdot v) + (w \cdot L)}{2 \cdot R}$$ $$v_l = \frac{(2 \...
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139 views

Find out a general expression for the coordinates of a point in a square based on certain distances and an angle

my problem appears to be a very simple one, but I just can't seem to figure it out, maybe I am just overlooking something… The problem is defined as the following (refer to the figure for better ...
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1answer
32 views

Using a robot arm to reach a specific point with arbitrary orientation

I want to use a 6-DoF robot arm to reach a user-given point $$P_{target} = (x, y, z)$$ with arbitrary orientation. My robot arm is equipped with a laser pen and what I want to do is to aim ...
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How to get effort values of a robotic joint in N.m?

I currently have the force and torque values (in 3D vectors) of the parent and child link (joint wrench) of a revolute joint. My question is how can I get the effort values of a joint? Not in vector ...
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Theoretical mechanics - Inverse Kinematicss

On theoretical mechanics essay at the university, I have stumbled in the issue below: Given $\textbf{u}^T \textbf{D}(\mathbf{\theta}, \alpha)\textbf{v}(\textbf{d}) = \textbf{m}(\textbf{d})$, find out ...
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237 views

2 wheel robot kinematics — transformation of coordinates

I am working my way through the Mobile Robot Kinematics book from CMU, available at http://www.cs.cmu.edu/~rasc/Download/AMRobots3.pdf. I am having a hard time deriving the derivative of the robot ...
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47 views

Calculating a rotation matrix

I am studying robotics as an undergraduate. One of the things we're doing is rotational matrices. As a general principle I understand them, and if given a point in A I can find the given point in B ...
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1answer
635 views

What's the difference between Spatial velocity and Body velocity?

Let us suppose a rigid body $\{B\}$ is undergoing rotational and translational motion,and the spatial frame is $\{S\}$. In this case, we say that its configuration space is the Special Euclidean group,...
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32 views

With circular vertical motion and linear horizontal motion, how to move in a straight vertical line.

I want to find the formula for how circular vertical movement affects horizontal movement. Imagine you set your elbow down and using a pen you move up and down(forming a portion of a circle), how much ...
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81 views

Solving ODEs with Lie group element as dependent variable

I would like to understand how to properly solve an ODE involving Lie group/algebra elements. As is commonly seen in robotics and engineering, consider the kinematic equation that describes the ...