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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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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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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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1answer
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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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error dynamics of rotation matrix (derivative of logrithm of ratation matrix)

In a paper, the author defined an error term as $e = \log(R^T\hat R)$, where $R, \hat R \in SO(3)$,$R$ is the true state and $\hat R$ is the estimated state. Then the author derived error dynamics by ...
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23 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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1answer
26 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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1answer
91 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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27 views

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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2answers
78 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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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
175 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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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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A frame {B} is rotating and translating with respect to inertial

A frame {B} is rotating and translating with respect to inertial
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How to work around manipulator Jacobian matrix singularity?

I have a robot and I'm trying to convert a desired linear end effector velocity to a corresponding representation as Joint Speeds. I'm having the arm being controlled by a controller and as the user ...
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Help to get Jacobian of triangular platform - from center point to apices

I'm creating a simulation of the parallel robot similar to this construction: https://i.stack.imgur.com/iQQFN.png Without getting into details - the robot is "closed" with the triangular platform, ...
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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 ...
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61 views

How to determine which angles of a parallelogram with extended side are required for a given point?

I am currently trying to determine what servo angles are necessary to align a robotic arm's claw to the given coordinates. Geometrically simplified, the robotic arm is a parallelogram with two servos ...
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28 views

Rotated Gyro Data

Given are two sets of gyro data received from two IMUs. One IMU is mounted on a car. X-Direction is in driving direction. Z is upwards to the sky. The second IMU is mounted to the steering wheel. ...
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1answer
87 views

Solving 4 unknown angles in a Quadrilateral given 4 sides and a constraint

I am trying to calculate the interior angles of a Quadrilateral when given the lengths of the sides and an equal angle constraint. Here is the diagram: Quadrilateral Diagram The Equations I have so ...
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1answer
77 views

Help to get partial differential from equation - robotics

I have system of two equations that describes position of robot end-effector ($X_C, Y_C, Z_C$), in accordance to prismatic joints position ($S_A, S_B$): $S^2_A - \sqrt3(S_A + S_B)X_C = S^2_B + (S_A - ...
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1answer
228 views

LQR Robotic Arm

I have a robotic arm model in Simulink and I'd like to control the position of the end-effector such that it follows a given trajectory. This is done by inputting joint angles and comparing the output ...
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22 views

Move robot to a specific position

I have a robot with 5 joints and 5 arms. And each joint moves(rotates) in a specific axis, I can get the angle of the joints, and by using rotation and transformation of matrices, I can get the ...
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Solving Inverse Kinematics Equations into Approximate Expansion with Higher Order Terms

I have two sets of kinematics equations for a physical system, the first is: $a = \phi_1 - \phi_2 - tan^{-1}(\frac{R_{1}cos(\phi_1) - y_1}{R_{1}sin(\phi_1)-x_1}) + tan^{-1}(\frac{R_{1}cos(\phi_2) - ...
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71 views

3D inverse transformation jacobian

I am working on robotics and I have to deal with transformations. In my case, $\pmb{t} = \left[x \; y \; z \; \psi \; \theta \; \phi \right]^T$ where $x$, $y$ and $z$ is the translation and $\psi$, $\...
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77 views

Can Gauss-Newton algorithm give better optimization performances than Newton algorithm?

I am currently facing the problem of a robotic manipulator calibration: the goal is to find the best correction that must be applied to a set of kinematic parameters describing the robot model, in ...
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1answer
34 views

Sampling 6D Relative Poses from a Normal Distribution

I'm fairly new to statistical mathematics, and needed to solve a problem that may rely heavily on it. Context: I'm working on 7D robot poses - i.e. 3 translation dimensions and 4 rotations ...
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1answer
38 views

Distance traveled forward from angled wheel.

I'm using a 3-omni-wheeled bot whose wheels are whose wheels are at an angle to the direction in which they are moving. Suppose you wanted to move in the forward direction and the two adjacent wheel ...
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36 views

How to get 2 DoF inverted pendulum degree?

I have a project about 2-DoF inverted pendulum using joystick (X-Y degree value) sensor and holonomic robot. Because the inverted pendulum able to move in X-Y planes, I need to get $\theta$ from $\...
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1answer
92 views

What do three question marks after an equation mean?

In the paper Robot Manipulability they use the symbol (???) after several equations ( (2.5), (2.6), (2.9), ...). Since I've never seen this before, I'm wondering is this should be some kind of ...
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Choice of correspondence points [duplicate]

Really struggling with a question on coursera robotics perception: Find the projective transformation $A$ which will keep the points $\boldsymbol{p}_{1}=(0,0,1)$ and $\boldsymbol{p}_{2} = (1,1,1)$...
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1answer
628 views

Derive equations for the roll, pitch, and yaw angles?

How to derive equations for the roll, pitch, and yaw angles corresponding to the rotation matrix R having ijth element rij?
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2answers
123 views

Given $a^2+b^2+c^2 = 1$ what type is this matrix?

With $ a^2 + b^2 + c^2 = 1$, what type of matrix is $A$? $A = \begin{bmatrix} 0 & a & -b \\ -a & 0 & c \\ b & -c & 0 \end{bmatrix}$ So far I've tested $A$ for several ...
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1answer
51 views

Trouble Understanding Diagram for Inverse Kinematics of 6-DoF Manipulator

I am having difficulties writing the Inverse Kinematics for a 6-DoF manipulator, particularly the ABB 4600. I am using this paper as a resource. Here is the image that I am having trouble with, which ...
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1answer
781 views

How to find slope, x and y intercepts given angle to the normal vector and a point on line

I have a situation where I have angle of the normal to a line in 2D plane and a point on line as well. I need to find slope, x and y intercepts of the line. Diagram of 2D plane, X-axis Horizontal ...
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1answer
79 views

What is $z$ in this state space model? - Robust control

There is two types of state space models: The classic one: $$\dot{x} = Ax + Bu + \omega$$ $$y = Cx + Du + \upsilon $$ Where $A$ is the system matrix, $B$ is the insignal matrix, $C$ is the output ...
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Holonomic constraint forces using Lagrange multipliers

Consider a multibody robotic system with Lagrangian $$ L =\frac{1}{2} \dot{q}^{T}M\dot{q} - V $$ and equations of motion of the form $$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+A^{T}(q)\lambda+N(q)=0 $$ where ...
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1answer
82 views

Question on flatness based control

I am currently studying flatness based control using the book: Sira-Ramirez, Hebertt, and Sunil K. Agrawal. Differentially flat systems. CRC Press, 2004. I have two questions on a particular example ...
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1answer
171 views

Quaternions disadvantages in Quadrotor UAV control on $SE(3)$

I am reading a paper which deals with the Geometric Control on $SE(3)$ of a Quadrotor UAV. At some point it says: Quaternions do not have singularities but, as the three-sphere double-covers the ...
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1answer
33 views

Is there a way to create a number from two others in a way that they can be found afterwards?

I have to find a way to send two variables between 1 and 8 between two robots, but the IR function only allows one. Is there a way to make a number out of these two that can be easily transformed back ...
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1answer
81 views

Controller for Non-holonomic agents

I have designed a certain controller for a group of holonomic agents (I was assuming that they were holonomic and that they were able to move in the 3D space) Now I want to use the same controller ...
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1answer
196 views

Lie Derivative interpretation for my system

I have a system of the form: $\dot{S}=f(S,u)=f_0(S)+\sum_{i=1}^Lf_i(S)u_i$ $y=h(S)$ In my case $L=2$ but I don't think it matters for the question I want to ask. The definition of Lie Derivative ...
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646 views

How to calculate angle between two points in 3d space when the three axis changes

I am working on a robot with multiple joints but just in 3DOF. I have resolved parameters of the first and second dof however in the third dof, there are 8 links. I have the base and target points of ...
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1answer
482 views

Angle of Elevation (Depression) Between two 3D points

I have some eight points with defined coordinates in 3D space. These are from a straigth but bent and connected with matlab code as in Figure 1. My challenge is that I need to compute the angle that ...
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1answer
34 views

Locus of of the third point on the circle with two fixed beacons in triangulation

I was studying triangulation technique for robot localization and came across this equation (x-x12)^2 + (y-y12)^2=R12^2. Points B1 and B2 are fixed beacons on the circle and point R is the location of ...
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2answers
369 views

How do I plot a 'field of view' in 2D space and find if a certain point lies within the space?

I am trying to model a robot arm (in 2D) that's supposed to have a camera at the end that moves with the arm. Given the field of view of the camera, I need to find whether a certain target is visible ...
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2answers
70 views

How to get alfa and beta from this image

I developed a robotic arm with 2 bars. I would like to move this robotic arm to a X,Y coordinate. In order to do that I can set "alfa" and "beta" angles in the motor so they move the arm to the ...
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2answers
66 views

Finding length of an edge with a few variables known

I need to solve an inverse kinematics problem with geometric approach for a robotic arm and I've constructed a geometric system for my system, I've uploaded the picture System geometry. I need to ...
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1answer
59 views

How to cumulatively add transformations (6DoF)

I am stuck with a time-series problem of estimating 6DOF. I will use a simple example to explain what I need. Suppose there are 4 points about an origin o in 3D space i.e. $A$, $B$, $C$, $D$. I ...