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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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How to calculate a dual $T^*$ given a member $T$ of $\textrm{SE}(3)$?

In reproducing "A Linear-Time Variational Integrator...", I encountered the undefined symbol ${T^k}^*$ in equations 16a and 16b. A professional acquaintance proved to me that ${T^k}^*$ is a ...
Reb.Cabin's user avatar
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Robotics - Euler Angles from Linear Transformation

In a robotics application (3d Cartesian Space), I need to transform my Point position and orientation in a particular frame to the world frame. The Frame Position and Orientation is known and I was ...
AlexMacabu's user avatar
2 votes
0 answers
91 views

Algebraic Topology and Robotics

How active is the current research scene on the application of algebraic and differential topology to robotics? I have spent a decent portion of time researching and reading introductory papers, but ...
Tom's user avatar
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Is Koopman operator just like curve fitting?

I am a beginner in Koopman operators,and I want to apply it to the robotics. But I think the Koopman operator approximated by EDMD is more like a fitting tool. Because we always choose some dictionary ...
xinqi chen's user avatar
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0 answers
37 views

Two State Implicit Filter Derivation

I've been reading The "Two-State Implicit Filter – Recursive Estimation for Mobile Robots" by Bloesch. The gist of the paper is it tries to find the balance between a Kalman Filter and a ...
chutsu's user avatar
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1 answer
54 views

Infinite-order polynomial convergence

This isn't a question about Taylor series. A little background: I'm a robotics engineering student looking at polynomial trajectories, specifically using polynomials to define the rate at which the ...
Samuel Rooney's user avatar
1 vote
0 answers
36 views

Pose matrices and robotics 2D movement

I have a robot starting from the origin. It first turns 90 degrees (yaw), then move to (5,10), then it starts to move along its own negative x direction at each step with a translation of 1. Here is ...
Nick X Tsui's user avatar
0 votes
1 answer
75 views

Cotangent lift of the embedding is zero

I am reading the work on variatonal collision integrators from the programmers point of view, since I want to implement it is the software. The work is publicly available here: caltech. I want to ...
m8dotpie's user avatar
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Convexity of minkowski space when two triangles collide

I am working on a Python program to show the collision of two triangles by using Minkowski difference. I am subtracting each point from one triangle from every other point on the other triangle. The ...
Hussain Bhavnagarwala's user avatar
0 votes
1 answer
20 views

Confused with understanding an equation written with inverse compositional operators

In the paper "Are we ready for Autonomous Driving? The KITTI Vision Benchmark suite" by Lenz and Urtasun (https://www.cvlibs.net/publications/Geiger2012CVPR.pdf) \ The translation error ...
Azmyin Md. Kamal's user avatar
0 votes
1 answer
94 views

Riemannian Metric from Hamiltonian?

Suppose I have a robot arm configuration space (c-space) $Q$ and with Lagrangian $L = T - V$ on $TQ$, and I set up the equation of motion $$\frac{\partial}{\partial t}\left\{\frac{\partial L}{\partial ...
Jeffrey Rolland's user avatar
2 votes
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How to calculate angle of rotation given a vector and a point

sorry if the title seems vague. English is not my first language and I dont know what to search to find the answer to my problem. I will preface this by explaining the purpose of this question. I have ...
ibrahim mohamed's user avatar
1 vote
1 answer
89 views

A single rotation to reach the final pose of a frame

The following question is from Kinematic Analysis of Robot Manipulators by Carl D. Crane, III, Joseph Duffy: "The transformation that relates the A and B coordinate systems is given as That is ...
Ali Kıral's user avatar
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0 answers
90 views

Find Lattice for 2-Torus with Given Riemannian Metric?

I have a (standard?) 2-torus $T^2$ with a non-standard Riemannian metric on it \begin{array}{lcr} g(\theta_1,\theta_2) & = & \begin{bmatrix}Izz1 + Izz2 + (L1^2*m1)/4 + L1^2*m2 + (L2^2*m2)/4 + ...
Jeffrey Rolland's user avatar
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Why is the energy cost functional mostly defined as $u.u^T$?

In optimal control theory, while minimizing the energy of a say mobile robot, the expression for the cost functional is generally $u.u^T$ where $u$ is the control vector. I searched why the energy ...
Phoenix8128's user avatar
2 votes
0 answers
173 views

Jacobian in SE(3)

I have the following 3D composition of SE(3) elements: $$ Z = (X \ T)^{-1} \ Y T = T^{-1} X^{-1} Y T $$ Following this paper I have managed to compute the jacobians of $\log Z$ wrt $\log X$ and $\log ...
castillon's user avatar
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2 votes
2 answers
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How to solve $\,A\sin(\theta_2-\theta_1) - B\sin(\theta_1) = 0$

I want to find the solutions of the following equation (In order to find the singular points of a robot). $A,B$ are positive numbers, and actually : $A = 0.2531,$ $B = 0.2455.$ $$ A\sin(\theta_2 - \...
MIKE PAPADAKIS's user avatar
1 vote
1 answer
113 views

What rigid graphs can be decomposed into triangles such that each edge is in exactly one triangle?

Is there a general algorithm/condition to tell if a graph can be decomposed into triangles such that each edge is in exactly one triangle (the graph $G$ has a set of subgraphs such that each subgraph ...
Nathan Usevitch's user avatar
0 votes
0 answers
122 views

PD control with gravity compensation

Given the robot dynamics of the form $$M(\theta)\ddot{\theta}+C(\theta, \dot{\theta})\dot{\theta}+G(\theta)=u$$ where the notations have the standard meaning ($M$ is the inertia matrix, $C$ is ...
The Limit Does Not Exist's user avatar
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0 answers
240 views

What is the correct derivation for the Rotation Matrix?

This might seem like a basic question, but I've been stuck on this for a bit. Upon looking at many different sources, I found 2 derivations of the rotation matrix. One of them considers a point at a ...
skinnybb's user avatar
1 vote
0 answers
98 views

3d rotation representation for multiple turns

Currently I am learning to use quaternions to represent rotations in the 3D world. The task is to make the object rotate for a given angle in certain time. I am now wondering which type of rotation ...
liamxqy's user avatar
  • 11
1 vote
2 answers
131 views

How to get the form of elements of the Lie algebra?

I'm leaning Lie theory in robotics. My question comes from a paper: A micro Lie theory for state estimation in robotics by Joan Sola et al. at page 4: For multiplicative groups this yields the new ...
James White's user avatar
1 vote
1 answer
89 views

Intuition Behind the EKF Approximation

I'm a student that recently started taking a course on cognitive robotics. The book I use is Probabilistic Robotics by Thrun Burgard and Fox. In the EKF algorithm, we linearized the action model in ...
Malzahar's user avatar
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Relating EKF Localization with EKF Equations

I have been trying to understand EKF localization from Probabilistic Robotics by Thrun Burgard and Fox. There the covariance prediction is given by $$\overline{\Sigma }_t=G_t\Sigma_{t-1}G^T_t+V_tM_{t-...
Malzahar's user avatar
  • 540
0 votes
0 answers
36 views

Why is the vector about which the frame is rotated is given by: A r  = [ 0.707, 0.707, 0]T

Im querying why the vector which the frame is rotated is given by [0.707,0.707,0]. does equal distance have an impact etc
B Hart's user avatar
  • 11
1 vote
2 answers
147 views

How do I solve this robot arm movement?

I am moving my robot arm's tool pitch. In this example, the tool is moving pitch by 80 degrees (lime green number). The red lines are the current position of the arm. The blue lines are the position ...
Evan's user avatar
  • 123
-2 votes
1 answer
279 views

Jacobian inverse in robotic

In robotics, we have $v=J\dot q$ ---------------- (1) to calculate the velocity ($v$) in cartesian space. So, we get. $\dot q={J^-}^1 v $ ---------------- (2) where, $v = [v_x, v_y, v_z, \omega_x,...
RobX's user avatar
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1 vote
1 answer
69 views

Trying to find an equation for distance you can go based on Xpos and Ypos of a robot, robot angle, and distance from an object.

So I have a robot, and I am trying to push an object into a red border without falling off the edge. the border is 100mm thick, the whitespace in between the 4 borders in the square is 2000x2000mm, ...
j4kj4k08's user avatar
-1 votes
1 answer
121 views

How to get the angle of a robot arm end tool?

I need to move a robot arm along a straight line by 10cm. image The red lines are the current position of the arm. The blue lines are the position the robot needs to be moved to. The black lines are ...
Evan's user avatar
  • 123
1 vote
0 answers
199 views

Orientational difference between two poses using axis angle representation

I am working on a problem in robotics where I have to compute the orientational difference $\mathbf{e}_O \in \mathbb{R}^{3}$ between a robot's current end-effector pose and a desired pose. I have ...
Julian's user avatar
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0 votes
0 answers
117 views

Notation for block of vectors/matrices holding elements with different shapes

I am interested in having a notation similar to block-matrix operations, where the elements of the block differ from each other, making it not truly a block-matrix. Its best to give an example (from ...
Danfoa's user avatar
  • 105
0 votes
0 answers
42 views

How to specify second degree of freedom while calculating rotation from one direction vector to another

I want to orient the robot endeffector using a direction vector that I calculate myself. The robot will always start from the same position with the endeffector pointing straight down. I already have ...
dmr's user avatar
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1 vote
0 answers
145 views

Diffeomorphism between star-space and sphere-space

I am a robotics student who has very poor knowledge of topology, thus I hope my question is not ill-posed. Studying the classical textbook [1], I found an interesting diffeomorphism from stars* to ...
Antonio Bono's user avatar
0 votes
1 answer
790 views

Relation between two frames in different coordinate systems

Salutations, I have the following problem, There exists two frames (by frame I refer to a point in $3$D space with known translation and orientation of where axis are pointing in relation to their ...
Bruce Jameson's user avatar
1 vote
1 answer
60 views

Analytic solution inverse kinematics - different solutions with different calculation steps

I have the following problem: $$5\cos \theta_1+3\sqrt{3}\sin \theta_1=4\qquad\qquad\textbf{(I)}$$ $$5\sin \theta_1-3\sqrt{3}\cos \theta_1=6\qquad\qquad\textbf{(II)}$$ I have two seemingly correct ...
meschi's user avatar
  • 11
1 vote
0 answers
31 views

Need help with a proof. Graph generation in an environment with obstacles.

Given is a set of points (PFeature) in a map which are at maximum distance from their closest obstacles. these points are obtained after generating the generalized voronoi diagram and applying a ...
bram verhulst's user avatar
1 vote
1 answer
1k views

Camera Calibration - Calculate Rotation and Translation

I have a calibration problem between two cameras, my setup contains two static cameras. Both cameras capture the same scene but from a different viewpoint. I estimate the individual cameras poses ...
Hannah Stark's user avatar
2 votes
1 answer
78 views

Pontryagin principle for a system $\dot{x}=M(x)u$ and quadratic cost

Context: I am studying systems of the form $\dot{x} = M(x)u$ for some state dependent matrix $M(x)\in\mathbb{R}^{n\times m}$ with $m<n$, $x\in\mathbb{R}^n, u\in\mathbb{R}^m$ and initial condition $...
FeedbackLooper's user avatar
0 votes
1 answer
352 views

When rotating reference frames using the XYZ fixed angle convention, why do we multiply matrices in the inverse order that rotation was done?

I'm reading about the XYZ fixed angle convention for relating reference frames. It says that to solve for the description of frame {B} in frame {A} we do the following: Start with the frame ...
ahzired's user avatar
0 votes
1 answer
192 views

Rotation of robotic arm (kinematics)

I have a defined robotic arm, consisting of one joint, base and the ending. The base of the arm is in point A (0,0,0) - this is not possible to rotate, first joint is in point B (0,1,0) and the ending ...
dobit03's user avatar
15 votes
2 answers
509 views

Least-squares solution to system of equations of $4 \times 4$ matrices with $2$ unknown matrices

This question is in the context of a robotics problem. The goal is to track a robot using both its onboard odometry system and a VR system (HTC Vive Pro) using a VR controller mounted to the robot. ...
couka's user avatar
  • 151
1 vote
1 answer
380 views

Defining a rigid sphere

Motivation I don't remember any reference, but I recall that many materials and papers related to robotics consider a rigid body; a rigid wheel, a rigid sphere but don't give the definition of it and ...
欲しい未来's user avatar
0 votes
0 answers
34 views

Bounding the uncertainty function in Robust Inverse Dynamic Control

Given the standard dynamical model of an n-DOF robotic system consists of only revolute joints: $ M(q)\ddot{q} + C(q,\dot{q})\dot{q}+g(q)=\tau $ The robust inverse dynamics control input $\tau$ can be ...
Demerzel's user avatar
0 votes
1 answer
710 views

Finding intersection of two lines in 3D space w/ Unit Vectors

I've recently started learning about 3D transformations in robotics and I was working through some problems on my own to get comfortable with working/visualizing in 3D. Now lets say I have two points ...
bumblyboi's user avatar
0 votes
0 answers
42 views

Relationship between geodesics and dimension of spheres?

Let n be an odd positive integer and $U\subset S^{n}\times S^{n}$ be the open subset consisting of all couples (A,B) such that $A\neq -B$. Let $\pi:(S^{n})^{I} \to S^{n}\times S^{n}$ be the fibration ...
user975332's user avatar
1 vote
1 answer
175 views

Inverse dynamics control: Proof of asymptotic stability of error system

The inverse dynamics control in robotic applications yields the error system \begin{equation} \ddot{\mathbf{e}} + \mathbf{K}_1 \dot{\mathbf{e}} + \mathbf{K}_0 {\mathbf{e}} = \mathbf{0} \end{equation} ...
Gerald's user avatar
  • 41
0 votes
1 answer
65 views

Which properties are used in this Jacobian equation from Denavit-Hartenberg method?

I was recreating an algorithm for a 4 DOF robot arm. In a code from GitHub I found that a way to do the inverse of the Jacobian was: $$|J^TJ|\geq 1 \Rightarrow (J^TJ)^{-1}J^T=J^{-1}$$ I tried with ...
DuravitHeisenberg's user avatar
0 votes
0 answers
141 views

Drive unicycle kinematics equations through the geometry

Consider a unicycle model as described here. The unicycle dynamics in discrete-time can be written as: $$ \begin{array}{l} {x_{k + 1}} = {x_k} + \Delta {s_{k + 1}} \times \cos ({\theta _{k + 1}})\\ {...
sci9's user avatar
  • 219
0 votes
1 answer
512 views

Pseudo Inverse of Jacobian Matrix

I have a script written by someone else that outputs end-effector velocities. I need to transform these end-effector velocities to joint velocities. This requires the pseudo-inverse of the Jacobian ...
user463102's user avatar
1 vote
1 answer
473 views

"Fusion" of multiple uncertain estimates with covariance matrices

this is my first post here. I tried my best to follow all the guidelines and to state the problem as clear as possible but should something be sloppy or unclear, I will be happy to update the question ...
domiinio's user avatar