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."
146
questions
0
votes
0
answers
6
views
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 ...
0
votes
1
answer
16
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 ...
0
votes
1
answer
64
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 ...
- 817
2
votes
0
answers
31
views
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 ...
1
vote
1
answer
75
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 ...
- 147
0
votes
0
answers
23
views
What is the correct function to minimize to calibrate 3D Inertial Measurement Unit (sensitivity matrix + offset of accelerometer and compass)
I have been experimenting with accelerometer and compass calibration and I can't decide how the function I am trying to minimize should look like.
Basically, I have number of measurements $x \in M$, ...
- 15
0
votes
0
answers
17
views
Computing covariances of features/landmarks in environment in scan-matching algorithm
I am reading a paper titled "Real-Time Correlative Scan Matching" which explains a scan-matching algorithm used to obtain pose-pose constraints in pose-graph Simultaneous Localization And ...
0
votes
0
answers
81
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 + ...
- 817
0
votes
0
answers
48
views
How to find the relationship between the quaternion rate and angular velocity?
I'm trying to find a solid proof of the relationship between the quaternion rate and angular velocity, but I keep running into the same problem.
Theorem:
If frame $B$ is rotating in frame $A$ at a ...
0
votes
0
answers
9
views
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 ...
- 77
2
votes
0
answers
102
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
$$
Following this paper I have managed to compute the jacobians of $\log Z$ wrt $\log X$ and $\log ...
- 109
2
votes
2
answers
79
views
How to solve $\,A\sin(\theta_2-\theta_1) - B\sin(\theta_1) = 0$
I want to find the solutions of the following equation (In order to find the singular points of a robot).
$A,B$ are positive numbers, and actually :
$A = 0.2531,$
$B = 0.2455.$
$$ A\sin(\theta_2 - \...
0
votes
1
answer
75
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 ...
0
votes
0
answers
74
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 ...
0
votes
0
answers
65
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 ...
- 1
0
votes
0
answers
38
views
What is the connection between extrinsic and intrinsic rotation?
The image below shows the frames $F1$ and $F2$ as well as the rotation matrix $R1$ which is a 90 degree rotation about the z axis of $F1$:
$$R1 = {}^{F_1}R_{F_2}(\pi/2)_z$$
Now let's say I wanted to ...
- 650
1
vote
0
answers
54
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 ...
- 11
1
vote
1
answer
91
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 ...
- 123
1
vote
1
answer
39
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 ...
- 510
0
votes
1
answer
18
views
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-...
- 510
0
votes
0
answers
27
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
- 11
0
votes
0
answers
18
views
What is the difference/relation between DMPs and Bezier curves?
I'm studying the Dynamical Movement Primitives (DMPs) for generating some trajectory from demonstration data, but I'm wondering why they are preferred to other solutions like Bezier curves (or also B-...
- 1
1
vote
2
answers
123
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 ...
- 123
-2
votes
1
answer
137
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,...
- 1
1
vote
1
answer
68
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, ...
- 11
-1
votes
1
answer
75
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 ...
- 123
1
vote
0
answers
131
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 ...
- 13
0
votes
0
answers
53
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 ...
- 105
0
votes
0
answers
36
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 ...
- 1
1
vote
0
answers
87
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 ...
- 21
0
votes
0
answers
29
views
How many vectors do I need to span the vector space for Velocity, Distance, Angles, Acceleration, Position, and Time?
I am working on a Robot Arm simulation project and trying to get those 6 varibles, in my question, coming from the Robot Arm. The robot arm has 6 joints and each joint can run the motor inside to ...
- 111
0
votes
1
answer
438
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 ...
1
vote
1
answer
54
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 ...
- 11
1
vote
0
answers
29
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 ...
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 ...
- 111
2
votes
1
answer
63
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 $...
- 1,674
0
votes
1
answer
229
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 ...
- 3
0
votes
1
answer
103
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 ...
- 1
15
votes
2
answers
497
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.
...
- 151
1
vote
1
answer
284
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 ...
- 881
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 ...
- 33
0
votes
1
answer
440
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 ...
- 85
0
votes
0
answers
40
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 ...
- 59
1
vote
1
answer
158
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}
...
- 41
0
votes
1
answer
61
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}$$
I tried with ...
0
votes
0
answers
103
views
Drive unicycle kinematics equations through the geometry
Consider a unicycle model as described here. The unicycle dynamics in discrete-time can be written as:
$$
\begin{array}{l}
{x_{k + 1}} = {x_k} + \Delta {s_{k + 1}} \times \cos ({\theta _{k + 1}})\\
{...
- 209
0
votes
1
answer
379
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 ...
- 449
1
vote
1
answer
235
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 ...
- 13
1
vote
1
answer
145
views
Proving Euler Angle Rotations of ZXZ spans SO(3)
I am looking for a succinct proof that showcases a ZXZ combination of rotations can reach and orientation in SO(3). I know this combination is one of the 6 (or 12 if you include both intrinsic and ...
0
votes
0
answers
60
views
Partial derivative of function by a vector
I am struggling to understand the results of a partial derivative of a vector function with respect to a vector.
A plane has equation $\begin{bmatrix} a&b&c&d\end{bmatrix}\begin{bmatrix}x\\...
- 33