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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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 ...
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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 ...
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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 ...
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124 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 ...
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53 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 $...
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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 ...
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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 ...
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Covariance of fused poses. Should it be normalised by the number of poses?

I came across this paper from T. Barfoot and P. Furgale: "Associating Uncertainty With Three-Dimensional Poses for Use in Estimation Problems" Link: http://ncfrn.mcgill.ca/members/pubs/...
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15 votes
2 answers
480 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. ...
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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 ...
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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 ...
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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 ...
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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 ...
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Make quaternion that aligns Z with a vector and rotates about that vector

I working with robots and am trying to align the end effector with a vector. The reference frame of the end effector is placed in such a way that Z is pointing directly out of it. The robot can rotate ...
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118 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} ...
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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 ...
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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}})\\ {...
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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 ...
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1 answer
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"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 ...
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Determine if a value falls between two limits when the upper limit can become lower than the lower limit

I have a rotary device that provides feedback in the range of 0-359.99 degrees, once the device moves past 359.99 the feedback restarts at 0. I command the device to a degree position and then I ...
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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 ...
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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\\...
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Inverse kinematics algebraic solutions: Multiplying each side of transform equation by an inverse

I am looking at closed form algebraic solutions to inverse kinematics problems (in this case for robot manipulators). The correct solution found the transform matrices via forward kinematics (using ...
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Finding inverse tangent from sine?

Im watching a video that goes from $ p*sin(\phi - \theta) = 0 $ to $ \phi - \theta = atan2(0,\pm1)$ without any intermediate steps. Could anyone explain the maths behind this? Unsure if its some ...
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Are there any advantages of doing the exponential map of an element $\in \mathfrak{se}(3)$ in order to get the translation component?

I'm currently learning about Lie Groups, concretely about the special Euclidean group $SE(3)$, which in the field that I am studying (state estimation for robotics) is commonly used for representing ...
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Help Understanding Proof for Relationship between SO(3) and so(3) Matrices

I am currently reading through a book titled "Modern Robotics," and in it, I have encountered a proof of a proposition stating: Given any $\omega \in \Bbb R^3$ and $R∈SO(3)$, the following ...
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Get a 3d Pose from Acceleration + rotation angles

I am trying to get a pose (x,y,z + angles x,y,z). What is given (i is a discrete time t_i): pos_x(i), pos_z(i), pos_z(i) rot_x(i), rot_y(i), rot_z(i) a_x(i), a_y(i), a_z(i) a_rot_x(i), a_rot_y(i), ...
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Rotate vector so it aligns with Z, by only rotating around two axes

My math skills are very rusty and I'm struggling with this question. I have a robot that can rotate around the Z axis and around the X axis and I'm trying to get the angles for the joints so that a ...
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Multidimensional obstacle avoidance in ODE. Part II

Multidimensional obstacle avoidance in ODE For some time, I studied this question more closely and came to the conclusion that it is best to assign its own constraint for each selected coordinate. ...
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Expressing linear and angular acceleration of a rigid body in terms of its homogeneous transformation

I am currently reading "A Mathematical Introduction to Robotic Manipulation" by R. Murray, Z. Li, and S. Sastry to learn about kinematics of rigid bodies. Given a homogeneous transformation $...
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Differential Form Integral (Work?) on C-Space of Robot Arm?

So, I would like to do an Extra Credit problem for my Vector Analysis course (the last half of a traditional Calc III course) that involves robotics (my new toy). However, it's Week 05 already, I want ...
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Rotating $3D$ one point to the other point

Let's say I have a point $A \ (1,2,3)$ and point $B\ (2,3,4)$ If I want to get point $B$ from point $A$ using angles between $A$ and $B$ in $x,y,z$ axis. How can I get point $B$ from point $A$? Here ...
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677 views

How do I find the roll, pitch, and yaw angles of a plane (/or a plane that coincides with 3 points in space ) in 3D?

Imagine that we have 3 points $P_1,P_2$ and $P_3$. $P_1,P_2,P_3$ creates a plane in 3D space. Let's say the plane equation is $Ax+By+Cz+D=0$. How can I find the roll, pitch, yaw angles of this plane? $...
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How to calculate "undo" rotation except for parallel rotation

Let's say we start with a vector $u = [0, 0, 1]$ which represents the positive z-axis. Now, let's say we arbitrarily transform this vector via a rotation $z' = R \begin{bmatrix}0 \\ 0\\ 1 \end{bmatrix}...
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3 answers
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Calculate path of vehicle with two wheels parallel to each other

There's a vehicle that starts at $P(0|0)$ oriented in positive y direction. This vehicle has two wheels that are a certain distance $d$ apart, have a diameter of $\frac{10}\pi cm$, are parallel to ...
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4 votes
1 answer
266 views

Problem designing a control law

I am trying to build a posture regulation control which works with acceleration inputs. Doing it with velocity inputs,I have well understood how it works. Moreover,for now, the controller only ...
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2 votes
1 answer
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Regressor-passivity robot control. Help with simulation (Simulink/Matlab).

I'm trying to simulate a 2DOF planar pendulum with a regresor-passivity control, the thing is I've been having some issues with my simulation, I'm using Simulink, but in theory I know my control law ...
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134 views

Derivative a Matrix quadratic form with respect to a inner variable? Lyapunov function and pasivity control.

I'm trying to derivate a Lyapunov candidate function in order to analize stability for a pasivity control strategy but I'm not sure how to proceed. I hope some of you could guide me here, the ...
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1 vote
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identify the 3D object in space using laser point sensor and bring its origin wrt laser values

Description : we are doing robotic application where i want to know the position of the object with respect to origin Purpose of application : here i am going to teach robot with respect to master ...
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Car overtaking — what function can be used to model this?

I want to compute the difference in time dependent on the maximum distance that is reached when a car overtakes another. Assuming the use of two variables (time and horizontal distance) what function ...
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3 answers
127 views

Can someone explain the proof of the following linear differential equation

I was working through a robotics book, and came across the following equation, solution, and proof where $A$ is a $n \times n$ constant matrix, and $x_0 = x(0)$ $$\dot x (t)=Ax(t)$$ whose solution is :...
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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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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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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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2 votes
1 answer
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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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38 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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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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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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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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1 answer
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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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