# Questions tagged [geometry]

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### Body angle of a centre-articulated robot

Wondering if anyone can help me out with this one, or point me in the right direction. I am working on a centre-articulated robot, which is steered via a push-pull chain drive. The chain drive is ...
23 views

### Explanation of the epipolar constraint in stereo imaging

I am watching this video, in which the epipolar constraint is defined as $x_l \cdot (x_l \times t)=0$ It means that the vector $x_l$ that passes through the observed point and the left camera origin ...
• 101
40 views

### How to find mathematical model of a wheeled robot (to compute robot's trajectory at given time steps) including its kinematic

I would like to learn, how to find proper kinematic model of robot in mathematical form. For example: I would like to create a model of a car, from which I could compute its position and rotation at ...
114 views

### How can I draw a line using rotation of two circles?

I’m building a drawbot with a self imposed constraint that it’s method of motion is just two rotating disks. One holding the paper and one holding the pen. However, the math to calculate the right ...
• 123
1 vote
61 views

### given current position and Quaternion and target local rotations (α, β, γ, in radians), how to calculate the new Quaternion

Say we have an object (e.g., end-effector of a robot) that is defined in a general coordinate system by a Cartesian position and Quaternion. since the Quaternion is with respect to a general and fixed ...
• 151
1 vote
72 views

### What is the idea behind calling configuration space a metric space?

In my robotics textbook 1 , the configuration space has been defined configuration space the following way: A configuration space is a metric space compromising of all given configuration of a ...
182 views

### Bearing landmark localization

I am trying to initialize the position of a set of landmarks using only bearing observations. Each robot pose, described by position (x,y) and orientation (theta), observes a small set of landmarks. ...
• 3
88 views

### given position and orientation of two coordinate frames, how to transfer a vector from one to another

given position and orientation of two coordinate frames, how can transfer a vector from one frame to another. The position is given in Cartesian space and the orientations in quaternion or Euler ...
• 151
1 vote
95 views

### How to calculate twist and wrench in local and global frames [closed]

I am rather new to screw theory and also lost in robotics books' formulas. we have a simulator of a robot arm within Mujoco physics engine and I'm wondering how I can calculate wrench and twist in the ...
• 151
251 views

### relationship between geometric twist jacobian and wrench

I read the robot textbook of Peter Corke and Richard M. Murray, in Peter’s, chapter 8 about jacobian, there are two jacobian, one is geometric jacobian $^0J$ from math, other is world coordinate frame ...
• 177
283 views

1 vote
47 views

### How to determine the angles between a UAV and a sphere

I have an UAV modeled in three dimensions with let's say position coordinates $p_{uav} = (x_1,y_1,z_1)$ that is moving in a direction $d = (d_x,d_y,d_z)$ and a moving obstacle modeled as a sphere with ...
2k views

### Most accurate rotation representation for small angles

Assume that I have a rigid body for which I know that it can rotate with respect to a global reference frame (which is considered fixed and already given) for only a few degrees of angle, so I can ...
• 129
218 views

### Angle to a circle tangent line

I want to simulate the detection of a moving object by a unicycle type robot. The robot is modelled with position (x,y) and direction theta as the three states. The obstacle is represented as a circle ...
1 vote
40 views

### Which geo-projection to use for odometry [closed]

I would like to make a little survey regarding the (geo)spatial projection that you use when elaborating your GPS and movement data for the spatial awareness of your robots. Moving all GPS ...
• 113
Given two robot arms with TCP (Tool Center Point) coordinates in the world frame is: $X_1 = [1, 1, 1, \pi/2, \pi/2, -\pi/2]$ and $X_2 = [2, 1, 1, 0, -\pi/2, 0]$ The base of the robots is at: \$...