# Questions tagged [geometry]

The tag has no usage guidance.

28 questions
Filter by
Sorted by
Tagged with
32 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 ...
94 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 ...
38 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 ...
41 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 ...
76 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. ...
51 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 ...
48 views

### How to calculate twist and wrench in local and global frames

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 ...
159 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 ...
61 views

42 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 ...
200 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 ...
38 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 ...
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: \$...