Questions tagged [geometry]

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7
votes
1answer
100 views

6D localization with 6 lasers

I have to know where a multi-rotor is, in a rectangular room, via 6 lasers, 2 on each axis. The problem is like this: Inputs : Room : square => 10 meters by 10 meters 6 positions of the lasers : ...
3
votes
1answer
41 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 ...
3
votes
1answer
131 views

Mobile robot algorithm implementation error

I am working in reproducing a robotics paper, first simulating it in MATLAB in order to implement it to a real robot afterwards. The robot's model is: $$\dot{x}=V(t)cos\theta $$ $$\dot{y}=V(t)sin\...
3
votes
2answers
90 views

Fence avoidance for manually controlled robot

I'm trying to find known techniques for keeping a manually controlled robot within a known polygon fence. More specifically, a pilot controls a robot by issuing desired velocity vectors, and the ...
3
votes
3answers
1k views

Generalized Voronoi Diagram

I need to compute the Voronoi diagram for a map with some obstacles but I can't find any pseudo-code or example in MATLAB. The "voronoi" function in MATLAB works with points, but in this case the ...
2
votes
4answers
1k 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 ...
2
votes
1answer
65 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 ...
2
votes
1answer
75 views

Efficient sphere surface area search

As shown in the figure, there are objects of arbitrary shapes placed on the surface of the sphere at arbitrary locations. The problem is to search the surface to locate these objects in most efficient ...
2
votes
1answer
904 views

Image coordinate to robot coordinate

I am working with a Nao robot. One if the things I want to do is the following: Take an image of geometrical objects in front of the Nao (done) Extract features from the objects in the image, such as ...
2
votes
1answer
41 views

Recognizing a line from three r-theta ultrasonic distance readings?

Anyone know of sample Python code, or a tutorial, on the polar coordinate math for recognizing that three ultrasonic distance readings form a straight line? ...
2
votes
2answers
194 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 ...
2
votes
0answers
81 views

Consitent Scale in Monocular pose estimation

I just wanted to know if scale is conserved across multiple images, when doing a process such as monocular odometry. I know in reality the scale tends to drift over time due to accumulation of small ...
1
vote
1answer
51 views

Representation of 2D coordinate space with orientation

I wanted to know what is the mathematical representation of 2D coordinate space with orientation in the same plane. 2D coordinate space is represented as $R^{2}$, how do I include orientation in the ...
1
vote
1answer
37 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 ...
1
vote
0answers
19 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 ...
1
vote
0answers
78 views

How to get RPY(Roll, Pitch, Yaw) from directional cosines from a single vector?

I'm trying to find the pose of an 3D vector in terms of RPY. Let's say the two end points of the vector is P0(x0, y0, z0) and P1(x1, y1, z1). So the centered vector I get is V(Vx, Vy, Vz) = P1 - P0 = (...
1
vote
0answers
73 views

Which Trajectory representation for optimization

I'm strugling on that problem for a while, so any help is welcome. I need a trajectory representation that is performant for optimization, i.e. I want something that computes quickly. The function I ...
1
vote
0answers
41 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 ...
0
votes
1answer
25 views

Finding orientation angles of end-effector from the DH parameter table and transformation matrices

Let's say we have a manipulator with the following DH parameter table: and transformation matrices: $$A_{01}= \begin{bmatrix} \cos(q_1) & \sin(q_1) & 0 & 95\cos(q_1)\\ \sin(q_1) & -\...
0
votes
1answer
1k views

6 axis robot arm with non-perpendicular axes?

Lately I've been thinking about 6 axis robots and noticed that all examples that I've seen on the internet use the same configuration of axes: Vertical axis waist (1), horizontal axis shoulder (2) ...
0
votes
1answer
127 views

Relative orientation of two robots

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: $...
0
votes
1answer
42 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. ...
0
votes
1answer
100 views

Do I need to use Inverse Kinematics if I have the coordinates of all joints?

So I have the positions of all the joints (x,y,z) of a robot arm. I need to calculate the angles of the joints to feed them to another similar robot arm. I cannot get the angles from the robot I need ...
0
votes
2answers
78 views

Vısual sensor.camera lenses with a field of view of more than 180 degree

What kind of camera models can be used for lenses with a field of view of more than 180 degree ? Is ıt possible if not why? Are fisheye lenses suitable for this purpose?