# 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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23 views

### 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 ...
27 views

### 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 ...
21 views

### 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 ...
24 views

### 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 ...
18 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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### Moore Penrose inverse of the end-point map

We consider the end-point map $\mathcal{E}$ of a nonlinear control system: $$\dot{x}(t) = f(t,x(t), u(t)), \quad x\in \mathbb{R}^n,\ u\in \mathcal{U}\subset L^{2}([0,T], \mathbb{R}^m)$$ starting ...
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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 ...
17 views

### 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 ...
21 views

### 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 ...
38 views

### Converting two magnitudes (of joysticks) to one single vector with direction

I'm working on a driver system for a robot and I intend to use a dual joystick "tank drive" system. Each joystick controls one half of the drive system - left stick controls left wheels, right stick ...
19 views

### Given a spherical 6-bar linkage with 3 angular actuators, can I find the *analytical* solution of the inverse kinematics problem?

Description: Scheme of the problem This is like a spherical 4-bar linkage, but with 6 bars. Everything's on a sphere. P1 and P6 are static, while ther rest is mobile. Parameters: r is the sphere ...
22 views

### How to compute the orientation error between two 3D coordinate frames?

For my master thesis in robotics I have to compute the orientation error between two coordinate frames, called E and H. Their orientation is expressed through rotation matrices (3x3) with respect to a ...
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### I need to estimate how narrow a passage is for a point surrounded by obstacles.

I find the nearest obstacle from a given point. For the obstacle on the opposite side which along the perpendicular between the given point and the obstacle in the first case, how do I find this point?...
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### Mathematical Description of Space of Points Reachable by Robot Hand

Consider a planar robot consisting of n rigid segments of length $l_i, 1 < i < n$, that are connected by revolute joints. The hand or tool is attached, by means of a freely orientable joint, to ...
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### Find out a general expression for the coordinates of a point in a square based on certain distances and an angle

my problem appears to be a very simple one, but I just can't seem to figure it out, maybe I am just overlooking something… The problem is defined as the following (refer to the figure for better ...
32 views

### Using a robot arm to reach a specific point with arbitrary orientation

I want to use a 6-DoF robot arm to reach a user-given point $$P_{target} = (x, y, z)$$ with arbitrary orientation. My robot arm is equipped with a laser pen and what I want to do is to aim ...
14 views

### How to get effort values of a robotic joint in N.m?

I currently have the force and torque values (in 3D vectors) of the parent and child link (joint wrench) of a revolute joint. My question is how can I get the effort values of a joint? Not in vector ...
30 views

### Theoretical mechanics - Inverse Kinematicss

On theoretical mechanics essay at the university, I have stumbled in the issue below: Given $\textbf{u}^T \textbf{D}(\mathbf{\theta}, \alpha)\textbf{v}(\textbf{d}) = \textbf{m}(\textbf{d})$, find out ...
237 views

### 2 wheel robot kinematics — transformation of coordinates

I am working my way through the Mobile Robot Kinematics book from CMU, available at http://www.cs.cmu.edu/~rasc/Download/AMRobots3.pdf. I am having a hard time deriving the derivative of the robot ...
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### Calculating a rotation matrix

I am studying robotics as an undergraduate. One of the things we're doing is rotational matrices. As a general principle I understand them, and if given a point in A I can find the given point in B ...
635 views

### What's the difference between Spatial velocity and Body velocity?

Let us suppose a rigid body $\{B\}$ is undergoing rotational and translational motion,and the spatial frame is $\{S\}$. In this case, we say that its configuration space is the Special Euclidean group,...