# Questions tagged [kinematics]

Kinematics is the branch of mechanics dealing with the motion of points and objects.

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### Calculate position of differential drive robot

How do you calculate or update the position of a differential drive robot with incremental sensors? There is one incremental sensor attatched to each of the two differential wheels. Both sensors ...
13k views

### How can the inverse kinematics problem be solved?

The forward kinematics of a robot arm can be solved easily. We can represent each joint using Denavit–Hartenberg transformation matrices. For example, if the $i^{th}$ joint is a linear actuator, it ...
5k views

### What are the advantages of using the Denavit-Hartenberg representation?

When one wants to model a kinematic chain and in particular define the frames attached to each body, it is common to use the Denavit-Hartenberg parameters. What are the advantages of this ...
4k views

### jacobian of Abb irb140 robot

Can someone please help me with the jacobian matrix equations for Abb irb140 robot. Or an easy way by which I can derive it given the DH parameters. I need it to implement some form of control that am ...
3k views

### Why do we generally prefer DH parameters over other kinematic representations of robot arms?

I am specifically interested in DH parameters versus other representations in terms of kinematic calibration. The best (clearest) source of information I could find on kinematic calibration is in the ...
4k views

### How to calculate the right and left speed for a tank-like rover?

I am trying to control the Rover 5 robot using an Android app with a touch-based joystick control in the app UI. I want to calculate the speed of the left and right motors in the rover when joystick ...
3k views

### How much accuracy could I get position tracking with a 3-axis accelerometer and gyro sensor, and compass, and how would I do it?

Given a 12' x 12' field (4m x 4m), a reasonably cheap 3-axis gyro sensor and accelerometer, and compass, I plan to design a device capable of tracking its position to sub-centimeter accuracy for a ...
3k views

### Jacobian-based trajectory following

I would like to control my 7 DOF robot arm to move along a Cartesian trajectory in the world frame. I can do this just fine for translation, but I am struggling on how to implement something similar ...
6k views

### Forward Kinematics/D-H parameters for perpendicular joint axes

I am trying to compute forward kinematics of the Kuka youBot using DH convention: http://www.youbot-store.com/youbot-developers/software/simulation/kuka-youbot-kinematics-dynamics-and-3d-model The ...
3k views

### How to design a differential steering mechanism?

I want to give my robot a differential mechanism for the system of turning and steering. Considering the case of turning a right-angled corner, the robot will achieve this by following a gradual ...
723 views

### inverse kinematics for 6 jointed robots

I am a uncertain about how to compute the right homogeneous transformation matrix to compute an inverse kinematic Q-configuration. Looking at robot like this Where at the end of this robot I have ...
4k views

I am the moment trying to compute the transformation matrix for robot arm, that is made of 2 joints (serial robot arm), with which I am having some issues. L = 3, L1 = L2 = 2, and q = ($q_1$,$q_2$,... 2answers 202 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 ... 3answers 20k views ### Position Control vs Velocity Control vs Torque Control Please can somebody explain to me the difference between Position Control, Velocity Control, and Torque Control? Specifically, I am thinking in terms of a robot arm. I understand that position control ... 4answers 24k views ### Computing the Jacobian matrix for Inverse Kinematics When computing the Jacobian matrix for solving an Inverse Kinematic analytically, I read from many places that I could use this formula to create each of the columns of a joint in the Jacobian matrix: ... 1answer 1k views ### Velocity Model Motion in Matlab (Probabilistic Robotics) I want to implement the velocity motion model in Matlab. According to Probabilistic Robotics page 124, the model is as following \begin{align*} \hat{v} &= v + sample(\alpha_{1} v^{2} + \... 2answers 3k views ### Solving Inverse Kinematics with Gradient Descent I am trying to implement my own inverse kinematics solver for a robot arm. My solution is a standard iterative one, where at each step, I compute the Jacobian and the pseudo-inverse Jacobian, then ... 2answers 3k views ### How to find the body jacobain, for each link in a robot manipulator? The links twist could be obtained, and thus The spatial manipulator Jacobian could be done, but when it comes to the body Jacobian, it is becomes difficult. Moreover, the adjoint transformation ... 3answers 3k views ### With a 6-axis robot, given end-effector position and range of orientations, how to find optimal joint values Given a six-axis articulated robot arm holding a tool at its end-effector, if I have a desired tool position and tool orientation, there will be exactly 1 solution to the inverse kinematics equation ... 1answer 630 views ### State prediction of vehicle with Ackermann steering geometry using Kalman-Filter I am trying to have a Kalman-Filter (or Extended-KF) give me positions for a small remotely controlled vehicle with an Ackermann steering geometry (moving on a plane surface). The control commands I ... 1answer 2k views ### Hand Eye Calibration Solver [closed] I have a rig for which I have a pretty good estimate of the static transformation between the camera and a joint based off of the CAD. It has some errors though and I was hoping to fix it by doing a ... 2answers 862 views ### Robot arm reachability of a pose in Cartesian space Given a set of robot joint angles (i.e. 7DoF)\textbf{q} = [q_1, ... , q_n]$one can calculate the resulting end-effector pose (denoted as$\textbf{x}_\text{EEF}$), using the foward kinematic map. ... 1answer 3k views ### Using pre multiply or post multipy for rotational matrix to get a new homogenous transformation matrix? I am confused about how do I multiply the rotational matrix in this case. I know that both T1 and T2 needs to be multiplied by a rotational matrix but I don't know how to multiply the rotational ... 1answer 10k views ### Getting pitch, yaw and roll from Rotation Matrix in DH Parameter I've calculated a DH Parameter matrix, and I know the top 3x3 matrix is the Rotation matrix. The DH Parameter matrix I'm using is as below, from https://en.wikipedia.org/wiki/Denavit%E2%80 Above is ... 0answers 35 views ### Formulas for calculating the passive joints angular velocities We have the following parallel robot architecture: Positions of the vectors$u_i, v_i, w_i$, the angles$\theta_i$, angular velocity$\dot{\theta_i}$and the Jacobian$J$, that mapping vector of ... 2answers 4k views ### Differences between Ackermann steering and standard bi/tricycles concerning kinematics? I got the following homework question: What are the general differences between robots with Ackermann steering and standard bicycles or tricycles concerning the kinematics? But, I don't see what ... 1answer 2k views ### How do I convert link parameters and angles (in kinematics) into transformation matrices in programming logic? I'm doing robotics research as an undergraduate, and I understand the conceptual math for the most part; however, when it comes to actually implementing code to calculate the forward kinematics for my ... 1answer 2k views ### How to convert between classic and modified DH parameters? I currently have a description of my 22 joint robot in "classic" DH parameters. However, I would like the "modified" parameters. Is this conversion as simple as shifting the$a$and$alpha$columns ... 2answers 3k views ### Derivative of a Jacobian matrix I have an RRR planar robot: Its forward kinematics transform is:$${}^{0}T_3 = \\ \left[\begin{array}{cccc} \cos\!\left(\mathrm{\theta_1} + \mathrm{\theta_2} + \mathrm{\theta_3}\right) & - \sin\... 2answers 969 views ### 3-RRP manipulator robot I'm having some issues with a planar manipulator I have to deal with. The first two moves are rotational and the third one is a prismatic one. The shoulder and elbow move around the X-axis, while the ... 1answer 544 views ### Optimization of link lengths for 3R serial manipulator I am trying to formulate an optimization problem for determining link lengths of 3R manipulator shown in picture below, Following are the constraints, Robot arm should be reachable at point x = 100, ... 1answer 2k views ### calculating differential drive robot ICC position I don't understand how to calculate the ICC position with the given coordinates. I somehow just have to use basic trigonometry but I just can't find a way to calculate the ICC position based on the ... 1answer 69 views ### Dexterity calculation with dual quaternions How can the manipulability of a robot arm be calculated when the kinematics are described with screw theory such as dual quaternions? These methods are sigularity-free, but what could we say about ... 1answer 183 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:$...
Let's say I have a robot consisting of a base $B$ and a manipulator $M$. The pose of the manipulator can be expressed as the transformation matrix $T_{BM}$. I also have a goal $G$ which I want to move ...