Questions tagged [dynamics]

Dynamics is a branch of applied mathematics (specifically classical mechanics) concerned with the study of forces and torques and their effect on motion, as opposed to kinematics, which studies the motion of objects without reference to its causes.

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Jacobian of Euler's rotation equations

I propagate the attitude of a satellite in a free-floating, torque free environment from $t_k$ to $t_{k+1}$ by integrating Euler's equation of motion: $$ \dot{\omega} = [J]^{-1}([\omega]_{\times}[J]\:\...
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how to find the kinematic and dynamic model of the mechanism

enter image description here 5 links 4 revolute joints find the kinematic and dynamic model ,link 3 should be horizontal with ground and one end of link 1 and 5 there are sliders enter image ...
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How to calculate center of mass with a prismatic joint

Suppose we a 1DoF planar robot with only 1 prismatic joint (for the sake of the example). The prismatic joint can extend the link or shrink the link. Suppose the length of link 1 is a, and suppose ...
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Multidimensional obstacle avoidance in ODE. Part II

Multidimensional obstacle avoidance https://math.stackexchange.com/questions/4146255/multidimensional-obstacle-avoidance-in-ode For some time, I studied this question more closely and came to the ...
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Multidimensional obstacle avoidance

Artificial potential barriers are known that allow robots to avoid obstacles. They are constructed as follows. https://authors.library.caltech.edu/106548/1/2010.09819.pdf Can you please tell me how ...
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Looking for a course (online?) RE: systems with XY stages

Using XY stages is common in many fields: 3D printing Genetics instruments semiconductor lithography automated microscope slide imaging See for example https://www.asml.com/en/technology/lithography-...
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I’m not sure how to calculate the torque of a tank chassis what values do I need?

So I plan to build a robot-tank thing. It’s max weight will be 35kg and it’s driving wheel will have a radius of 0.05m. Those are the two values I know for certain and there will be no gears between ...
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Range of a heading angle [0,2π) or [−π,π)

Consider the unicycle dynamics in 2D plane: $$\begin{array}{l} \dot x = v\cos \varphi \\ \dot y = v\sin \varphi \\ \dot \varphi = \omega \end{array}$$ What is the range of the heading angle $\phi$? ...
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What does SE mean in robotics literature?

I've come across the abbreviation SE several times recently. I know it has to do with the pose of the robot, and the degrees of freedom. Most recently I found it on page 8 of this paper: D. Kragic ...
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70 views

How to calculate potential enegy of manipulator?

I'm trying to obtain dynamics of a 4 DOF robot. Firstly, I calculated all Transformation matrices and Jacobians. While solving Lagrangian there is two main things one is kinetic energy and the other ...
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56 views

Velocity-Control of a manipulator without a dynamic model

I have a five DoF robot. Each axis is connected to a cylinder. You can send PWM values to each cylinder and you are able to read out the position values of each cylinder which makes it possible to ...
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Ground based path generation from RGBD camera

How does one generate a trajectory for a ground vehicle using an RGBD camera? For a drone it's simpler since you're not constrained by having to move on the ground but it's not clear to me how ...
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Stationary/inertial reference frame

In Modern Robotics by Kevin Lynch, there is a term "stationary" frame, but this is never defined. Googling shows that this is synonymous with inertial frame. Apparently inertial frame means ...
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Quadrotor dynamics: How is torque created

I'm a software engineer and I've recently engaged into Robotics field. I've started by a course on Coursera which talks about Aerial robotics and thus quad-rotors. I'm trying to understand how quad-...
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Path curvature in kinematic bicycle model

I'm trying to develop an understanding of the control law for longitudinal and lateral control for self driving cars. While doing so, I came across the kinematic bicycle model which is used to derive ...
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Adding an Actuator or Force to a (Featherstone) Articulated Rigid Body Model

I'm working on a project where I need to model a system that is essentially comprised of a series of ball-and-socket joints attached to a base, which is attached in turn to a prismatic joint (rail). ...
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119 views

Free-floating sphere dynamics using Roy Featherstone's spatial_v2 toolbox

I am using Roy Featherstone's spatial_v2 to model a mobile robot. I encountered a problem so I went back to modeling a free-floating sphere to familiarize myself with the library and the algorithms. ...
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What is the difference between screw and wrench in rigid body motion?

A screw is defined by a six dimensional vector of forces and torques. It can represent any spatial movement of a rigid body (as written here). But I don't get the following distinction between screw ...
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Newton-Euler Inverse Dynamics by Screw

I paste this algorithm from textbook Modern Robotics P294 in chapter 8: This is coordinate invariance of Newton-Euler equations. In the textbook, they use the ...
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184 views

Why using screws instead of homogeneous transforms in kinematics and dynamics?

Can anyone give a justification for using screws (twists, wrenches) instead of the traditional approach (rotation matrices, homogeneous transforms)? Even if screws are more compact, the situation gets ...
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When is the Quadcopter out of the control?

Assuming ideal environment/hardware flying conditions, is it possible that the autopilot loses the control of the quadcopter? What is the maximum tilt in roll and pitch that is allowed for the ...
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How to calculate potential enegy of manipulator dynamics?

I'm trying to obtain dynamics of a 4 DOF robot. Firstly, I calculated all Transformation matrices and Jacobians. While solving Lagrangian there is two main things one is kinetic energy and the other ...
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2answers
578 views

How do I calculate the direction robot is facing, pose from velocity and yaw rate?

I have a simple car robot with four wheels moving relatively slowly (5~10 mph). The robot has a velocity magnitude and yaw rate sensor and the sensor samples about every 0.1 seconds. I want to map the ...
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What is the difference between The state-space equation and The configuration-space equation

The craig(p.180) states that equations can be made to represent the dynamic equations. The first one being the state space equation. $\tau=M(\Theta)\cdot\ddot{\Theta} + V(\Theta,\dot{\Theta}) + G(\...
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how to find Singularity and jacobian Inverseof 5 DOF Robotic arm?

I am working on calculating the Jacobian Determinant to find the singularity of my 5 DOF Robotic arm, I have calculated the jacobian matrix, and the matrix I got is a very large value As it is non ...
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What are the best approaches and limitations for calculating the Inverse dynamics for a floating base quadruped?

Given a quadruped standing on all fours, or trotting with 2 legs down/2 up, I've seen a few methods of computing inverse dynamics. All derive from centroidal momentum physics, and I think all distill ...
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Motion profile and Motion control scheme, how do they interact?

I'm studying motion control and I start with the simplest case, I have to go from A to B in a straight line using a trapezoidal motion profile. I understand that in a real case, due to the fact that ...
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64 views

How to calculate Inertia tensor?

I'm trying to obtain dynamics of a 4 DOF robot. Firstly, I calculated all Transformation matrices and Jacobians. While solving Lagrangian there is a term I - Inertia tensor . I couldn't understand the ...
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41 views

Maximum value of norm of mass matrix M

How do I compute the maximum values for ||M(q)|| and ||M_dot(q)||, the induced 2-norms, where M(q) is the mass matrix from the standard dynamical model of a robotic manipulator. I have the numerical ...
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How to properly model a non-holonomic system?

I'm trying to model a robot which is composed of a non-holonomic and a holonomic system overall is non-holonomic. Basically it's a robot arm + mobile platform. So far I have found a similar work like ...
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What is a “vacuous matrix”?

I am currently learning about robotic grasping and came across a matrix $H_i \in \mathbb{R} ^{l_i \times 6}$ which selects $l_i$ components of the relative contact twists and sets them to zero. My ...
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Is it possible to control a 5 DOF manipulator in the 6 DOF Task Space?

I am referring to pre-computed torque control techniques that are based on the Task Space dynamic model. Maybe by using pseudo-inverse for the Jacobian and the task space inertia matrix ? Cheers, ...
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Moment of Inertia of a Dumbbell

hope you are all doing well. I am taking a course at Coursera about Robotics and in one of the quizes, I had some problem with a particular question. I passed the quiz (4/5 correct answers), however I ...
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38 views

How to find inertia parameter of payload automatically

I know of several robot manufacturers who can perform automatic inertial measurement for 6 axis robots. Fanuc, for example, moves with axes 5 and 6 each from +180 to -180 °, once with and once without ...
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How do quadcopters turn left and right?

In this picture, a sketch of a quadcopter is displayed with rotor's direction of motion. The magnitude of the rotational velocity is depicted by the thickness of the lines (thicker lines are higher ...
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Cartesian Impedance control Damping Design (Double Diagonalization)

In the literature, it is often seen that for a system: \begin{align} \Lambda \ddot{e} + D_d \dot{e} + K_d e = F_{ext} \end{align} A dynamic damping matrix is required for a robot to take ...
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How to solve dynamics of cardan joint manipulator

We can use the Recursive Newton-Euler Algorithm to solve the dynamic problems of open chains manipulator, but how about the Cardan-joint manipulator? For example, if we have one Cardan joint (...
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2k views

D(q) Inertia Matrix and the Jacobian Matrix

There is something I need to verify. Say we have the following RPR robot manipulator. The DH table yields 3 rotational matrices: \begin{equation} R^0_1, R^0_2, R^0_3 \end{equation} Using these ...
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Can workspace of a manipulator change after considering its dynamics?

As per my knowledge, the workspace of a manipulator can be determined if one knows the forward and inverse kinematics. But is it possible that the workspace of the manipulator can change after ...
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Why applied joint torque will affect another joint?

I want to ask a very simple question. For the robot dynamics Newton-Euler algorithm, suppose there is a two-link planar robot, we can write the simple dynamic equation form as $M(\theta)\ddot{\theta} ...
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How to find inverse kinematic equations for a quadruped robot to make it walk?

I have made a model of quadruped robot (sprawling/spider type and not dog type) in V-rep and now I want to make it walk by using creep gait. (i.e moving 1 leg at a time) As I understand, I have to ...
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Understanding Impedance Control

I have a question regarding impedance control for a robotic manipulator. Given that we have a task space trajectory: $\ddot{x}$, $\dot{x}$ and $x$ And the dynamics model of the robot: $$\tau = M(q)\...
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What do I need to know about the dynamics of an industrial robot?

Apart from kinematics, what do i need to know about the dynamics and other things of a robot in order to calculate the angles of the joints for positions of the end effector exactly? that means: if i ...
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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 ...
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Modeling of Robots

There are mainly two approaches for controlling robots (mobile robots and static robots): 1) working with kinematic equations, controlling joint or wheel speeds , 2) working with dynamic equations and ...
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Moment of Inertia of a planar rotation link with a 6-DOF base

I'm interested in analytic calculation of a moment of inertia of a robot's arm in the following situation. Let us assume the following: Stationary reference frame $ \{b\} = \{X_B, Y_B, Z_B\}$ and ...
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What is the difference between multi-link flexible manipulators and continuum robots?

I read the review[1] on flexible manipulators, the modeling method of multi-link(even if single-link) flexible manipulators seems very different from the continuum robots like OctArm(multi-section), ...
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Can knowledge of robot's dynamics help in motion planning?

Some planners assume a kinematic model of the robot for example diff drive or omni directional etc. while generating motion plans for the robot. Can knowledge of the dynamics of the robot help ...
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Determination of the operational space dynamic model (Task space)

I am trying to implement a hybrid Force/Motion controller for a quadruped. To do that I first need the Inverse Dynamic Model of the robot in Operational Space. I found a lot of resources on how to ...
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4 wheeled differential wheeled (skid-steer) robot steering problem

My question is about a square shaped differential wheeled robot, I built, that has a hub-motor (BLDC motor) attached to each corner, i.e., the wheels on the same side, either left or right, have the ...