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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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When are non-diagonal matrices advantageous for linear quadratic regulators?

When setting up an optimal control problem using a linear quadratic regulator, one often chooses semi-definite matrices Q and R such that the objective function J has the form $$J=\int_{t_0}^{t_f}(...
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Determine moments of inertia of a tool experimentally

I've mounted a broom as an effector of the Kuka IIWA. I've configured a tool in the Kuka Sunrise Workbench software with approximative mass and center of gravity. However, when control is started with ...
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Doubt linearizing 2D planar quadrotor equation of motion

Equation of motion for 2D planar quadrotor are as follows $\ddot{x} = \frac{1}{m} (u1+u2)sin(\theta)$ $\ddot{y} = \frac{1}{m} (u1+u2)cos(\theta) - mg$ $\ddot{\theta} = \frac{r}{I} (u1+u2)$ How to ...
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Free Multibody Dynamics Software?

I'm working on modelling a feller buncher, its end effector consists of a saw to cut trees and claws to bundle them together. I'm looking for a free/open source software that can simulate dynamics of ...
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32 views

Calculate the inertia matrix of complex robotic mechanism

Motor, irregular rigid body of Different materials Forming a single robotic. For example, Industrial robot, every geometric shape of the link is very complex. But we can find inertia matrix form CAD ...
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43 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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146 views

Finding Mass/Inertia Matrix of a robot

Hi I am trying to model my humanoid robot. The general EoM is $M(q)\ddot{q}+C(q,\dot{q})+G(q)=U$ I know $M(q)$ is Inertia matrix which depends on joint positions $\textbf{q}$. However, I am having ...
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Bullet vs SimMechanics: Inverse Dynamics and sensed forces/torques

This question may be a little broad, but I could not find any other information. How accurate are the inverse dynamics functions in SimMechanics compared to Bullet? How accurate are the sensed/...
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25 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 introduce 2 inputs into a matlab block function that processes only one variable at a time? [closed]

Using SIMULINK, I wanted to optimize 2 variables with the ant colony optimization algorithm; which is written in a matlab function block, the function is of type function y = f (x) it has only one ...
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Reachable Position with endeffector robotic arm

I have a 7 DOF robotic Arm. All the 7 Joints are rotational and have upper and lower joint angle limits. Now assume my end effector has a certain Pose $x = [X, Y, Z, a, b, c]$. My Question now is ...
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OpenRAVE “fast-forward” physics simulation?

I am working with OpenRAVE simulator and I am using ODE Physics (OpenRAVE plugin to support ODE). I have a robot in an environment and multiple other objects that are subject to the physics engine. I ...
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137 views

Understanding the kinetic energy expressions for a 1 link vs 2 link robot arm

I'm studying these lecture notes on dynamic models of robot arm links, slides 33-36, where two examples are given for the kinetic energies for a single link and two link robot arm. In the single ...
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Why we want to write all linear system into form of first order differential equations?

It seems to be taken granted that when we deal with some control system, the first thing we want to do is to linearize the system and put it in form of first order differential equations like $\dot x =...
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60 views

PID control related to lagrange equation

I'm a beginner in robotics and so far followed the lecture series by Prof. Oussama Khatib and some blogs and papers. currently I'm following this studywolf blog. in the end I plan on building a simple ...
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60 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 and when not to use the Inertia tensor in Kinetic energy computing?

I'm trying to obtain the dynamic model of a 3D robot (academic problem), I have obtained the D-H table, the transformation matrix for each pair of links and the total transformation matrix. Now I'm ...
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58 views

Two 4 bar mechanism vs stepper motor on each linkage in a 4 DOF robotic arm

I am planning to make a 4 Degree of Freedom(DOF) robotic arm. I have a confusion in mechanical design of the robot. Shall I use two 4 bar mechanisms to reduce the number of actuators? or a stepper ...
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63 views

Doing a project for college for a manned drone theortically only

Weight of the Drone in total will be 240 Kg. It Will be a quad copter drone setup but with 8 rotors(two on each corner) for redundancy purpose. Aim is achieve Thrust/weight ratio of 2. So need total ...
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114 views

Dynamic model using identification for control

I'm currently working of a 5 DOF robot, for which i'd like to compute the dynamic model through identification. I have experimental data representing torques (inputs) and positions (outputs). How can ...
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146 views

Quadcopter mathematical model and controller design

if we just examine the translational dynamics (X and Y direction), the dynamics are coupled, So if I want to design a PID controller to control the position, the outcome will be unpredictable because ...
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“modern contact dynamics” - Why are spring-damper contact models not being used anymore for dynamic simulations in robotics?

While researching different physics engines for dynamic simulations in robotics I found the following statement on the MoJoCo documentation website: Physics engines have traditionally separated in ...
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Calculation of inertia values of Ic and Im

In my dynamic model of two wheeled mobile robot, it has the total equivalent inertia, noted $I$, described by the equation below, $I_c$ is the moment of inertia of the DDMR about the vertical axis ...
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121 views

Dynamic model of two wheeled mobile robot

I wanted to design a LQR controller for my two wheel mobile robot. What are the equation of two wheeled mobile robot can be rearranged into state space model? My two wheeled mobile robot is nonlinear ...
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Jacobian of kinematic IMU Model

I have the following problem: given two Input Vectors $x = \begin{pmatrix}x\\y\\z\\v_x\\v_y\\v_z\\q_1\\q_2\\q_3\\q_4\end{pmatrix}$, $u = \begin{pmatrix}a_x\\a_y\\a_z\\w_x\\w_y\\w_z\end{pmatrix}$ time $...
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2answers
182 views

Calculating C for a 6-DOF robotic arm

I've seen this equation for calculating the dynamics of a robotic arm a bunch: $\boldsymbol{\tau} = \boldsymbol{M}(\boldsymbol{q})\ddot{\boldsymbol{q}} + \boldsymbol{C}(\boldsymbol{q},\dot{\...
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Confusion about Jacobians stemming from class notes

So I thought I understood well enough what a Jacobian was (in the context of an $n$-DOF robot) -- a function that takes a vector of n joint positions and returns an $n \times n$ matrix that can be ...
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391 views

6DOF serial robot (PUMA robot) dynamic model equations

I'm trying to find the most simplified (though accurate) calculations for the dynamic model of a standard 6DOF serial robot (PUMA robot). I found this great paper: https://www-cs.stanford.edu/group/...
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robotic arm DOF

I'm working on an assignment and was wondering aobut the degrees of freedom this system has. The generalized coordinates are: $\underline{q}:$ \begin{bmatrix} x \\ \theta_{1} \\ \theta_{2} \\ \end{...
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1answer
72 views

Quadrotor SE3 Controller: Calculating Rd_dot

I am trying to simulate and implement the controller in the paper Geometric Tracking Control of a Quadrotor UAV on SE(3). I have the dynamics implemented, however I am stuck at one part in the ...
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53 views

How to interpret and apply results from Inverse Dynamics

I am applying Recursive Newton Euler Inverse Dynamics to a simple two link model. If I apply the result torques and forces using PhysX or Bullet Physics I get unexpected results. The model spins and ...
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457 views

Quadrotor Dynamics: Calculating angular velocity of quadrotor

I am trying to simulate and implement the controller of the paper Geometric Tracking Control of a Quadrotor UAV on SE(3). To do this I need to first implement the dynamics of the quadrotor. According ...
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801 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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80 views

Urdf as a way to model dynamics?

Since urdf format serves the purpose of kinematic model but also extends for dynamical properties such as mass,moment of inertia and centre of masses, can it be considered a viable dynamical model of ...
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198 views

Dynamics of a robot manipulator with a force acting on the end-effector

I have this exercise The dynamic model is $B(q)\ddot{q}+S(q,\dot{q})\dot{q}=\tau+\tau_k$ Where $B(q)$ is the inertia matrix, $S(q,\dot{q})\dot{q}$ are the centrifugal and Coriolis terms, $\tau$ is ...
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FPGAs and stepper motors for precision control

I'm looking at this Dexter robot that uses FPGA controllers to get really accurate position and force sensing on a cheap ($2K) arm. They say that the speed of the processor lets them get this accurate ...
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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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Holonomic constraint forces using Lagrange multipliers

Consider a multibody robotic system with Lagrangian $ L = \dot{q}^{T}M\dot{q} + V $ and equations of motion of the form $$M(q)\ddot{q}+C(q,\dot{q})\dot{q}+A^{T}(q)\lambda+N(q)=0 $$ where $N=\frac{\...
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65 views

clarity in understanding the moment of inertia matrix D and Coriolisis and centripetal matrix C as per attached equations

Would appreciate if anyone could help me understand the how if equation 6 and 7 are derived. Helping with any one D22 and C32 would suffice.
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417 views

Euler-Lagrange Dynamic model

I'm working on a masters thesis and need to calculate Mass inertia matrix ($M$), Coriolis/Centrifugal matrix ($C$), and the gravity matrix ($G$) in the equation $M\ddot{\theta} + C\theta + G = \tau$ (...
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647 views

What's the diffrence between $H_2$ and $H_\infty$ controll?

There a two controllers named $H_2$ and $H_\infty$. Can someone explain if: They have have guaranteed stability margins? Do they have a Kalman filter? Are they for both SISO and MIMO systems? Can I ...
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87 views

Robot with Double Integrator Model

Does the robot described by Double Integrator Model is holonomic ? Let's say we have a robot with dynamics described by equations \begin{cases} \dot x = v, & \\ \dot v = \frac {1}{m}u \end{...
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221 views

Robot with Double Integrator Model [duplicate]

Does the robot described by Double Integrator Model is holonomic ? Let's say we have a robot with dynamics described by equations \begin{cases} \dot x = v, & \\ \dot v = \frac {1}{m}u \end{...
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459 views

Linear State Space of a 6DOF robot

I'm new to the field of robotics, so this is a pretty basic question: I'm assigned with the task of constructing a linear state space model of a 6DOF robotic arm that moves in 3D space. I believe the ...
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216 views

6DOF Robot Dynamics from Newton-Euler Iterative Algorithm [closed]

I don't know if someone can help me with this but I'm calculating the dynamics of a 6DOF robot using the Newton-Euler iterative dynamics algorithm. I'm following the recursive method (inwards and ...
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66 views

PI with poor sampling rate

I have a 1-DOF electromechanical application whereby I am controlling the contact-force at the tip of the end-effector. The force sensor on the end-effector unfortunately gives me force data and an ...
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54 views

Theory behind wheeled inverted pendulum robots [closed]

I'm trying to get a deeper understanding of the theory behind wheeled self-balancing robots. Can anyone point me to a text on dynamic modelling and control theory that might help?
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444 views

Guessing the K matrix gain for the Optimal Control LQR?

I'm are going to create a LQR to control a system. The problem is to choose the Q and R weighting matrices for the cost function. The Q and R matrices are going to minimize the cost function so the ...
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201 views

Inertia Tensors in 3D objects for robot dynamics

I'm trying to obtain the dynamics of a 6DOF robot. Firstly, I calculated the combined centres of mass (between each link and the respective actuator) in order to calculate the gravity term, since it ...
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1answer
144 views

Can a state matrix have a row of zeros?

While formulating a state matrix of a system, say a system of a typical cruise controller, \begin{equation} \begin{bmatrix} \dot{v} \end{bmatrix} = \begin{bmatrix} -\frac{b}{m} \end{bmatrix} \begin{...