Skip to content

Latest commit

 

History

History
135 lines (93 loc) · 7.67 KB

README.md

File metadata and controls

135 lines (93 loc) · 7.67 KB
Raw

Franka Emika Panda Matlab Simulation

Authors: Seonghyeon Jo([email protected])

Date: Des, 24, 2021

This repository is a MATLAB simulation of franka emika panda robot control using Runge-Kutta. The robot manipulator dynamic model (M, C, G, F) uses the functions provided in [1]. The kinematic function matches the actual panda robot data. However, Jacobian's derivative and Jacobian have some errors.

Function

  • real_data : Franka emika panda robot actual data files

  • model : Franka emika panda robot model library folder

    • get_CoriolisMatrix.m : Coriolis matrix function [1]
    • get_CoriolisVector.m : Coriolis vector function [1]
    • get_FrictionTorque.m : Friction torque function [1]
    • get_GravityVector.m : Gravity vector function [1]
    • get_MassMatrix.m : Inertia matrix function [1]
    • get_Jacobian_dot.m : Jacobian Differential Functions
    • get_JacobianZ2YZ1.m : Jacobian function (direction z2-y-z1)
    • get_pose.m : kinematic function
    • plant.m : robot manipulator plant function
    • simple_plant.m : robot manipulator plant 함수
    • rk.m /simple_rk.m : Runge-Kutta 함수
    1. test_model_kinematics.m : kinematics test code
    1. test_model_jacobain.m : jacobian test Code
    1. test_model_dot_jacobain.m : jacobian dot test Code
    1. main_cartesian_pd_control_playback.m : Cartesian PD controller code
    1. main_impedance_control.m : Cartesian Impedance Controller Code
    1. main_simple_pd_control_playback.m : Simple PD controller code

Controller

  • simple pd controller

control_simplePD_playback

- catesian pd controller

control_catesianPD_playback

- position based impendace controller

control_catesian_imp

Kinematics Test

  • Franka Emika Robot DH parameters
i 1 2 3 4 5 6 7 8
theta q1 q2 q3 q4 q5 q6 q7 0
d 0.333 0.000 0.316 0.000 0.384 0.000 0.000 0.107
a 0.000 0.000 0.000 0.0825 -0.0825 0.000 0.088 0.000
alpha 0 -pi/2 pi/2 pi/2 -pi/2 pi/2 pi/2 0
  • Modified DH parameters {} ^{i-1} T_{i} = \text{rot}_{x,\alpha_{i-1}} \text{trans}_{x,a_{i-1}}\text{rot}_{z,\thata_{i}} \text{trans}_{z,d_{i}}

{} ^{i-1} T_{i} = \left[{\begin{array}{ccc|c}\cos \theta _{i} & -\sin \theta _{i} & 0 & a_{i-1}\\ \sin \theta _{i}\cos \alpha _{i-1} & \cos \theta _{i}\cos \alpha _{i-1} & -\sin \alpha _{i-1} & -d_{i}\sin \alpha _{i-1}\\\sin \theta _{i}\sin \alpha _{i-1} & \cos \theta _{i}\sin \alpha _{i-1} & \cos \alpha _{i-1} & d_{i}\cos \alpha _{i-1}\\\hline 0 & 0 & 0 & 1\end{array}}\right]

Ti= cell(n,1); 
for j=1:n
    if(j == 1)
        Ti{j} = Rhx(alpha(j)) * Rt(a(j), 0, 0)  * Rhz(q(j)) * Rt(0,0,d(j));
    else
        Ti{j} = Ti{j-1}*Rhx(alpha(j)) * Rt(a(j), 0, 0)  * Rhz(q(j)) * Rt(0,0,d(j));
   end
end
p = Ti{n}(1:3,4);
R = Ti{n}(1:3,1:3);
  • kinematics test plot

kin_test1 kin_test2

Jacobian Test

  • Jacobian test plot

    Cartesian derivative(real) : \dot{x} = J(q)\dot{q}

    • data1: \dot{x} = (k(q)_{t+1}-k(q)_{t})\Delta t
    • data2:\dot{x} = (x_{t+1}-x_{t})\Delta t
    • data3:\dot{x} = \hat{J}(q)\dot{q}

  • jacobain test plot

Jac_test_simple_test Jac_test_joint1~7 movement

Jac_test_joint5 movement Jac_test_joint7 movement

jacobian derivative

  • Jacobian derivative test plot

    Cartesian second derivative(real) : \ddot{x} = (\dot{x}_{t+1}-\dot{x}_{t})\Delta t

    • com: \ddot{x} = J(q)\ddot{q} +\dot{J}(q,\dot{q})\dot{q}

  • jacobain dot test plot

Jac_dot_test_simple_test Jac_dot_test_joint1~7 movement

Jac_dot_test_joint5 movement Jac_dot_test_joint7 movement

[1] Gaz, Claudio, et al. "Dynamic identification of the franka emika panda robot with retrieval of feasible parameters using penalty-based optimization." IEEE Robotics and Automation Letters 4.4 (2019): 4147-4154.

(https://github.com/marcocognetti/FrankaEmikaPandaDynModel)