Is the algorithm for Coriolis Matrix applicable to the Modified Denavit-Hartenberg (MDH) representation?

[yanlong658]

Hello sir,

Currently, I have established my MDH coordinate system as follows, defining the origins of the dynamic parameters on each axis.

Upon setting both angles and angular velocities to zero and using the Coriolis Matrix function, I observed differences in the inertia matrices obtained compared to employing angular accelerations with unit length in the six iterations of Rne. According to my understanding, regardless of whether it is MDH or DH, the algorithm in the paper should be applicable. Is my interpretation correct

Thanks.

[pwensing]

Hi there,

All the algorithms are compatible with MDH — the model data structure is independent of the convention you choose to use.

Regarding your issue, note that if we write the equations of motion as:
$$H(q) \ddot{q} + C(q, \dot{q}) \dot{q} + g(q) = \tau$$
Then the CoriolisMatrix function gives $C(q, \dot{q})$. It sounds like what you are looking for is the joint space inertia matrix $H(q)$ instead. The HandC function should do that for you — it gives two outputs, $H(q)$ and $C(q,\dot{q})\dot{q} +g(q)$.

Best,
-Pat

[yanlong658]

Hi Pat,

I indeed need the inertia matrix of the joint.
The following is the MATLAB script file I created for a robotic arm.

========================================================
function robot = VA_model()
% spatial_v2 dynamics library.
a2 = 0.155;
a3 = 0.600;
a4 = 0.180;
d1 = 0.450;
d4 = 0.637;
d6 = 0.100;
% Modified Denavit Hartenberg parameters alpha_{i-1}, a_{i-1}, and d_i
% as in J.J.Craig's classic text
mdhTable = [ 0 d1 0 ;
-pi/2 0 a2 ;
0 0 a3 ;
-pi/2 d4 a4 ;
pi/2 0 0 ;
-pi/2 d6 0 ];

% dhTable = [ 0 0 d1 ;
% -pi/2 a2 0 ;
% 0 a3 0 ;
% -pi/2 a4 d4 ;
% pi/2 0 0 ;
% -pi/2 0 d6 ];

robot.NB = 6;
robot.parent = [0 1 2 3 4 5];
robot.jtype = {'Rz', 'Rz', 'Rz','Rz','Rz','Rz'};
robot.jtype_rotor = {'Rz', 'Rz', 'Rz','Rz','Rz','Rz'};
% robot.has_rotor = ones(6,1);

robot.gr = { 126, 104, 107.66 , 89.379 , 81.77 , 50 };

robot.Xtree = { };
for i = 1:6
alpha = mdhTable(i,1);
a = mdhTable(i,2);
d = mdhTable(i,3);
robot.Xtree{i} = rotx(alpha) * xlt([a 0 0]) * xlt([0 0 d]); % I change it to R(\alpha) * Trnas(a) * Rot(\theta) * Trans(d)
robot.Xrotor{i} = robot.Xtree{i};
end

robot.gravity = [0 0 0];
for i = 1:robot.NB
robot.I{i} = eye(6);
robot.I_rot{i} = eye(6);
end

============================= main Function =============================
clc;clear;
addpath(genpath(pwd))
robot = VA_model();
model = postProcessModel(robot);

% a = [m hx hy hz Ixx Iyy Izz Iyz Ixz Ixy]

a = [1. 1. 1. 1. 1. 1. 1. 0. 0. 0.];
b = [0. 0. 0. 0. 0. 0. 0. 0. 0. 0.];
for i = 1:6
model.I{i} = inertiaVecToMat(a);
model.I_rotor{i} = inertiaVecToMat(b);
end
q = zeros(model.NV, 1);
qd = zeros(model.NV, 1);

[H, C, info] = HandC( model, q, qd);
H

==========================================================================

I use the RNE (Recursive Newton-Euler) algorithm using MDH model six times to calculate the numerical values by setting the joint accelerations to 1.By ( Peter Croke mdh_rne)
The following are the results when setting q, qd, and qdd to zero.
H matrix is:

The following are the results when I use the HandC function recommended by you earlier.
H matrix is:

I'm not sure if the information I provided is sufficient. If there's anything I haven't filled out correctly, please guide me.
Thank you for your response, and I wish you a wonderful day.

Best regards,
Long"