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merge into: Robotics:feature/Add_Inertia
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Robotics:main
Robotics:feature/Jacobian_sym
Robotics:feature/Add_Inertia
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pull from: Robotics:main
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Robotics:main
Robotics:feature/Jacobian_sym
Robotics:feature/Add_Inertia

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feature/Ad ... main

Author SHA1 Message Date
Rui 21a459d8fc Merge branch 'feature/Jacobian_sym' into 'main' 
Feature/jacobian sym

See merge request robotics/modern-robotics!3
 2024-01-07 03:11:18 +00:00
Rui abeadfdbb7 Feature/jacobian sym 2024-01-07 03:11:17 +00:00
Rui 876f5e64d5 Merge branch 'feature/Add_Inertia' into 'main' 
Feature/add inertia and FK expand

See merge request robotics/modern-robotics!2
 2023-11-05 02:04:04 +00:00
Rui 9dfa837e8c Feature/add inertia and FK expand 2023-11-05 02:04:04 +00:00
9 changed files with 219 additions and 0 deletions
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8
packages/MATLAB/mr/BodyVelToLinearVel.m Normal file
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function Vlinear = BodyVelToLinearVel(V,G)
% *** CHAPTER x: DYNAMICS OF OPEN CHAINS ***
% Takes V: Body frame velocity,
% G: Spactial frame G
% Returns Glist: Spatial inertia matrices Gi of the links
[R, p] = TransToRp(G);
Vlinear = R*V(4:6);

36
packages/MATLAB/mr/FKinSpaceExpand.m Normal file
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function Tlist = FKinSpaceExpand(Mlist, Slist, thetalist)
% *** CHAPTER 4: FORWARD KINEMATICS ***
% Takes M: the home configuration (position and orientation) of the
% end-effector,
% Slist: The joint screw axes in the space frame when the manipulator
% is at the home position,
% thetalist: A list of joint coordinates.
% Returns T in SE(3) representing the end-effector frame, when the joints
% are at the specified coordinates (i.t.o Space Frame).
% Example Inputs:
%
% clear; clc;
% M = [[-1, 0, 0, 0]; [0, 1, 0, 6]; [0, 0, -1, 2]; [0, 0, 0, 1]];
% Slist = [[0; 0; 1; 4; 0; 0], ...
% [0; 0; 0; 0; 1; 0], ...
% [0; 0; -1; -6; 0; -0.1]];
% thetalist =[pi / 2; 3; pi];
% T = FKinSpace(M, Slist, thetalist)
%
% Output:
% T =
% -0.0000 1.0000 0 -5.0000
% 1.0000 0.0000 0 4.0000
% 0 0 -1.0000 1.6858
% 0 0 0 1.0000
Tlist = zeros(4,4,size(thetalist,1));
Mi = eye(4);
for i = size(thetalist): -1: 1
for j = 1:i
Mi = Mi * Mlist(:, :, j);
end
Tlist(:,:,i) = FKinSpace(Mi, Slist(:,1:i), thetalist(1:i));
Mi = eye(4);
end
end

36
packages/MATLAB/mr/FKinSpaceExpand_Sym.m Normal file
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function Tlist = FKinSpaceExpand_Sym(Mlist, Slist, thetalist)
% *** CHAPTER 4: FORWARD KINEMATICS ***
% Takes M: the home configuration (position and orientation) of the
% end-effector,
% Slist: The joint screw axes in the space frame when the manipulator
% is at the home position,
% thetalist: A list of joint coordinates.
% Returns T in SE(3) representing the end-effector frame, when the joints
% are at the specified coordinates (i.t.o Space Frame).
% Example Inputs:
%
% clear; clc;
% M = [[-1, 0, 0, 0]; [0, 1, 0, 6]; [0, 0, -1, 2]; [0, 0, 0, 1]];
% Slist = [[0; 0; 1; 4; 0; 0], ...
% [0; 0; 0; 0; 1; 0], ...
% [0; 0; -1; -6; 0; -0.1]];
% thetalist =[pi / 2; 3; pi];
% T = FKinSpace(M, Slist, thetalist)
%
% Output:
% T =
% -0.0000 1.0000 0 -5.0000
% 1.0000 0.0000 0 4.0000
% 0 0 -1.0000 1.6858
% 0 0 0 1.0000
Tlist = sym(zeros(4,4,size(thetalist,1)));
Mi = sym(eye(4));
for i = size(thetalist): -1: 1
for j = 1:i
Mi = Mi * Mlist(:, :, j);
end
Tlist(:,:,i) = FKinSpace_Sym(Mi, Slist(:,1:i), thetalist(1:i));
Mi = sym(eye(4));
end
end

31
packages/MATLAB/mr/FKinSpace_Sym.m Normal file
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function T = FKinSpace(M, Slist, thetalist)
% *** CHAPTER 4: FORWARD KINEMATICS ***
% Takes M: the home configuration (position and orientation) of the
% end-effector,
% Slist: The joint screw axes in the space frame when the manipulator
% is at the home position,
% thetalist: A list of joint coordinates.
% Returns T in SE(3) representing the end-effector frame, when the joints
% are at the specified coordinates (i.t.o Space Frame).
% Example Inputs:
%
% clear; clc;
% M = [[-1, 0, 0, 0]; [0, 1, 0, 6]; [0, 0, -1, 2]; [0, 0, 0, 1]];
% Slist = [[0; 0; 1; 4; 0; 0], ...
% [0; 0; 0; 0; 1; 0], ...
% [0; 0; -1; -6; 0; -0.1]];
% thetalist =[pi / 2; 3; pi];
% T = FKinSpace(M, Slist, thetalist)
%
% Output:
% T =
% -0.0000 1.0000 0 -5.0000
% 1.0000 0.0000 0 4.0000
% 0 0 -1.0000 1.6858
% 0 0 0 1.0000
T = M;
for i = size(thetalist): -1: 1
T = MatrixExp6_Sym(VecTose3(Slist(:, i) * thetalist(i))) * T;
end
end

33
packages/MATLAB/mr/JacobianBody_Sym.m Normal file
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function Jb = JacobianBody_Sym(Blist, thetalist)
% *** CHAPTER 5: VELOCITY KINEMATICS AND STATICS ***
% Takes Blist: The joint screw axes in the end-effector frame when the
% manipulator is at the home position, in the format of a
% matrix with the screw axes as the columns,
% thetalist: A list of joint coordinates.
% Returns the corresponding body Jacobian (6xn real numbers).
% Example Input:
%
% clear; clc;
% Blist = [[0; 0; 1; 0; 0.2; 0.2], ...
% [1; 0; 0; 2; 0; 3], ...
% [0; 1; 0; 0; 2; 1], ...
% [1; 0; 0; 0.2; 0.3; 0.4]];
% thetalist = [0.2; 1.1; 0.1; 1.2];
% Jb = JacobianBody(Blist, thetalist)
%
% Output:
% Jb =
% -0.0453 0.9950 0 1.0000
% 0.7436 0.0930 0.3624 0
% -0.6671 0.0362 -0.9320 0
% 2.3259 1.6681 0.5641 0.2000
% -1.4432 2.9456 1.4331 0.3000
% -2.0664 1.8288 -1.5887 0.4000
Jb = sym(Blist);
T = sym(eye(4));
for i = length(thetalist) - 1: -1: 1
T = T * expm(VecTose3(-1 * Blist(:, i + 1) * thetalist(i + 1)));
Jb(:, i) = Adjoint(T) * Blist(:, i);
end
end

33
packages/MATLAB/mr/JacobianSpace_Sym.m Normal file
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function Js = JacobianSpace_Sym(Slist, thetalist)
% *** CHAPTER 5: VELOCITY KINEMATICS AND STATICS ***
% Takes Slist: The joint screw axes in the space frame when the manipulator
% is at the home position, in the format of a matrix with the
% screw axes as the columns,
% thetalist: A list of joint coordinates.
% Returns the corresponding space Jacobian (6xn real numbers).
% Example Input:
%
% clear; clc;
% Slist = [[0; 0; 1; 0; 0.2; 0.2], ...
% [1; 0; 0; 2; 0; 3], ...
% [0; 1; 0; 0; 2; 1], ...
% [1; 0; 0; 0.2; 0.3; 0.4]];
% thetalist = [0.2; 1.1; 0.1; 1.2];
% Js = JacobianSpace(Slist, thetalist)
%
% Output:
% Js =
% 0 0.9801 -0.0901 0.9575
% 0 0.1987 0.4446 0.2849
% 1.0000 0 0.8912 -0.0453
% 0 1.9522 -2.2164 -0.5116
% 0.2000 0.4365 -2.4371 2.7754
% 0.2000 2.9603 3.2357 2.2251
Js = sym(Slist);
T = sym(eye(4));
for i = 2: length(thetalist)
T = T * expm(VecTose3(Slist(:, i - 1) * thetalist(i - 1)));
Js(:, i) = Adjoint(T) * Slist(:, i);
end
end

23
packages/MATLAB/mr/MatrixExp6_Sym.m Normal file
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function T = MatrixExp6_Sym(se3mat)
% *** CHAPTER 3: RIGID-BODY MOTIONS ***
% Takes a se(3) representation of exponential coordinates.
% Returns a T matrix in SE(3) that is achieved by traveling along/about the
% screw axis S for a distance theta from an initial configuration T = I.
% Example Input:
%
% clear; clc;
% se3mat = [ 0, 0, 0, 0;
% 0, 0, -1.5708, 2.3562;
% 0, 1.5708, 0, 2.3562;
% 0, 0, 0, 0]
% T = MatrixExp6(se3mat)
%
% Output:
% T =
% 1.0000 0 0 0
% 0 0.0000 -1.0000 -0.0000
% 0 1.0000 0.0000 3.0000
% 0 0 0 1.0000
T = expm(se3mat);
end

9
packages/MATLAB/mr/SpaceVelToLinearVel.m Normal file
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function Vlinear = BodyVelToLinearVel(V,G)
% *** CHAPTER x: DYNAMICS OF OPEN CHAINS ***
% Takes V: Body frame velocity,
% G: Space frame G
% Returns Glist: Spatial inertia matrices Gi of the links
[R, p] = TransToRp(G);
Vlienar = se3ToVec(V)*[p;1];
Vlienar = Vlienar(1:3);

10
packages/MATLAB/mr/SpatialInertia.m Normal file
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function Glist = SpatialInertia(G)
% *** CHAPTER x: DYNAMICS OF OPEN CHAINS ***
% Takes G: A list of inertia,
% Returns Glist: Spatial inertia matrices Gi of the links
n = size(G,1);
Glist = zeros(6,6,n);
for i = 1:n
Glist(:,:,i) = diag(G(i,1:6));
end