add FK at each joint

packages/MATLAB/mr/BodyVelToLinearVel.m

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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);

packages/MATLAB/mr/FKinSpaceExpand.m

@@ -0,0 +1,36 @@
+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

packages/MATLAB/mr/FKinSpaceExpand_Sym.m

@@ -0,0 +1,36 @@
+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

packages/MATLAB/mr/FKinSpace_Sym.m

@@ -0,0 +1,31 @@
+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

packages/MATLAB/mr/MatrixExp6_Sym.m

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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

packages/MATLAB/mr/SpaceVelToLinearVel.m

@@ -0,0 +1,9 @@
+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);

packages/MATLAB/mr/SpatialInertia.m

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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