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ETS.m
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%ETS Elementary Transform Sequence class
%
% Manipulate a sequence (vector) of elementary transformations
% - ETS.TX
% - ETS.TY
% - ETS.TZ
% - ETS.RX
% - ETS.RY
% - ETS.RZ
%
% Methods::
% ETS Construct a sequence from string
% isrot True if rotational transform
% istrans True if translational transform
% isjoint Is ETS a function of qj
% njoints Maximum joint variable index
% axis Axis of translation or rotation
% find Find ETS that is a function of qj
% subs Substitute element of sequence
%-
% eval Evaluate ETS
% jacobian Compute Jacobian of ETS
%-
% display Display a sequence in human readable form
% char Convert sequence to a string
%
% Example::
% ets = ETS('Rx(q1)Tx(a1)Ry(q2)Ty(a3)Rz(q3)Rx(pi/2)')
% ets.eval([1 2 3]);
%
% Notes::
% - Still experimental
%
% See also trchain, trchain2.
% TODO:
% - handle 2D case
% - do DHFactor
% - accept parameters from a passed struct rather as well as workspace
% Copyright (C) 1993-2015, by Peter I. Corke
%
% This file is part of The Robotics Toolbox for MATLAB (RTB).
%
% RTB is free software: you can redistribute it and/or modify
% it under the terms of the GNU Lesser General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% RTB is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU Lesser General Public License for more details.
%
% You should have received a copy of the GNU Leser General Public License
% along with RTB. If not, see <http://www.gnu.org/licenses/>.
%
% http://www.petercorke.com
classdef ETS < handle
properties
type % ETS.TX, ETS.TY, ETS.TZ, ETS.RX, ETS.RY, ETS.RZ
val
joint % joint number, if a joint, else 0
constant
sign
symconstant
end
properties (Constant)
TX = 0;
TY = 1;
TZ = 2;
RX = 3;
RY = 4;
RZ = 5;
names = {'Tx', 'Ty', 'Tz', 'Rx', 'Ry', 'Rz'};
end
% Element.java
% // one of ETS.TX, ETS.TY ... ETS.RZ, DH_STANDARD/MODIFIED
% int type;
%
% // transform parameters, only one of these is set
% String var; // eg. q1, for joint var ETS.TYpes
% String symconst; // eg. L1, for lengths
% int constant; // eg. 90, for angles
%
% // DH parameters, only set if ETS.TYpe is DH_STANDARD/MODIFIED
% int theta,
% alpha;
% String A,
% D;
% int prismatic;
% int offset;
methods
function ets = ETS(s, varargin)
%ETS.ETS Construct elementary transform element or sequence
%
% e = ETS() is a new ETS object.
%
% e = ETS(t) is a clone of the ETS object t and all properties are copied.
%
% e = ETS(op, v) is a new ETS object of type op and value v. OP can be any
% of
% 'Rx' rotation about the x-axis
% 'Ry' rotation about the y-axis
% 'Rz' rotation about the z-axis
% 'Tx' translation along the x-axis
% 'Ty' translation along the y-axis
% 'Tz' translation along the z-axis
% 'transl' sequence of finite translations along the x-, y- and z-directions.
% 'rpy' sequence of finite rotations about the x-, y- and z-directions.
%
% e = ETS(str) is a sequence of ETS objects, each described by a
% subexpression in the string STR. Each subexpression comprises an
% operation as per the table above followed by parentheses and a value.
% For example:
%
% ets = ETS('Rx(q1)Tx(a1)Ry(q2)Ty(a3)Rz(q3)Rx(pi/2)')
if nargin == 0
ets.joint = false;
ets.constant = [];
return;
end
if isstr(s)
if strfind(s, '(')
% string of tokens
tokens = regexp(s, '\s*(?<op>R.?|T.)\(\s*(?<arg>[^)]*)\s*\)\s*', 'names');
joint = 1;
ets = [];
for token = tokens
% get the argument for this transform element
% deal with case of symbolic arg or workspace expression
if token.arg(1) == 'q'
x = ETS(token.op, []);
x.joint = joint;
joint = joint+1;
else
x = ETS(token.op, token.arg);
x.joint = 0;
end
ets = [ets x]; % append to the list
end
else
% ETS('transl', [v])
% ETS('rpy', [v]);
switch s
case 'transl'
v = varargin{1};
ets = [];
if v(1) ~= 0
ets = [ets ETS('Tx', v(1))];
end
if v(2) ~= 0
ets = [ets ETS('Ty', v(2))];
end
if v(3) ~= 0
ets = [ets ETS('Tz', v(3))];
end
case 'rpy'
v = varargin{1};
ets = [];
if v(1) ~= 0
ets = [ets ETS('Rx', v(1))];
end
if v(2) ~= 0
ets = [ets ETS('Ry', v(2))];
end
if v(3) ~= 0
ets = [ets ETS('Rz', v(3))];
end
case 'Rx'
ets = ETS(ETS.RX, varargin{1});
case 'Ry'
ets = ETS(ETS.RY, varargin{1});
case 'Rz'
ets = ETS(ETS.RZ, varargin{1});
case 'Tx'
ets = ETS(ETS.TX, varargin{1});
case 'Ty'
ets = ETS(ETS.TY, varargin{1});
case 'Tz'
ets = ETS(ETS.TZ, varargin{1});
otherwise
error('RTB:trchain:badarg', 'unknown operator/option %s', s);
end
end
elseif isnumeric(s)
ets = ETS();
ets.type = s;
ets.val = varargin{1};
elseif isa(s, 'ETS')
% clone the object
ets.type = s.type;
ets.joint = s.joint
ets.val = s.val;
ets.symconstant = s.symconstant;
if nargin > 1
ets.type = varargin{1};
end
if nargin > 2
if varargin{2} < 0
ets = ets.negate();
end
end
end
end
function s = op(ets)
s = ets.names{ets.type+1};
end
function s = char(ets)
s = '';
for x=ets
e = x.op;
if isjoint(x)
e = [e '(q' num2str(x.joint) ')'];
else
e = [e '(' num2str(x.val) ')'];
end
s = strcat(s, e);
end
end
function display(ets)
%ETS.display Display parameters
%
% ETS.display() displays the transform parameters in compact single line format.
%
% Notes::
% - This method is invoked implicitly at the command line when the result
% of an expression is a Link object and the command has no trailing
% semicolon.
%
% See also Link.char, Link.dyn, SerialLink.showlink.
loose = strcmp( get(0, 'FormatSpacing'), 'loose');
if loose
disp(' ');
end
disp([inputname(1), ' = '])
disp( char(ets) );
end % display()
%-------------------------------------------------------------
function xo = subs(ets, k, x)
xo = [ets(1:k-1) x ets(k+1:end)];
end
function k = find(ets, j)
[~,k] = find([ets.joint] == j);
end
function n = njoints(ets)
n = max([ets.joint]');
end
function b = isjoint(ets, j)
b = [ets.joint] ~= 0;
end
function b = istrans(ets)
b = ([ets.type] >= ets(1).TX) & ([ets.type] <= ets(1).TZ)
end
function b = isrot(ets)
b = ([ets.type] >= ets(1).RX) & ([ets.type] <= ets(1).RZ)
end
function b = axis(ets)
b = char( mod([ets.type],3) + 'x' );
end
%-------------------------------------------------------------
function T = eval(ets, q)
T = eye(4,4);
for x = ets
% get the argument for this transform element
if x.isjoint()
% from the passed in vector q
arg = q(x.joint);
else % or the workspace
try
arg = evalin('base', x.val);
catch
error('RTB:ETS:badarg', 'variable %s does not exist', x.val);
end
end
% now evaluate the element and update the transform chain
switch x.type
case ETS.RX
T = T * trotx(arg);
case ETS.RY
T = T * troty(arg);
case ETS.RZ
T = T * trotz(arg);
case ETS.TX
T = T * transl(arg, 0, 0);
case ETS.TY
T = T * transl(0, arg, 0);
case ETS.TZ
T = T * transl(0, 0, arg);
otherwise
error('RTB:ETS:badarg', 'unknown operator %s', x.op);
end
end
% if isa(q, 'symfun')
% T = formula(T);
% end
end
function negate(ets)
ets.constant = -ets.constant;
s = ets.symconst;
% add initial sign char if none
if s(1) ~= '+' && s(1) ~= '-'
s = ['+' s];
end
% go through the string and flip all sign chars
kp = strfind(s, '+');
kn = strfind(s, '-');
s(kp) = '-';
s(kn) = '+';
% if inital sign is + remove it
if s(1) == '+';
s = s(2:end);
end
ets.symconst = s;
end
function J = jacobian(ets, q)
n = ets.njoints();
J = zeros(6, n);
for j=1:n
% find derivative with respect to q_j
k = ets.find(j);
deriv = ets(k).deriv(q(j));
pre = ets(1:k-1).eval(q);
post = ets(k+1:end).eval(q);
Td = pre*deriv*post
T = ets.eval(q);
t2r(T)*t2r(T)';
end
end
function T = deriv(ets, q)
switch ets.type
case ETS.RX
T = r2t([0 0 0; 0 -sin(q) -cos(q); 0 cos(q) -sin(q)]);
case ETS.RY
T = r2t([-sin(q) 0 cos(q); 0 0 0; -cos(q) 0 -sin(q)]);
case ETS.RZ
T = r2t([-sin(q) -cos(q) 0; cos(q) -sin(q) 0; 0 0 0]);
case ETS.TX
T = transl(1, 0, 0);
case ETS.TY
T = transl(0, 1, 0);
case ETS.TZ
T = transl(0, 0, 1);
end
T(4,4) = 0;
end
% methods from Element.java
% * public boolean istrans()
% * public boolean isrot()
% * public int axis()
% * public boolean isjoint() {
% * public boolean factorMatch(int dhWhich, int i, int verbose) {
% * public void add(Element e) {
% * public Element(int ETS.TYpe, int constant) {
% * public Element(int ETS.TYpe) // new of specified ETS.TYpe
% *
% * public static String toString(Element [] e) {
% * public String argString() {
% * public String toString() {
% *
% * Constructors:
% * Element(Element e) // clone of argument
% * Element(Element e, int ETS.TYpe, int sign) // clone of argument with new ETS.TYpe
% * Element(Element e, int ETS.TYpe) // clone of argument with new ETS.TYpe
% * Element(String s)
function plus(ets, e)
end
function symPlus(ets, e)
end
function merge(ets, e)
end
function b = swap(ets, next, dhWhich)
b = false
% don't swap if both are joint variables
if ets.isjoint() && next.isjoint()
return
end
switch (dhWhich)
case 'standard'
% we want to sort terms into the order: RZ TX TZ RX
if ((ets.type == ETS.TZ) && (next.type == ETS.TX)) || ...
((ets.type == ETS.TX) && (next.type == ETS.RX) && next.isjoint()) || ... % push constant translations through rotational joints of the same ETS.TYpe
((ets.type == ETS.TY) && (next.type == ETS.RY)) && next.isjoint() || ...
((ets.type == ETS.TZ) && (next.type == ETS.RZ)) && next.isjoint() || ...
(~ets.isjoint() && (this.type == ETS.RX) && (next.type == ETS.TX)) || ...
(~ets.isjoint() && (this.type == ETS.RY) && (next.type == ETS.TY)) ||....
(~ets.isjoint() && ~next.isjoint() && (this.type == ETS.TZ) && (next.type == ETS.RZ)) || ...
((ets.type == ETS.TY) && (next.type == ETS.TZ)) || ... % move ETS.TY terms to the right
((ets.type == ETS.TY) && (next.type == ETS.TX))
fprintf(['Swap: ' char(ets) ' <-> ' char(next)] );
b = true;
end
case 'modified'
if ((ets.type == ETS.RX) && (next.type == ETS.TX)) || ...
((ets.type == ETS.RY) && (next.type == ETS.TY)) || ...
((ets.type == ETS.RZ) && (next.type == ETS.TZ)) || ...
((ets.type == ETS.TZ) && (next.type == ETS.TX))
fprintf(['Swap: ' char(ets) ' <-> ' char(next)] );
b = true;
end
otherwise
error('bad DH ETS.TYpe');
end
b = false;
end
% /**
% * Substitute this transform for a triple of transforms
% * that includes an ETS.RZ or ETS.TZ.
% *
% * @return - null if no substituion required
% * - array of Elements to substitute
% */
function s = substituteToZ(ets, prev)
if nargin == 2
switch ets.type
case ETS.RY
s(1) = ETS(RZ, 90);
s(2) = ETS(ets, ETS.RX);
s(3) = ETS(RZ, -90);
case ETS.TY
if prev.type == ETS.RZ
s(1) = ETS(RZ, 90);
s(2) = ETS(ets, ETS.TX);
s(3) = ETS(RZ, -90);
else
s(1) = ETS(RX, -90);
s(2) = ETS(ets, ETS.TZ);
s(3) = ETS(RX, 90);
end
otherwise
s = [];
end
else
switch ets.type
case ETS.RX
s(1) = ETS(RY, 90);
s(2) = ETS(ets, ETS.RZ);
s(3) = ETS(RY, -90);
case ETS.RY
s(1) = ETS(RX, -90);
s(2) = ETS(ets, ETS.RZ);
s(3) = ETS(RX, 90);
case ETS.TX
s(1) = ETS(RY, 90);
s(2) = ETS(ets, ETS.TZ);
s(3) = ETS(RY, -90);
case ETS.TY
s(0) = ETS(RX, -90);
s(1) = ETS(ets, ETS.TZ);
s(2) = ETS(RX, 90);
otherwise
s = [];
end
end
end
% /**
% * Simple rewriting rule for adjacent transform pairs. Attempt to
% * eliminate ETS.TY and ETS.RY.
% * @param previous element in list
% * @return - null if no substituion required
% * - array of Elements to subsitute
% */
function s = substituteY(this, prev, next)
s = [];
if (prev.isjoint() || e.isjoint())
return
end
% note that if rotation is -90 we must make the displacement -ve */
if ((prev.type == ETS.RX) && (this.type == ETS.TY))
% ETS.RX.TY -> ETS.TZ.RX
s(1) = ETS(this, ETS.TZ, prev.constant);
s(2) = ETS(prev);
elseif ((prev.type == ETS.RX) && (this.type == ETS.TZ))
% ETS.RX.TZ -> ETS.TY.RX
s(1) = ETS(this, ETS.TY, -prev.constant);
s(2) = ETS(prev);
elseif ((prev.type == ETS.RY) && (this.type == ETS.TX))
% ETS.RY.TX-> ETS.TZ.RY
s(1) = ETS(this, ETS.TZ, -prev.constant);
s(2) = ETS(prev);
elseif ((prev.type == ETS.RY) && (this.type == ETS.TZ))
% ETS.RY.TZ-> ETS.TX.RY
s(1) = ETS(this, ETS.TX, prev.constant);
s(2) = ETS(prev);
elseif ((prev.type == ETS.TY) && (this.type == ETS.RX))
% ETS.TY.RX -> ETS.RX.TZ
s(1) = ETS(this);
s(2) = ETS(prev, ETS.TZ, -this.constant);
%%return s;
s = [];
elseif ((prev.type == ETS.RY) && (this.type == ETS.RX))
% ETS.RY(Q).RX -> ETS.RX.RZ(-Q)
s(1) = ETS(this);
s(2) = ETS(prev, ETS.RZ, -1);
elseif ((prev.type == ETS.RX) && (this.type == ETS.RY))
% ETS.RX.RY -> ETS.RZ.RX
s(1) = ETS(this, ETS.RZ);
s(2) = ETS(prev);
elseif ((prev.type == ETS.RZ) && (this.type == ETS.RX))
% ETS.RZ.RX -> ETS.RX.RY
s(1) = ETS(this);
s(2) = ETS(prev, ETS.RY);
s = [];
end
end
end
end