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trchain.m
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trchain.m
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%TRCHAIN Compound SE(3) transforms from string
%
% T = TRCHAIN(S) is a homogeneous transform (4x4) that results from
% compounding a number of elementary transformations defined by the string
% S. The string S comprises a number of tokens of the form X(ARG) where
% X is one of Tx, Ty, Tz, Rx, Ry, or Rz. ARG is an arbitrary MATLAB expression
% that can include constants or workspace variables. For example:
%
% trchain('Tx(1) Rx(90) Ry(45) Tz(2)')
%
% is equivalent to computing
%
% transl(1,0,0) * trotx(90, 'deg') * troty(45, 'deg') * transl(0,0,2)
%
% T = TRCHAIN(S, Q) as above but the expression for ARG can also contain
% a variable 'qJ' which selects the Jth value from the passed vector Q (1xN).
% For example:
% trchain('Rx(q1)Tx(a1)Ry(q2)Ty(a3)Rz(q3)', [1 2 3])
%
% [T,TOK] = TRCHAIN(S ...) as above but return an array of tokens which can
% be passed in, instead of the string.
%
% T = TRCHAIN(TOK ...) as above but chain is defined by array of tokens
% instead of a string.
%
% Options::
% - 'deg' all angular variables are in degrees (default radians)
% - 'qvar',V treat the string V as the joint variable name rather than 'q'
%
% Notes::
% - Variables used in the string must exist in the caller workspace.
% - The string can contain arbitrary characters between the elements, for
% example space, +, *, . or even |.
% - Works for symbolic variables in the workspace and/or passed in via the
% vector Q.
% - For symbolic operations that involve use of the value pi, make sure you
% define it first in the workspace: pi = sym('pi');
% - The tokens are simply a parsed version of the input string and provide
% some efficiency for repeated calls on the same chain.
%
% See also trchain2, trotx, troty, trotz, transl, SerialLink.trchain, ETS.
%## 3d homogeneous
% Copyright (C) 1993-2017, 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
function [T,tokens_out] = trchain(s, varargin)
opt.deg = false;
opt.qvar = 'q';
[opt,args] = tb_optparse(opt, varargin);
if opt.deg
unit = {'deg'};
else
unit = {};
end
if length(args) > 0
q = args{1};
if isa(q, 'symfun')
q = formula(q);
end
else
q = [];
end
if ischar(s) || isstring(s)
% tokenise the input
% tok.op = {Tx, Ty, Tz, Rx, Ry, Rz}
% tok.arg = expression
% tok.index = J if qJ is present, else is 0
% get list of tokens
tokens = regexp(char(s), '(?<op>R.?|T.)\((?<arg>[^\)]+)\)', 'names');
% look for presence of a joint variable
re = sprintf('%s(?<idx>[1-9][0-9]*)', opt.qvar);
for i=1:length(tokens)
qtok = regexp(tokens(i).arg, re, 'tokens');
assert(length(qtok) <= 1, 'RTB:trchain:badarg', 'Only one qN variable allowed in any factor');
if isempty(qtok)
tokens(i).index = 0;
else
tokens(i).index = str2num(qtok{1}{1});
end
end
else
% token array provided, check it's good
tokens = s;
assert(all(isfield(s, {'arg', 'op', 'index'})), 'RTB:trchain:badarg', 'tokens are not a valid structure array');
end
T = eye(4,4);
for token = tokens
% for each token, evaluate the argument
if token.index > 0
% expression contains a joint variable
% take value from the passed in vector q
assert(token.index <= length(q), 'RTB:trchain:badarg', 'vector q has insufficient values');
% substitute the joint value into the expression string
if isa(q, 'sym')
arg = subs(str2sym(token.arg), [opt.qvar num2str(token.index)], q(token.index));
else
expr = strrep(token.arg, [opt.qvar num2str(token.index)], num2str(q(token.index), '%g'));
% evaluate and catch any errors
try
arg = evalin('caller', expr);
catch
error('RTB:trchain:badarg', 'can''t evaluate %s', expr);
end
end
else
% expression contains no joint variable
% evaluate and catch any errors
try
arg = evalin('caller', token.arg);
catch
error('RTB:trchain:badarg', 'can''t evaluate %s', token.arg);
end
end
% now compute the particular transform and update the transform chain
switch token.op
case 'Rx'
T = T * trotx(arg, unit{:});
case 'Ry'
T = T * troty(arg, unit{:});
case 'Rz'
T = T * trotz(arg, unit{:});
case 'Tx'
T = T * transl(arg, 0, 0);
case 'Ty'
T = T * transl(0, arg, 0);
case 'Tz'
T = T * transl(0, 0, arg);
otherwise
error('RTB:trchain:badarg', 'unknown operator %s', token.op);
end
end
if isa(q, 'sym')
T = formula(T);
end
if nargout > 1
tokens_out = tokens;
end
end