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63 lines
1.9 KiB
63 lines
1.9 KiB
% Copyright (C) 1993-2013, by Peter I. Corke
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%
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% This file is part of The Robotics Toolbox for MATLAB (RTB).
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%
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% RTB is free software: you can redistribute it and/or modify
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% it under the terms of the GNU Lesser General Public License as published by
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% the Free Software Foundation, either version 3 of the License, or
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% (at your option) any later version.
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%
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% RTB is distributed in the hope that it will be useful,
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% but WITHOUT ANY WARRANTY; without even the implied warranty of
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% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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% GNU Lesser General Public License for more details.
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%
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% You should have received a copy of the GNU Leser General Public License
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% along with RTB. If not, see <http://www.gnu.org/licenses/>.
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%
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% http://www.petercorke.com
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%%begin
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% In the field of robotics there are many possible ways of representing
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% positions and orientations, but the homogeneous transformation is well
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% matched to MATLABs powerful tools for matrix manipulation.
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%
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% Homogeneous transformations describe the relationships between Cartesian
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% coordinate frames in terms of translation and orientation.
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% A pure translation of 0.5m in the X direction is represented by
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transl(0.5, 0.0, 0.0)
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% a rotation of 90degrees about the Y axis by
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troty(pi/2)
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% and a rotation of -90degrees about the Z axis by
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trotz(-pi/2)
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% these may be concatenated by multiplication
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t = transl(0.5, 0.0, 0.0) * troty(pi/2) * trotz(-pi/2)
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%
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% If this transformation represented the origin of a new coordinate frame with respect
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% to the world frame origin (0, 0, 0), that new origin would be given by
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t * [0 0 0 1]'
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% the orientation of the new coordinate frame may be expressed in terms of
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% Euler angles
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tr2eul(t)
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% or roll/pitch/yaw angles
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tr2rpy(t)
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% It is important to note that tranform multiplication is in general not
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% commutative as shown by the following example
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trotx(pi/2) * trotz(-pi/8)
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trotz(-pi/8) * trotx(pi/2)
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