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ETS3.m
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ETS3.m
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%ETS3 Elementary transform sequence in 3D
%
% This class and package allows experimentation with sequences of spatial
% transformations in 3D.
%
% import +ETS3.*
% L1 = 0; L2 = -0.2337; L3 = 0.4318; L4 = 0.0203; L5 = 0.0837; L6 = 0.4318;
% E3 = Tz(L1) * Rz('q1') * Ry('q2') * Ty(L2) * Tz(L3) * Ry('q3') * Tx(L4) * Ty(L5) * Tz(L6)
%
% Operation methods::
% fkine
%
% Information methods::
% isjoint test if transform is a joint
% njoints the number of joint variables
% structure a string listing the joint types
%
% Display methods::
% display display value as a string
% plot graphically display the sequence as a robot
% teach graphically display as robot and allow user control
%
% Conversion methods::
% char convert to string
% string convert to string with symbolic variables
%
% Operators::
% * compound two elementary transforms
% + compound two elementary transforms
%
% Notes::
% - The sequence is an array of objects of superclass ETS3, but with
% distinct subclasses: Rx, Ry, Rz, Tx, Ty, Tz.
% - Use the command 'clear imports' after using ETS2.
%
% See also ETS2.
% 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
classdef ETS3
properties
what % type of transform (string): Rx, Ry, etc
param % the constant numerical parameter (if not joint)
qvar % the integer joint index 1..N (if joint), else NaN
qlim % for prismatic joint, a 2 vector [min,max]
end
methods
function obj = ETS3(what, x, varargin)
%ETS3.ETS3 Create an ETS3 object
%
% E = ETS3(W, V) is a new ETS3 object that defines an elementary transform where
% W is 'Rx', 'Ry', 'Rz', 'Tx', 'Ty' or 'Tz' and V is the paramter for the transform. If V is a string
% of the form 'qN' where N is an integer then the transform is considered
% to be a joint and the parameter is ignored. Otherwise the transform is a constant.
%
% E = ETS3(E1) is a new ETS3 object that is a clone of the ETS3 object E1.
%
% See also ETS2.Rz, ETS2.Tx, ETS2.Ty.
% if nargin > 0
% disp(['ETS3 constructing ', what]);
% else
% disp('ETS3 constructor: no args');
% end
opt.qlim = [];
opt = tb_optparse(opt, varargin);
obj.qvar = NaN;
obj.param = 0;
if ~isempty(opt.qlim)
assert(length(opt.qlim) == 2, 'ETS2: qlim must be a 2-vector');
end
obj.qlim = opt.qlim;
if nargin > 1
if isa(x, 'ETS3')
% clone it
obj.what = x.what;
obj.qvar = x.qvar;
obj.param = x.param;
obj.qlim = x.qlim;
else
assert(ismember(what, {'Tx','Ty','Tz','Rx','Ry','Rz'}), 'ETS3: invalid transform type given');
if ischar(x)
% create a new one
obj.qvar = str2num(x(2:end));
else
obj.param = x;
end
obj.what = what;
end
end
end
function r = fkine(ets, q, varargin)
%ETS3.fkine Forward kinematics
%
% ETS.fkine(Q, OPTIONS) is the forward kinematics, the pose of the end of the
% sequence as an SE3 object. Q (1xN) is a vector of joint variables.
%
% ETS.fkine(Q, N, OPTIONS) as above but process only the first N elements
% of the transform sequence.
%
% Options::
% 'deg' Angles are given in degrees.
r = SE3;
opt.deg = false;
[opt,args] = tb_optparse(opt, varargin);
if opt.deg
opt.deg = pi/180;
else
opt.deg = 1;
end
n = length(ets);
if ~isempty(args) && isreal(args{1})
n = args{1};
end
assert(n>0 && n <= length(ets), 'RTB:ETS2:badarg', 'bad value of n given');
for i=1:n
e = ets(i);
if e.isjoint
v = q(e.qvar);
else
v = e.param;
end
switch e.what
case 'Tx'
r = r * SE3(v, 0, 0);
case 'Ty'
r = r * SE3(0, v, 0);
case 'Tz'
r = r * SE3(0, 0, v);
case 'Rx'
r = r * SE3.Rx(v*opt.deg);
case 'Ry'
r = r * SE3.Ry(v*opt.deg);
case 'Rz'
r = r * SE3.Rz(v*opt.deg);
end
end
r = r.simplify(); % simplify it if symbolic
end
function b = isjoint(ets)
%ETS3.isjoint Test if transform is a joint
%
% E.isjoint is true if the transform element is a joint, that is, its
% parameter is of the form 'qN'.
b = ~isnan(ets.qvar);
end
function v = isprismatic(ets)
%ETS3.isprismatic Test if transform is prismatic joint
%
% E.isprismatic is true if the transform element is a joint, that is, its
% parameter is of the form 'qN' and it controls a translation.
v = isjoint(ets) && (ets.what(1) == 'T');
end
function k = find(ets, j)
%ETS3.find Find joints in transform sequence
%
% E.find(J) is the index in the transform sequence ETS(1xN) corresponding
% to the J'th joint.
[~,k] = find([ets.qvar] == j);
end
function n = njoints(ets)
%ETS3.njoints Number of joints in transform sequence
%
% E.njoints is the number of joints in the transform sequence.
%
% See also ETS2.n.
n = max([ets.qvar]);
end
function v = n(ets)
%ETS3.n Number of joints in transform sequence
%
% E.njoints is the number of joints in the transform sequence.
%
% Notes::
% - Is a wrapper on njoints, for compatibility with SerialLink object.
%
% See also ETS3.n.
v = ets.njoints;
end
function s = string(ets)
%ETS3.string Convert to string with symbolic variables
%
% E.string is a string representation of the transform sequence where
% non-joint parameters have symbolic names L1, L2, L3 etc.
%
% See also trchain.
constant = 1;
for i = 1:length(ets)
e = ets(i);
if e.isjoint
term = sprintf('%s(q%d)', e.what, e.qvar);
else
term = sprintf('%s(L%d)', e.what, constant);
constant = constant + 1;
end
if i == 1
s = term;
else
s = [s ' ' term];
end
end
end
function out = mtimes(ets1, ets2)
%ETS3.mtimes Compound transforms
%
% E1 * E2 is a sequence of two elementary transform.
%
% See also ETS3.plus.
assert( strcmp(superclasses(ets1), superclasses(ets2)), 'ETS3: both operands must have superclass ETS3, perhaps run ''clear import'', and start over');
out = [ets1 ets2];
end
function out = plus(ets1, ets2)
%ETS3.plus Compound transforms
%
% E1 + E2 is a sequence of two elementary transform.
%
% See also ETS3.mtimes.
assert( strcmp(superclasses(ets1), superclasses(ets2)), 'ETS3: both operands must have superclass ETS3, perhaps run ''clear import'', and start over');
out = [ets1 ets2];
end
function s = structure(ets)
%ETS2.structure Show joint type structure
%
% E.structure is a character array comprising the letters 'R' or 'P' that
% indicates the types of joints in the elementary transform sequence E.
%
% Notes::
% - The string will be E.njoints long.
%
% See also SerialLink.config.
s = '';
for e = ets
if e.qvar > 0
switch e.what(1)
case 'T'
s = [s 'P'];
case 'R'
s = [s 'R'];
end
end
end
end
function display(ets)
%ETS3.display Display parameters
%
% E.display() displays the transform or transform sequence parameters in
% compact single line format.
%
% Notes::
% - This method is invoked implicitly at the command line when the result
% of an expression is an ETS3 object and the command has no trailing
% semicolon.
%
% See also ETS3.char.
loose = strcmp( get(0, 'FormatSpacing'), 'loose');
if loose
disp(' ');
end
disp([inputname(1), ' = '])
disp( char(ets) );
end % display()
function s = char(ets)
%ETS3.char Convert to string
%
% E.char() is a string showing transform parameters in a compact format. If E is a transform sequence (1xN) then
% the string describes each element in sequence in a single line format.
%
% See also ETS3.display.
s = '';
function s = render(z)
if isa(z, 'sym')
s = char(z);
else
s = sprintf('%g', z);
end
end
for e = ets
if e.isjoint
s = [s ' ' sprintf('%s(q%d)', e.what, e.qvar) ];
else
s = [s ' ' sprintf('%s(%s)', e.what, render(e.param))];
end
end
end
function teach(robot, varargin)
%ETS3.teach Graphical teach pendant
%
% Allow the user to "drive" a graphical robot using a graphical slider
% panel.
%
% ETS.teach(OPTIONS) adds a slider panel to a current ETS plot. If no
% graphical robot exists one is created in a new window.
%
% ETS.teach(Q, OPTIONS) as above but the robot joint angles are set to Q (1xN).
%
% Options::
% 'eul' Display tool orientation in Euler angles (default)
% 'rpy' Display tool orientation in roll/pitch/yaw angles
% 'approach' Display tool orientation as approach vector (z-axis)
% '[no]deg' Display angles in degrees (default true)
%
% GUI::
% - The Quit (red X) button removes the teach panel from the robot plot.
%
% Notes::
% - The currently displayed robots move as the sliders are adjusted.
% - The slider limits are derived from the joint limit properties. If not
% set then for
% - a revolute joint they are assumed to be [-pi, +pi]
% - a prismatic joint they are assumed unknown and an error occurs.
%
% See also ETS3.plot.
%-------------------------------
% parameters for teach panel
bgcol = [135 206 250]/255; % background color
height = 0.06; % height of slider rows
%-------------------------------
%---- handle options
opt.deg = true;
opt.orientation = {'rpy', 'eul', 'approach'};
opt.d_2d = false;
opt.callback = [];
[opt,args] = tb_optparse(opt, varargin);
if nargin == 1
q = zeros(1,robot.n);
else
q = varargin{1};
varargin = varargin{2:end};
end
if isempty(findobj('Tag', 'ETS3'))
robot.plot(q, varargin{:})
end
RTBPlot.install_teach_panel('ETS3', robot, q, opt);
end
function plot(ets, qq, varargin)
%ETS3.plot Graphical display and animation
%
% ETS.plot(Q, options) displays a graphical animation of a robot based on
% the transform sequence. Constant translations are represented as pipe segments, rotational joints as cylinder, and
% prismatic joints as boxes. The robot is displayed at the joint angle Q (1xN), or
% if a matrix (MxN) it is animated as the robot moves along the M-point trajectory.
%
% Options::
% 'workspace', W Size of robot 3D workspace, W = [xmn, xmx ymn ymx zmn zmx]
% 'floorlevel',L Z-coordinate of floor (default -1)
%-
% 'delay',D Delay betwen frames for animation (s)
% 'fps',fps Number of frames per second for display, inverse of 'delay' option
% '[no]loop' Loop over the trajectory forever
% '[no]raise' Autoraise the figure
% 'movie',M Save an animation to the movie M
% 'trail',L Draw a line recording the tip path, with line style L
%-
% 'scale',S Annotation scale factor
% 'zoom',Z Reduce size of auto-computed workspace by Z, makes
% robot look bigger
% 'ortho' Orthographic view
% 'perspective' Perspective view (default)
% 'view',V Specify view V='x', 'y', 'top' or [az el] for side elevations,
% plan view, or general view by azimuth and elevation
% angle.
% 'top' View from the top.
%-
% '[no]shading' Enable Gouraud shading (default true)
% 'lightpos',L Position of the light source (default [0 0 20])
% '[no]name' Display the robot's name
%-
% '[no]wrist' Enable display of wrist coordinate frame
% 'xyz' Wrist axis label is XYZ
% 'noa' Wrist axis label is NOA
% '[no]arrow' Display wrist frame with 3D arrows
%-
% '[no]tiles' Enable tiled floor (default true)
% 'tilesize',S Side length of square tiles on the floor (default 0.2)
% 'tile1color',C Color of even tiles [r g b] (default [0.5 1 0.5] light green)
% 'tile2color',C Color of odd tiles [r g b] (default [1 1 1] white)
%-
% '[no]shadow' Enable display of shadow (default true)
% 'shadowcolor',C Colorspec of shadow, [r g b]
% 'shadowwidth',W Width of shadow line (default 6)
%-
% '[no]jaxes' Enable display of joint axes (default false)
% '[no]jvec' Enable display of joint axis vectors (default false)
% '[no]joints' Enable display of joints
% 'jointcolor',C Colorspec for joint cylinders (default [0.7 0 0])
% 'jointcolor',C Colorspec for joint cylinders (default [0.7 0 0])
% 'jointdiam',D Diameter of joint cylinder in scale units (default 5)
%-
% 'linkcolor',C Colorspec of links (default 'b')
%-
% '[no]base' Enable display of base 'pedestal'
% 'basecolor',C Color of base (default 'k')
% 'basewidth',W Width of base (default 3)
%
% The options come from 3 sources and are processed in order:
% - Cell array of options returned by the function PLOTBOTOPT (if it exists)
% - Cell array of options given by the 'plotopt' option when creating the
% SerialLink object.
% - List of arguments in the command line.
%
% Many boolean options can be enabled or disabled with the 'no' prefix. The
% various option sources can toggle an option, the last value encountered is used.
%
% Graphical annotations and options::
%
% The robot is displayed as a basic stick figure robot with annotations
% such as:
% - shadow on the floor
% - XYZ wrist axes and labels
% - joint cylinders and axes
% which are controlled by options.
%
% The size of the annotations is determined using a simple heuristic from
% the workspace dimensions. This dimension can be changed by setting the
% multiplicative scale factor using the 'mag' option.
%
% Figure behaviour::
%
% - If no figure exists one will be created and the robot drawn in it.
% - If no robot of this name is currently displayed then a robot will
% be drawn in the current figure. If hold is enabled (hold on) then the
% robot will be added to the current figure.
% - If the robot already exists then that graphical model will be found
% and moved.
%
%
% Notes::
% - The options are processed when the figure is first drawn, to make different options come
% into effect it is neccessary to clear the figure.
% - Delay betwen frames can be eliminated by setting option 'delay', 0 or
% 'fps', Inf.
% - The size of the plot volume is determined by a heuristic for an all-revolute
% robot. If a prismatic joint is present the 'workspace' option is
% required. The 'zoom' option can reduce the size of this workspace.
%
% See also ETS3.teach, SerialLink.plot3d.
% heuristic to figure robot size
reach = 0;
for e=ets
switch e.what
case {'Tx', 'Ty', 'Tz'}
if isjoint(e)
reach = reach + e.qlim(2);
else
reach = reach + e.param;
end
end
end
opt = RTBPlot.plot_options([], [varargin 'reach', reach]);
if isempty(findobj('Tag', 'ETS3'))
h = draw_ets(ets, qq, opt);
end
set(gca, 'Tag', 'RTB.plot');
set(gcf, 'Units', 'Normalized');
pf = get(gcf, 'Position');
if opt.raise
% note this is a very time consuming operation
figure(gcf);
end
if strcmp(opt.projection, 'perspective')
set(gca, 'Projection', 'perspective');
end
if isstr(opt.view)
switch opt.view
case 'top'
view(0, 90);
case 'x'
view(0, 0);
case 'y'
view(90, 0)
otherwise
error('RTB:plot:badarg', 'view must be: x, y, top')
end
elseif isnumeric(opt.view) && length(opt.view) == 2
view(opt.view)
end
% enable mouse-based 3D rotation
rotate3d on
ets.animate(qq);
end
function animate(ets, qq)
assert(numcols(qq) == ets.n, 'RTB:ETS3:badarg', 'Joint angles should have %d columns', ets.n);
handles = findobj('Tag', 'ETS3');
h = handles.UserData;
opt = h.opt;
ets = h.ets;
for q = qq'
for i=1:length(ets)
e = ets(i);
if i == 1
T = SE3;
else
T = ets.fkine(q, i-1, 'setopt', opt);
end
% create the transform for displaying this element (joint cylinder + link)
set(h.element(i), 'Matrix', T.T);
if isprismatic(e)
switch e.what
case 'Tx'
set(h.pjoint(e.qvar), 'Matrix', diag([q(e.qvar) 1 1 1]));
case 'Ty'
set(h.pjoint(e.qvar), 'Matrix', diag([1 q(e.qvar) 1 1]));
end
end
end
% update the wrist frame
T = ets.fkine(q, 'setopt', opt);
if ~isempty(h.wrist)
trplot(T, 'handle', h.wrist);
end
% render and pause
if opt.delay > 0
pause(opt.delay);
drawnow
end
end
end
end
methods (Access=private)
function h_ = draw_ets(ets, q, opt)
clf
disp('creating new ETS plot');
axis(opt.workspace);
view(3); % 3D plot
s = opt.scale;
% create an axis
ish = ishold();
if ~ishold
% if hold is off, set the axis dimensions
axis(opt.workspace);
hold on
end
group = hggroup('Tag', 'ETS3');
h.group = group;
% create the graphical joint and link elements
for i=1:length(ets)
e = ets(i);
if opt.debug
fprintf('create graphics for %s\n', e.char );
end
% create a graphical depiction of the transform element
% This is drawn to resemble orthogonal plumbing.
if i == 1
T = SE3;
else
T = ets.fkine(q, i-1, 'setopt', opt);
end
% create the transform for displaying this element (joint cylinder + link)
h.element(i) = hgtransform('Tag', sprintf('element%d', i), 'Matrix', T.T, 'Parent', h.group);
if isjoint(e)
% it's a joint element: revolute or prismatic
switch e.what
case 'Tx'
h.pjoint(e.qvar) = hgtransform('Tag', 'prismatic', 'Parent', h.element(i), 'Matrix', diag([q(e.qvar) 1 1 1]));
RTBPlot.box('x', opt.jointdiam*s, [0 1], opt.pjointcolor, [], 'Parent', h.pjoint(i));
case 'Ty'
h.pjoint(e.qvar) = hgtransform('Tag', 'prismatic', 'Parent', h.element(i), 'Matrix', diag([1 q(e.qvar) 1 1]));
RTBPlot.box('y', opt.jointdiam*s, [0 1], opt.pjointcolor, [], 'Parent', h.pjoint(i));
case 'Tz'
h.pjoint(e.qvar) = hgtransform('Tag', 'prismatic', 'Parent', h.element(i), 'Matrix', diag([1 1 q(e.qvar) 1]));
RTBPlot.box('z', opt.jointdiam*s, [0 1], opt.pjointcolor, [], 'Parent', h.pjoint(i));
case 'Rx'
RTBPlot.cyl('x', opt.jointdiam*s, opt.jointlen*s*[-1 1], opt.jointcolor, [], 'Parent', h.element(i));
case 'Ry'
RTBPlot.cyl('y', opt.jointdiam*s, opt.jointlen*s*[-1 1], opt.jointcolor, [], 'Parent', h.element(i));
case 'Rz'
RTBPlot.cyl('z', opt.jointdiam*s, opt.jointlen*s*[-1 1], opt.jointcolor, [], 'Parent', h.element(i));
end
else
% it's a constant transform
switch e.what
case 'Tx'
RTBPlot.cyl('x', s, [0 e.param], opt.linkcolor, [], 'Parent', h.element(i));
case 'Ty'
RTBPlot.cyl('y', s, [0 e.param], opt.linkcolor, [], 'Parent', h.element(i));
case 'Tz'
RTBPlot.cyl('z', s, [0 e.param], opt.linkcolor, [], 'Parent', h.element(i));
case 'Rx'
RTBPlot.cyl('x', opt.jointdiam*s, opt.jointlen*s*[-1 1], opt.linkcolor, [], 'Parent', h.element(i));
case 'Ry'
RTBPlot.cyl('y', opt.jointdiam*s, opt.jointlen*s*[-1 1], opt.linkcolor, [], 'Parent', h.element(i));
case 'Rz'
RTBPlot.cyl('z', opt.jointdiam*s, opt.jointlen*s*[-1 1], opt.linkcolor, [], 'Parent', h.element(i));
end
end
assert( ~(opt.jaxes && opt.jvec), 'RTB:ETS3:plot:badopt', 'Can''t specify ''jaxes'' and ''jvec''')
% create the joint axis line
if opt.jaxes
if e.isjoint
line('XData', [0 0], ...
'YData', [0 0], ...
'ZData', 14*s*[-1 1], ...
'LineStyle', ':', 'Parent', h.element(i));
% create the joint axis label
text(0, 0, 14*s, sprintf('q%d', e.qvar), 'Parent', h.element(i))
end
end
% create the joint axis vector
if opt.jvec
if e.isjoint
daspect([1 1 1]);
ha = arrow3([0 0 -12*s], [0 0 15*s], 'c');
set(ha, 'Parent', h.element(i));
% create the joint axis label
text(0, 0, 20*s, sprintf('q%d', e.qvar), 'Parent', h.element(i))
end
end
end
% display the wrist coordinate frame
if opt.wrist
if opt.arrow
% compute arrow3 scale factor...
d = axis(gca);
if length(d) == 4
d = norm( d(3:4)-d(1:2) ) / 72;
else
d = norm( d(4:6)-d(1:3) ) / 72;
end
extra = {'arrow', 'width', 1.5*s/d};
else
extra = {};
end
h.wrist = trplot(eye(3,3), 'labels', upper(opt.wristlabel), ...
'color', 'k', 'length', opt.wristlen*s, extra{:});
else
h.wrist = [];
end
xlabel('X')
ylabel('Y')
zlabel('Z')
grid on
% deal with some display options
if opt.shading
lighting gouraud
light('position', opt.lightpos)
end
% restore hold setting
if ~ish
hold off
end
h.opt = opt;
h.ets = ets;
if nargout > 0
h_ = h;
end
% attach the handle structure to the top graphical element
h.q = q;
handles.opt = opt;
set(group, 'UserData', h);
end
end
end