IEEE Robotics & Automation Magazine - September 2017 - 166
tion matrix. To solve the inverse kinematics, we first create an
inverse kinematics solver object:
0.6
ik = robotics.InverseKinematics
('RigidBodyTree', puma1);
0.5
0.4
Next, we define an arbitrary pose for our PUMA robot with
its end-effector pointing downward:
(z )
0.3
0.2
T = trvec2tform([0.4 0.4 0.2]) *
eul2tform([0 0 pi], 'ZYX'),
0.1
0
-0.1
-0.4
-0.2
-0.2
0
0.2
0.4
-0.3
Figure 1. A display of the PUMA 560 robot coordinate frames,
produced by the show method of the RigidBodyTree class.
academic teaching and research. This tutorial is concerned
with the robot manipulator kinematic functionality that
has been available since MATLAB release 2016b.
The Toolbox comes with several robot models, which can
be loaded by
and then solve for the joint angles:
>> [q, info] = ik('L6', T, ones(1,6),
puma1.homeConfiguration);
where the passed arguments are the name of the robot frame
to solve for, the pose of that frame, the weights applied to the
pose error (three components for the orientation error and
three for the position error), and the initial solution. The
return values are the joint angles and the status of the solution. We can display a graphical representation of the PUMA
robot in this configuration by
>> puma1.show(q),
>> load exampleRobots
and includes PUMA 560, KUKA LBR, and Baxter robots,
each represented as a tree of rigid bodies by objects
of the RigidBodyTree class. This class allows general
branched-mechanism representation, such as multiarm robots.
The model puma1 is a standard Denavit-Hartenberg representation of the classical PUMA 560 serial-link manipulator.
The joint angles for the home configuration are given by
>> q = puma1.homeConfiguration;
and the forward kinematics is simply
>> puma1.getTransform(q, 'L6')
ans =
1.0000
0
0
0.4521
0
1.0000
0
-0.1500
0
0
1.0000
0.4318
0
0
0
1.0000,
where we specify by name the frame whose pose we wish to
compute, and the result is a 4 × 4 homogeneous transforma-
166
*
IEEE ROBOTICS & AUTOMATION MAGAZINE
*
SEPTEMBER 2017
and the result is shown in Figure 1, where the individual link
coordinate frames can be clearly seen.
This short tutorial has
barely scratched the surMore detail can be found
face of the capabilities,
which include, f rom
in the extended version
MATLAB release 2017a
and onwards: Universal
of this article, including
Rob otic D es cr iption
Format (URDF) import,
code examples, which
rigid body tree dynamics,
and multiconstraint inaccompanies this
verse kinematics. More
detail can be found in the
tutorial in IEEE Xplore.
extended version of this
article, including code examples, which accompanies this tutorial in IEEE Xplore.
Peter Corke, Queensland University of Technology, Brisbane,
Australia. Acts as a consultant to The MathWorks Inc.
E-mail: peter.corke@qut.edu.au.
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