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4 is harder than 6:
Inverse kinematics for underactuated robots
Peter Corke
February 2014
Many low-cost hobby class robots, such as shown in Figure 1 have only 4 joints
(degrees of freedom). This document describes how to determine inverse kinematics for
such a robot using the Robotics Toolbox[1] for MATL AB.
Underactuation complicates the process of finding an inverse kinematic solution, and
it frustrates those who are new to robotics — those who just want to run the code and
get an answer. For a robot with 6 joints it’s quite straightforward, but underactuation
requires some careful thought about the problem that you are trying to solve — you
can’t just blindly use the tools.
We will consider the problem in two parts. First the problem of moving the robot
tool to a particular position. Second, moving the tool to a particular position and tool
orientation.
z
t
y
t
x
t
x
0
y
0
z
0
Figure 1: The PhantomX robot sitting on my desk. The world frame {0} and the tool
frame {t} are shown. Note I’m using a book over the back feet to keep it from toppling
over.
1
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