Date of Award


Document Type



Santa Clara : Santa Clara University, 2016.

Degree Name

Master of Science (MS)


Mechanical Engineering

First Advisor

Christopher Kitts


Multirobot systems have characteristics such as high formation re-configurability that allow them to perform dynamic tasks that require real time formation control. These tasks include gradient sensing, object manipulation, and advanced field exploration. In such instances, the Cluster Space Control approach is attractive as it is both intuitive and allows for full degree of freedom control. Cluster Space Control achieves this by redefining a collection of robots as a single geometric entity called a cluster. To implement, it requires knowing the inverse Jacobian of the robotic system for use in the main control loop. Historically, the inverse Jacobian has been computed by hand which is an arduous process. However, a set of frame propagation equations that generate both the inverse position kinematics and inverse Jacobian has recently been developed. These equations have been used to manually compile the inverse Jacobian Matrix. The objective of this thesis was to automate this overall process. To do this, a formal method for representing cluster space implementations using graph theory was developed. This new graphical representation was used to develop an algorithm that computes the new frame propagation equations. This algorithm was then implemented in Matlab and the algorithm and its associated functions were organized into a Matlab toolbox. A collection of several cluster definitions were developed to test the algorithm, and the results were verified by comparing to a derivation based technique. The result is the initial version of a Matlab Toolbox that successfully automates the computation of the inverse Jacobian Matrix for a cluster of robots.