General Stiffness Model for Programmable Matter and Modular Robot Structures

We developed a stiffness model for programmable matter and modular robot structures. In the model, modules or module components are linked by 6 degree-of-freedom stiffness matrices. We demonstrated that the stiffness matrix can be determined by approximation, analysis, or experiment. In the case of folded chain programmable matter (left two figures), we show that the folding patterned can be used to change the apparent elasticity of the structure. In the case of CKBot modular robot structures (right two figures), we are able to fit and predict experimental displacement under a static load.


External Actuation for Modular Robotics

Right Angle Tetrahedron Chain Externally Actuated Testbed (RATChET) System

Modules in the Right Angle Tetrahedron Chain Externally Actuated Testbed (RATChET) system can be programmed to form arbitrary shapes. Using an external manipulator to fold the chain under the force of gravity simplifies the module design since they do not require a motor at each joint. We developed two RATChET systems: a first generation (left three photos) capable of assembling various shapes from a single chain using external energy and a second miniaturized generation that uses external energy to both assemble and disassemble shapes.


Simulation Videos


XBot System

The XBot system is a lattice style modular self-reconfigurable robot that uses external actuation to deterministically reconfigure XBot modules. Using the principle of external actuation facilitates module miniaturization as modules do not require motors or servos to reconfigure. One module is fixed to a movable table. When the table accelerates in a predetermined motion profile, inertial forces cause the desired module or group of modules to relocate. We have demonstrated this method can realize reliable, deterministic self-reconfiguration.

XY Stage Videos

X Stage Videos

Simulation Videos


Stochastic Modular Robotics


I worked on this project at the Cornell Computational Synthesis Lab with Victor Zykov, Josh Bongard and Hod Lipson. Stochastic modular robotic systems provide an alternative to more traditional deterministic self-reconfigurable systems. Rather than executing a determined motion plan, these systems consist of modules that move about randomly due to the energy of environment (in this case, cubes floating in agitated oil.) Modules attach to the substrate and each other using a switchable bonding mechanism. Modules use an onboard rule set and make decisions (maintain or break bond) to form a desired structure.

The goal of this project is to demonstrate a method that can be used to develop a large number of modules at scales that are orders of magnitude smaller. This method of reconfiguration is beneficial in that modules are not required to have a locomotion mechanism. Distributed power eliminates the need for batteries in each module.

For more information, see the project page.


This work is a precursor to the 3D Stochastic Modular Robotic system. I worked on this project with Kris Kopanski and Hod Lipson. We developed proof of concept systems that demonstrate that modules moving randomly in a simulated Brownian environment can form desired configurations.

For more information, see the project page.

Kinematics Simulator

Developed a Java applet based kinematic simulator for the Kinematic Models For Design Digital Library, KMODDL, a site with numerous models and multimedia to aid in the teaching of kinematics. There are numerous interactive simulations of classic kinematic mechanisms such as the Peaucellier Straight Line Mechanism