Autonomous formation flight concepts and algorithms have great potential to revolutionize spacecraft operations enabling missions to perform autonomous docking, in-space refueling, in-space robotic assembly, and space debris removal. Such tasks require the implementation of speed and path control algorithms to maneuver satellites along relative paths with specified rates along those paths. This thesis uses MATLAB® and SIMULINK® to design and simulate a control algorithm capable of providing relative speed and path control between satellites with a pointing error of less than two degrees, a position error of less than two millimeters, and a millimeter per second of velocity error. The enclosed research provides enhancements to Massachusetts Institute of Technology\u27s SPHERES (Synchronized Position Hold Engage Reorient Experimental Satellites) program, a testbed for multi-object rendezvous and docking research. This control algorithm is to be used on-board the International Space Station to allow MIT\u27s SPHERES program to continue to provide a practical intermediate step to develop, test, and validate autonomous formation spaceflight algorithms. Furthermore, the simulation tool used to develop the control algorithm allows a greater community of control engineers to interact with SPHERES purely in the MATLAB® development environment
