A student-based university environment for engineering design and development is much different from a product development environment within the aerospace industry. Therefore, a different approach to systems engineering should be considered. By its very nature, a university product development laboratory thrives on creativity and rejects bureaucracy. Experience shows that continuity and discipline within a project is crucial for success. The practice of systems engineering enables technical project discipline. Systems engineering is the art and science of developing an operable system that meets requirements within imposed constraints. The purpose of this thesis is to describe the systems engineering processes and techniques necessary for a student-based project, and explicitly show how to implement these processes. Although attempts have been made to utilize a few systems engineering techniques in past projects, many students did not properly and consistently apply those techniques to the technical design work. The goal of the thesis is to tailor the NASA systems engineering processes to a student-based design laboratory environment and to apply the methodologies to the mission design of Paradox. The Picosatellite for Autonomous Rendezvous and Docking on-Orbit eXperiment, or Paradox, is the second of four missions to demonstrate autonomous rendezvous and docking with a picosatellite-class satellite. A strong technical contribution highlighted within the thesis involves developing an open architecture rendezvous targeting algorithm for the Paradox mission in the face of large mission architecture uncertainties. The robust targeting algorithm builds from previous work utilizing an optimizer based on the Clohessey-Wiltshire equations and an iterative Lambert targeter. The contribution extends the rendezvous transfer times by including a multi-revolution Lambert targeter. The rendezvous algorithm will perform successfully given any launch vehicle and target spacecraft vehicle supporting the notion of an open architecture to satisfy the mission. The development of the algorithm is embedded within the context of the systems engineering processes to clearly showcase the intimate connection between systems engineering processes and the technical engineering design of a mission. / text