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Hanspeter Schaub

This specialization studies spacecraft relative orbits. This is of interest to mission scenarios including rendezvous and docking, inspection circumnavigation trajectories, on orbit assembly, space debris mitigation, or interferometric science applications in space. It assumes the learner has already had a complete course on orbital mechanics of a single spacecraft including solutions to the 2-body problem, solving time of flight problems, and understanding J2-perturbations on a spacecraft, as well as how to develop relative orbit feedback control solutions. The specialization is of interest to researchers who need to learn the fundamentals of deriving relative equations of motion about circular, elliptical or even hyperbolic reference orbits. Both nonlinear and linearized relative orbit descriptions are explored and compared, including curvilinear Cartesian coordinates and orbit element differences. Analytical relative motion solutions are developed to understand fundamental relative motion prototypes. Next, the impact of the J2 perturbation is explored for the relative motion, including how to develop J2-invariant relative orbits. Finally, nonlinear relative motion feedback control laws are developed to actively control the relative motion. The specialization targets learners interested in rendezvous and docking, orbital servicing, or developing relative orbit missions.

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What's inside

Three courses

Spacecraft Relative Motion Kinematics and Kinetics

(0 hours)
Spacecraft relative motion control has many applications, including rendezvous and docking, circumnavigation, on orbit assembly, servicing, etc. This course covers the fundamentals of describing the motion of one spacecraft as seen by another spacecraft.

Spacecraft Relative Motion Control

(0 hours)
Spacecraft relative motion control solutions stabilize the spacecraft relative to another spacecraft. This is useful to control the approach prior to docking, to circumnavigate while inspecting the target object, or to remain in a bounded vicinity about the target. This course covers the basics of nonlinear control theory to apply Lyapunov's direct method to the relative motion control problem.

Spacecraft Formation Flying and Control Capstone Project

(0 hours)
This capstone design challenge involves developing, simulating, and studying how to approach a tumbling debris object. The servicer starts from far away and carefully maneuvers closer while accounting for relative attitude motion. The final approach is in a debris body-fixed manner, illustrating non-Keplerian motion control.

Learning objectives

  • Describe relative orbits using a range of coordinates
  • Describe the impact of orbit perturbations on the relative orbit geometry
  • Design relative formations that exploit orbital perturbations
  • Develop feedback control laws to stabilize desired relative orbits

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