Time-optimal, constrained, satellite reorientation maneuver using inverse dynamics

Open Access
Nino, Michael
Graduate Program:
Aerospace Engineering
Master of Science
Document Type:
Master Thesis
Date of Defense:
April 01, 2019
Committee Members:
  • Robert Graham Melton, Thesis Advisor
  • Amy Ruth Pritchett, Committee Member
  • Puneet Singla, Committee Member
  • Reorientation
  • Rigidbody Satellite
  • Satellite
  • Optimal Reorientation
  • PSO
  • Particle Swarm Optimization
  • Quaternion
  • Euler Angle
  • Optimal Control
  • Time Optimal Control
  • Michael Nino
  • Mike Nino
  • Melton
  • Dr. Melton
  • Robert G. Melton
  • Aerospace Engineering
Being able to quickly reorient certain satellites, such as orbiting astronomical observatories, is critical to mission objectives. If an event of interest occurs, the goal is to measure that event before it disappears. This can be difficult when the path of reorientation between the sensor and the event is constrained. An electromagnetic (EM) sensor is designed to record EM radiation within certain intensity tolerances. Celestial bodies, such as the Earth, Moon, and Sun, can output EM radiation well above those tolerances depending on the objective of the satellite. This requires that the sensor not only be reoriented from its current pointing to the direction of the event, but also avoid the EM output of those bodies in the range that exceeds the tolerances of the sensor. This leads to an optimal control problem that needs to be solved computationally. For a rigid body satellite with three-axis control capabilities, the use of Euler’s rotation equations can lead to different attitude parameterizations, such as the use of a quaternion representation or Rodrigues parameters, to solve the system of equations. In this thesis, an inverse-dynamics representation is used, which involves parameterizing the attitude of the satellite into three separate orientation angles constituting the 3-2-1 Euler angle sequence. This is converted to a quaternion formulation to achieve compatibility with on board satellite control systems. Genetic algorithms, also called hybrid or heuristic methods, provide a framework for solving optimal control problems quickly. Particle Swarm Optimization (PSO) is a method that invokes a relationship between a particle (a single solution element) and a swarm (a group of solution elements) to search the solution space for an optimal solution. Combining PSO and inverse-dynamics has been shown in previous analyses to be a contender for a way to produce solutions to the reorientation problem efficiently. The method in this analysis determined to be the best contender for producing real-time solutions to this problem involves modeling the orientation angles of the inverse-dynamics problem using 5th order polynomials that exactly meet the end point conditions of the problem. Using a normalized time unit, a relationship between the control profile and the final time can be used to determine a final time that guarantees the constraints associated with the satellite’s design. This allows PSO to address just the maneuver path that avoids the constraint bodies. This implementation was found to consistently produce results that are both closer to optimality and more computationally efficient than those in the literature.