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Optimal Control of Nonholonomic Mechanical Systems

  • Author / Creator
    Rogers, Stuart M.
  • This thesis investigates the optimal control of two nonholonomic mechanical systems, Suslov's problem and the rolling ball. Suslov's problem is a nonholonomic variation of the classical rotating free rigid body problem, in which the body angular velocity must always be orthogonal to a prescribed, time-varying body frame vector. The motion of the rigid body in Suslov's problem is actuated via the prescribed body frame vector, while the motion of the rolling ball is actuated via internal point masses that move along rails fixed within the ball. First, by applying Lagrange-d'Alembert's principle with Euler-Poincaré's method, the uncontrolled equations of motion are derived. Then, by applying Pontryagin's minimum principle, the controlled equations of motion are derived, a solution of which obeys the uncontrolled equations of motion, satisfies prescribed initial and final conditions, and minimizes a prescribed performance index. Finally, the controlled equations of motion are solved numerically by a continuation method, starting from an initial solution obtained analytically (in the case of Suslov's problem) or via a direct method (in the case of the rolling ball).

  • Subjects / Keywords
  • Graduation date
    2017-11:Fall 2017
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R30863K4P
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Applied Mathematics
  • Supervisor / co-supervisor and their department(s)
    • Putkaradze, Vakhtang (Department of Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Flynn, Morris R. (Department of Mechanical Engineering)
    • Lewis, James D. (Department of Mathematical and Statistical Sciences)
    • Hillen, Thomas (Department of Mathematical and Statistical Sciences)
    • Venkataramani, Shankar C. (Department of Mathematics - University of Arizona)
    • Lewis, Mark (Department of Mathematical and Statistical Sciences)