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Dynamic Modeling and Control of Spherical Robots


Burkhardt, Matthew Ryan (2018) Dynamic Modeling and Control of Spherical Robots. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/E5CW-8H41.


In this work, a rigorous framework is developed for the modeling and control of spherical robotic vehicles. Motivation for this work stems from the development of Moball, which is a self-propelled sensor platform that harvests kinetic energy from local wind fields. To study Moball's dynamics, the processes of Lagrangian reduction and reconstruction are extended to robotic systems with symmetry-breaking potential energies, in order to simplify the resulting dynamic equations and expose mathematical structures that play an important role in subsequent control-theoretic tasks. These results apply to robotic systems beyond spherical robots. A formulaic procedure is introduced to derive the reduced equations of motion of most spherical robots from inspection of the Lagrangian. This adaptable procedure is applied to a diverse set of robotic systems, including multirotor aerial vehicles.

Small time local controllability (STLC) results are derived for barycentric spherical robots (BSR), which are spherical vehicles whose locomotion depends on actuating the vehicle's center of mass (COM) location. STLC theorems are introduced for an arbitrary BSR on flat, sloped, or smooth terrain. I show that STLC depends on the surjectivity of a simple steering matrix. An STLC theorem is also derived for a class of commonly encountered multirotor vehicles.

Feedback linearizing and PID controllers are proposed to stabilize an arbitrary spherical robot to a desired trajectory over smooth terrain, and direct collocation is used to develop a feedforward controller for Moball specifically. Moball's COM is manipulated by a novel system of magnets and solenoids, which are actuated by a "ballistic-impulse" controller that is also presented. Lastly, a motion planner is developed for energy-harvesting vehicles. This planner charts a path over smooth terrain while balancing the desire to achieve scientific objectives, avoid hazards, and the imperative of exposing the vehicle to environmental sources of energy such as local wind fields and topology. Moball's design details and experimental results establishing Moball's energy-harvesting performance (7W while rolling at a speed of 2 m/s), are contained in an Appendix.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Nonholonomic mechanics, advected parameters, geometric mechanics.
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Burdick, Joel Wakeman
Thesis Committee:
  • Murray, Richard M. (chair)
  • Ames, Aaron D.
  • Chung, Soon-Jo
  • Backes, Paul G.
  • Burdick, Joel Wakeman
Defense Date:7 May 2018
Funding AgencyGrant Number
NASA Space Technology Research FellowshipNNX15AP54H
Record Number:CaltechTHESIS:05302018-110559204
Persistent URL:
Related URLs:
URLURL TypeDescription reduction and reconstruction as applied to spherical robots, included in Chapter 3. analysis of three-dimensional Moball with preliminary control experiments, forming part of the Appendix. of Moball's electromechanical subsystem, included in the Appendix. simulations of Moball's energy-harvesting mechanism, forming part of the Appendix.
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:10973
Deposited By: Matthew Burkhardt
Deposited On:01 Jun 2018 18:18
Last Modified:04 Oct 2019 00:21

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