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The mechanics and control of undulatory robotic locomotion


Ostrowski, James Patrick (1996) The mechanics and control of undulatory robotic locomotion. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Y1TF-RF86.


In this dissertation, we examine a formulation of problems of undulatory robotic locomotion within the context of mechanical systems with nonholonomic constraints and symmetries. Using tools from geometric mechanics, we study the underlying structure found in general problems of locomotion. In doing so, we decompose locomotion into two basic components: internal shape changes and net changes in position and orientation. This decomposition has a natural mathematical interpretation in which the relationship between shape changes and locomotion can be described using a connection on a trivial principal fiber bundle.

We begin by reviewing the processes of Lagrangian reduction and reconstruction for unconstrained mechanical systems with Lie group symmetries, and present new formulations of this process which are easily adapted to accommodate external constraints. Additionally, important physical quantities such as the mechanical connection and reduced mass-inertia matrix can be trivially determined using this formulation. The presence of symmetries then allows us to reduce the necessary calculations to simple matrix manipulations.

The addition of constraints significantly complicates the reduction process; however, we show that for invariant constraints, a meaningful connection can be synthesized by defining a generalized momentum representing the momentum of the system in directions allowed by the constraints. We then prove that the generalized momentum and its governing equation possess certain invariances which allows for a reduction process similar to that found in the unconstrained case. The form of the reduced equations highlights the synthesized connection and the matrix quantities used to calculate these equations.

The use of connections naturally leads to methods for testing controllability and aids in developing intuition regarding the generation of various locomotive gaits. We present accessibility and controllability tests based on taking derivatives of the connection, and relate these tests to taking Lie brackets of the input vector fields.

The theory is illustrated using several examples, in particular the examples of the snakeboard and Hirose snake robot. We interpret each of these examples in light of the theory developed in this thesis, and examine the generation of locomotive gaits using sinusoidal inputs and their relationship to the controllability tests based on Lie brackets.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:geometric mechanics; nonlinear control and dynamics; robotic locomotion; snake robots; snakeboard; undulatory locomotion
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:
  • Burdick, Joel Wakeman (chair)
  • Chirikjian, Gregory S.
  • Marsden, Jerrold E.
  • Murray, Richard M.
  • Wiggins, Stephen R.
Defense Date:19 September 1995
Non-Caltech Author Email: jpo (AT),
Record Number:CaltechETD:etd-10202005-153514
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4194
Deposited By: Imported from ETD-db
Deposited On:21 Oct 2005
Last Modified:21 Dec 2019 04:25

Thesis Files

PDF (Ostrowski_jp_1996.pdf) - Final Version
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