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The International Journal of Robotics Research
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Towards a Unified Approach to Motion Planning for Dynamic Underactuated Mechanical Systems with Non-holonomic Constraints

Elie A. Shammas

The Robotics Institute, Carnegie Mellon University 5000 Forbes Avenue, Pittsburgh, PA 15213, USA

Howie Choset

The Robotics Institute, Carnegie Mellon University 5000 Forbes Avenue, Pittsburgh, PA 15213, USA, choset{at}ri.cmu.edu

Alfred A. Rizzi

The Robotics Institute, Carnegie Mellon University 5000 Forbes Avenue, Pittsburgh, PA 15213, USA

In this paper, we generalize our prior results in motion analysis to design gaits for a more general family of underactuated mechanical systems. In particular, we analyze and generate gaits for mixed mechanical systems which are systems whose motion is simultaneously governed by both a set of non-holonomic velocity constraints and a notion of a generalized momentum being instantaneously conserved along allowable directions of motion. Through proper recourse to geometric mechanics, we are able to show that the resulting motion from a gait has two portions: a geometric and a dynamic contribution. The main challenge in motion planning for a mixed system is understanding how to separate the geometric and dynamic contributions of motion due to a general gait, thus simplifying gait analysis. In this paper, we take the first step towards addressing this challenge in a generalized framework. Finally, we verify the generality of our approach by applying our techniques to novel mechanical systems which we introduce in this paper as well as by verifying that seemingly different prior motion planning results could actually be explained using the gait analysis presented in this paper.

Key Words: gait generation • motion control • underactuated robots • non-holonomic motion planning • mixed mechanical systems • generalized momentum • scaled momentum • variable inertia snakeboard • Stokes' theorem

The International Journal of Robotics Research, Vol. 26, No. 10, 1075-1124 (2007)
DOI: 10.1177/0278364907082098
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R. Balasubramanian, A. A. Rizzi, and M. T. Mason
Legless Locomotion: A Novel Locomotion Technique for Legged Robots
The International Journal of Robotics Research, May 1, 2008; 27(5): 575 - 594.
[Abstract] [PDF]