Multimedia  

 

Volume 26 Issue 10 - Publication Date: 1 September 2007
 
Towards a Unified Approach to Motion Planning for Dynamic
Underactuated Mechanical Systems with Non-holonomic Constraints
 
E. A. Shammas, H. Choset, and A. 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.
 
Multimedia Key
= Video = Data = Code = Image
 
Extension
Type
Description
1
Example 1:Video showing the actual motion of the variable inertia snakeboard while performing the purely dynamic gait, PDVS 1 . The frames are chosen to depict one complete gait where is the gait’s period. (1.5 MB) wmv
2
Example 2: Video Showing the actual motion of the variable inertia snakeboard while performing the purely dynamic gait, PDVS 2 . The frames are chosen to depict one complete gait where is the gait’s period.(1.5 MB) wmv
3
Example 3: Video Showing the actual motion of the variable inertia snakeboard while performing the kino-dynamic gait, KDVS 3 . The frames are chosen to depict one complete gait where is the gait’s period. (1.5 MB) avi
 
Return to Contents