# Algorithms for Steering on the Group of Rotations

### G. Walsh, A. Sarti and S. Shankar Sastry

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/ERL M93/44

1993

The paper focuses on the problem of explicitly generating open loop strategies for steering control systems with left-invariant vector fields on the Lie group of rigid rotations SO(3). Both systems with and without drift are considered as well as systems with three, two or one input(s). For each of these cases, if possible, we present a constructive solution to the steering problem. The most interesting cases are those of systems with drift and either only or two inputs. Having two inputs gives us the freedom to choose the steering time. In the case of only one input our algorithm will drive the system to the desired orientation in a finite time. There are, however, limitations on the choice of the arrival time. Simulations have been developed and the results animated on a Silicon Graphics Iris workstation. In particular, an executable for the Indigo II workstation which demonstrates the algorithms mentioned above is available by an anonymous. ftp.

BibTeX citation:

@techreport{Walsh:M93/44, Author = {Walsh, G. and Sarti, A. and Sastry, S. Shankar}, Title = {Algorithms for Steering on the Group of Rotations}, Institution = {EECS Department, University of California, Berkeley}, Year = {1993}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2360.html}, Number = {UCB/ERL M93/44}, Abstract = {The paper focuses on the problem of explicitly generating open loop strategies for steering control systems with left-invariant vector fields on the Lie group of rigid rotations SO(3). Both systems with and without drift are considered as well as systems with three, two or one input(s). For each of these cases, if possible, we present a constructive solution to the steering problem. The most interesting cases are those of systems with drift and either only or two inputs. Having two inputs gives us the freedom to choose the steering time. In the case of only one input our algorithm will drive the system to the desired orientation in a finite time. There are, however, limitations on the choice of the arrival time. Simulations have been developed and the results animated on a Silicon Graphics Iris workstation. In particular, an executable for the Indigo II workstation which demonstrates the algorithms mentioned above is available by an anonymous. ftp.} }

EndNote citation:

%0 Report %A Walsh, G. %A Sarti, A. %A Sastry, S. Shankar %T Algorithms for Steering on the Group of Rotations %I EECS Department, University of California, Berkeley %D 1993 %@ UCB/ERL M93/44 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2360.html %F Walsh:M93/44