Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

A Multi-Steering Trailer System: Conversion into Chained Form Using Dynamic Feedback

D. Tilbury, O. Sordalen, L. Bushnell and S. Shankar Sastry

EECS Department
University of California, Berkeley
Technical Report No. UCB/ERL M93/55
1993

In this paper, we examine in detail the kinematic model of an autonomous mobile robot system consisting of a chain of steerable cars and passive trailers, connected together with rigid bars. We define the state space and kinematic equations of the system, modeling the pair of wheels on each axle as able to roll but not slip. we then investigate how this system of kinematic equations may be converted into multi-input chained form. The advantages of the chained form are that many methods are available for the open-loop steering of such systems as well as for point-stabilization. In order to convert the system to this multi-input chained form, we use dynamic state feedback. We draw some motivation from the very simple example of a kinematic unicycle and the relationships of the angular velocities therein, and we show how the dynamic state feedback that we use corresponds to adding, in front of the steerable cars, a chain of virtual axles which diverges from the original chain of trailers. We briefly discuss how some of the methods which have been proposed for steering and stabilizing two-input chained form systems can be generalized to multi-chained systems. for concreteness, we also present two different example systems: a fire truck (three axles) and a five-axle, two-steering system. Simulation results for a parallel-parking maneuver for the five-axle system are included in the form of margin movies.


BibTeX citation:

@techreport{Tilbury:M93/55,
    Author = {Tilbury, D. and Sordalen, O. and Bushnell, L. and Sastry, S. Shankar},
    Title = {A Multi-Steering Trailer System: Conversion into Chained Form Using Dynamic Feedback},
    Institution = {EECS Department, University of California, Berkeley},
    Year = {1993},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2390.html},
    Number = {UCB/ERL M93/55},
    Abstract = {In this paper, we examine in detail the kinematic model of an autonomous mobile robot system consisting of a chain of steerable cars and passive trailers, connected together with rigid bars.  We define the state space and kinematic equations of the system, modeling the pair of wheels on each axle as able to roll but not slip.  we then investigate how this system of kinematic equations may be converted into multi-input chained form.  The advantages of the chained form are that many methods are available for the open-loop steering of such systems as well as for point-stabilization.  In order to convert the system to this multi-input chained form, we use dynamic state feedback.  We draw some motivation from the very simple example of a kinematic unicycle and the relationships of the angular velocities therein, and we show how the dynamic state feedback that we use corresponds to adding, in front of the steerable cars, a chain of virtual axles which diverges from the original chain of trailers.  We briefly discuss how some of the methods which have been proposed for steering and stabilizing two-input chained form systems can be generalized to multi-chained systems.  for concreteness, we also present two different example systems:  a fire truck (three axles) and a five-axle, two-steering system.  Simulation results for a parallel-parking maneuver for the five-axle system are included in the form of margin movies.}
}

EndNote citation:

%0 Report
%A Tilbury, D.
%A Sordalen, O.
%A Bushnell, L.
%A Sastry, S. Shankar
%T A Multi-Steering Trailer System: Conversion into Chained Form Using Dynamic Feedback
%I EECS Department, University of California, Berkeley
%D 1993
%@ UCB/ERL M93/55
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/1993/2390.html
%F Tilbury:M93/55