Our long term plans call for an accurate, very maneuverable, self-powered ...... In Proceedings of the Inrernatiotial Conference on Robotics. Applications. IEEE ...... s2 = xrnax+ymax, s3 = 2xmax+ymax, s4 = s(xmax+ymax). ...... sun will go nova, or we will be invaded from the stars, or a black hole will swallow the galaxy.
The Mobile Robot Laboratory
Sonar Mapping, Imaging and Navigation
Visual Navigation
Road Following
i
Motion Control
The Robots
Motivation
Publications
Autonomous Mobile Robots Annual Report 1985 Mobile Robot Laboratory
CM U-KI-TK-86-4
Mobile Robot Laboratory The Robotics Institute Carncgie Mcllon University Pittsburgh, Pcnnsylvania 15213 February 1985
Copyright @ 1986 Carnegie-Mellon University
This rcscarch was sponsored by The Office of Naval Research, under Contract Number NO00 14-81-K-0503.
1
Table of Contents The Mobile Robot Laboratory ‘I’owards Autonomous Vchiclcs
-
Moravcc ct 31.
1
Sonar Mapping, Imaging and Navigation High Resolution Maps from Wide Angle Sonar - Moravec, et al. A Sonar-Based Mapping and Navigation System - Elfes Three-Dirncnsional Imaging with Cheap Sonar - Moravec
19 25 31
Visual Navigation Experiments and Thoughts on Visual Navigation - Thorpe et al. Path Relaxation: Path Planning for a Mobile Robot - Thorpe Uncertainty Handling in 3-D Stereo Navigation - Matthies
35 39 43
Road Following First Resu!ts in Robot Road Following - Wallace et al. A Modified Hough Transform for Lines - Wallace Progress in Robot Road Following - Wallace et al.
65 73 77
Motion Control Pulse-Width Modulation Control of Brushless DC Motors - Muir et al. Kinematic Modelling of Wheeled Mobile Robots - Muir et al. Dynamic Trajectories for Mobile Robots - Shin
85 93 111
The Robots The Neptune Mobile Robot - Podnar The Uranus Mobile Robot, a First Look
-
Podnar
123 127
Motivation Robots that Rove
-
Moravec
131
Bibliography 147
ii
Abstract Sincc 13s 1. (lic Mobilc I
where
...,
i=l, n q' : trajectory in generalized frame These dynamic trajectories must satisfy the equation of motion under the constraints (2) and (3).
(5)
115
As an example, we consider a simplified model of a tricycle which moves on a planar surface and is
configured in Fig 2. It goes only forward and has one steered and driven front wheel and two rear idle wheels with same radius.
6
/7
1
Fig. 2.
Simple m o d e l ~ o fa t r i c y c l e
where, X , Ylz are the inertial global coordinates x,y,z are the body coordinateswhich is fixed to the mass center of the robot and translates with velocity Vgand yaws with angular velocity 8, with respect to the inertial coordinate frame. 9, : steering angle of the driven wheel : rolling angle of the driven wheel : torque to steer the wheel : torque to turn the wheel v
3 r'
If we consider the degrees of freedom for the tricycle model, the three coordinates XIY and 8,
constitute a complete set to express the position and the orientation of the robot. The variation dX,dY and de, are not, however, independent, since the requinnent that any translation must be in the heading direction impliesthe constraining relation
.
In other words, there is one nonholonomic constraint. Thus the degrees of freedom of the tricycle model for the planar motion is two, which is known as the minimum degree of freedom for the two dimensional planar motiojn [6], as the conventional steered vehicle has two degrees of freedom.
116
Then, two generalized coordinates and forces for the tricycle model can be taken as
The simple operating region of the tricycle can be represented as 0
'
p ',
Id
9,,max
p ',
'
9-
I'p,I
9&=
And the limit on contrd inputs can be specified as
O s T , s T %lTzl 5 T&The dynamic trajectory with respect to the mass center of the tricycle can be generated in the inertial coordinate frame as
x = fX(0 y = f.4 and these trajectories can be converted into the generalized coordinates as
v,, = 'p,
=
r,co f,
