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[资源] [F]Robot Motion Planning and Control.Springer.1998

Robot Motion Planning and Control
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Authors(Editors):
J.-P. Laumond
Publisher: Springer
Pub Date: 1998
Pages: 354
ISBN: 9783540762195

Foreword
How can a robot decide what motions to perform in order to achieve tasks in
the physical world ?
The existing industrial robot programming systems still have very limited
motion planning capabilities. Moreover the field of robotics is growing: space
exploration, undersea work, intervention in hazardous environments, servicing
robotics ... Motion planning appears as one of the components for the necessary
autonomy of the robots in such real contexts. It is also a fundamental issue
in robot simulation software to help work cell designers to determine collision
free paths for robots performing specific tasks.
Robot Motion Planning and Control requires interdisciplinarity
The research in robot motion planning can be traced back to the late 60's,
during the early stages of the development of computer-controlled robots. Nevertheless,
most of the effort is more recent and has been conducted during the
80's (Robot Motion Planning, J.C. Latombe's book constitutes the reference in
the domain).
The position (configuration) of a robot is normally described by a number
of variables. For mobile robots these typically are the position and orientation
of the robot (i.e. 3 variables in the plane). For articulated robots (robot arms)
these variables are the positions of the different joints of the robot arm. A
motion for a robot can, hence, be considered as a path in the configuration
space. Such a path should remain in the subspace of configurations in which
there is no collision between the robot and the obstacles, the so-called free
space. The motion planning problem asks for determining such a path through
the free space in an efficient way.
Motion planning can be split into two classes. When all degrees of freedom
can be changed independently (like in a fully actuated arm) we talk about
hotonomic motion planning. In this case, the existence of a collision-free path
is characterized by the existence of a connected component in the free configuration
space. In this context, motion planning consists in building the free
configuration space, and in finding a path in its connected components.
Within the 80's, Roboticians addressed the problem by devising a variety
of heuristics and approximate methods. Such methods decompose the configuration
space into simple cells lying inside, partially inside or outside the free
space. A collision-free path is then searched by exploring the adjacency graph
of free cells.
In the early 80's, pioneering works showed how to describe the free configuration
space by algebraic equalities and inequalities with integer coefficients
(i.e. as being a semi-algebraic set). Due to the properties of the semi-algebraic
sets induced by the Tarski-Seidenberg Theorem, the connectivity of the free
configuration space can be described in a combinatorial way. From there, the
road towards methods based on Real Algebraic Geometry was open. At the
same time, Computational Geometry has been concerned with combinatorial
bounds and complexity issues. It provided various exact and efficient methods
for specific robot systems, taking into account practical constraints (like
environment changes).
More recently, with the 90's, a new instance of the motion planning problem
has been considered: planning motions in the presence of kinematic constraints
(and always amidst obstacles). When the degrees of freedom of a robot system
are not independent (like e.g. a car that cannot rotate around its axis
without also changing its position) we talk about nonholonomic motion planning.
In this case, any path in the free configuration space does not necessarily
correspond to a feasible one. Nonholonomic motion planning turns out to be
much more difficult than holonomic motion planning. This is a fundamental
issue for most types of mobile robots. This issue attracted the interest of an
increasing number of research groups. The first results have pointed out the
necessity of introducing a Differential Geometric Control Theory framework in
nonholonomic motion planning.
On the other hand, at the motion execution level, nonholonomy raises another
difficulty: the existence of stabilizing smooth feedback is no more guaranteed
for nonholonomic systems. Tracking of a given reference trajectory computed
at the planning level and reaching a goal with accuracy require nonstandard
feedback techniques.
Four main disciplines are then involved in motion planning and control.
However they have been developed along quite different directions with only
little interaction. The coherence and the originality that make motion planning
and control a so exciting research area come from its interdisciplinarity.
It is necessary to take advantage from a common knowledge of the different
theoretical issues in order to extend the state of the art in the domain.

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