A state space is defined that considers the configurations of all
robots simultaneously,
|
(7.6) |
A state specifies all robot configurations and may be
expressed as
. The dimension of is
, which is
.
There are two sources of obstacle regions in the state space: 1) robot-obstacle collisions, and 2) robot-robot collisions. For
each such that
, the subset of that
corresponds to robot
in collision with the obstacle region,
, is
|
(7.7) |
This only models the robot-obstacle collisions.
For each pair,
and
, of robots, the subset of that
corresponds to
in collision with
is
|
(7.8) |
Both (7.7) and (7.8) will be
combined in (7.10) later to yield .
Formulation 7..2 (Multiple-Robot Motion Planning)
- The world and obstacle region are the
same as in Formulation 4.1.
- There are robots,
, ,
, each of
which may consist of one or more bodies.
- Each robot
, for from to , has an associated
configuration space,
.
- The state space is defined as the Cartesian product
|
(7.9) |
The obstacle region in is
|
(7.10) |
in which and
are the robot-obstacle and
robot-robot collision states from (7.7) and
(7.8), respectively.
- A state
is designated as the initial
state, in which
. For each
such that
, specifies the initial
configuration of
.
- A state
is designated as the goal
state, in which
.
- The task is to compute a continuous path
such that
and
.
Subsections
Steven M LaValle
2020-08-14