Page 209 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

184 MOTION PLANNING FOR TWO-DIMENSIONAL ARM MANIPULATORS

system. Note that such identification is a local operation that does not require
global information about the environment. (As an example of this ability, recall
that a blindfolded person can easily indicate a point of his body that touches an
object). We do not discuss here specific ways in which this capability can be
realized. For our purposes, assume that the arm body is covered with sensors
such that when one sensor contacts an obstacle, the point of contact on the arm
body is known.
For the third operation, following the obstacle boundary, imagine that while
being in contact with an obstacle, the arm follows the obstacle boundary while
a weak constant force pushes it against the obstacle. (This situation is simi-
lar to a blindfolded person walking around a building while keeping his finger
on the wall.) At any given moment during the motion, there is a variable
point of contact between the obstacle boundary and the arm body. In the algo-
rithm, the arm will plan its next step along the obstacle boundary in such a
way that, after the step has been made, the arm is still in contact with the
obstacle. Again, we will not discuss here how this important capability can
be realized in the physical system. Note that if the arm endpoint follows an
obstacle boundary up to the W-space boundary—for example, the arm is fully
outstretched—it is not clear whether on the boundary the arm is still in con-
tact with the obstacle. To avoid this limit case, we assume that no point of the
W-space boundary may be a point of contact between an obstacle and the arm
endpoint.
Passing around an obstacle is a continuous motion of the arm during which the
arm is in constant contact with some obstacle. Because of the arm and obstacle
interaction, some areas of the W-space not occupied by the actual obstacle may
be inaccessible by the arm endpoint. Such areas create a shadow of the obstacle;
for the arm endpoint, a shadow presents as real an obstacle as points of the actual
obstacle. The actual obstacle and its shadow(s) constitute the virtual obstacle of
a given obstacle. When the arm is passing around an actual obstacle, the arm
endpoint follows the virtual line, which is the boundary of the virtual obstacle.
Below we will study this phenomenon in more detail.

Input Information. Sensing. At the start, the only information available to the
arm are coordinates of its current position S and its target position T .
When moving, the arm obtains its information about the surrounding world
from its sensors. Sensors can be of any type—tactile, proximal, vision, range
sensing, and so on—as long as they provide sufficient input information. As
explained in Section 1.2.3, richer sensing will often result in better efficiency
(for example, shorter paths), but will not guarantee algorithm convergence or
produce better performance bounds. A property of robot sensing that is abso-
lutely necessary for the planning algorithms to operate successfully is that sensing
should encompass the whole robot body; that is, it should allow the robot arm to
detect a potential collision at any point of its body. No blind spots are allowed.
To develop motion planning algorithms, we will first assume whole-body tactile
sensing.