Page 166 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

PROBLEM STATEMENT 141

jogger’s mass and speed to the visible field of view. It is better to slow down at
the corner—who knows what is behind the corner?
Third, when the jogger starts turning the street corner and suddenly sees a pile
of sand right on the path that he contemplated (it was not there last time), some
quick local planning must occur to take care of collision avoidance. The jogger’s
speed may temporarily decrease and the path will smoothly divert from the object.
The jogger will likely want to locally optimize this path segment, in order to come
back to his preplanned path quicker or along a shorter path. Other options not
being feasible, the jogger may choose to “brake” to a halt and start a detour path.
As we see, the jogger’s speed, mass, and quality of vision, as well as the
speed of reaction to sudden changes—which represents the quality of his control
system—are all tied together in a certain relationship, affecting the real-time
decision-making process. The process will go on nonstop, all the time; the jog-
ger cannot afford to take his eyes off the route for more than a fraction of a
second. Sensing, local planning, global planning, and actual movement are in
this process taking place simultaneously and continuously. Locally, unless the
right relationship is maintained between the velocity when noticing an object,
the distance to it, and the jogger’s mass, collision may occur. A bigger mass
may dictate better (farther) sensing to maintain the same velocity. Myopic vision
may require reducing the speed.
Another interesting detail is that in the motion planning strategies considered
in Chapter 3, each step of the path could be decided independently from other
steps. The control scheme that takes into account robot dynamics cannot afford
such luxury anymore. Often a decision will likely affect more than calculation
of the current step. Consider this: Instead of turning on the dime as in our prior
algorithms, the robot will be likely moving along relatively smooth curves. How
do we know that the smooth path curve dictated by robot dynamics at the current
step will not be in conflict with collision considerations at the next step? Perhaps
at the current step we need to think of the next step as well. Or perhaps we need
to think of more than one step ahead. Worse yet, what if a part of that path curve
cannot be checked because it is bending around the corner of a nearby obstacle
and hence is invisible?
These questions suggest that in a planning/control system with included
dynamics a path step cannot be planned separately from at least a few steps
that will follow it. The robot must make sure that the step it now contemplates
will not result in some future steps where the collision is inevitable. How many
steps look-ahead is enough? This is one thing that we need to figure out.
Below we will study the said effects, with the same objective as before—to
design provably correct sensor-based motion planning algorithms. As before, the
presence of uncertainty implies that no global optimality of the path is feasible.
Notice, however, that given the need to plan for a few steps ahead, we can attempt
local optimization. While improving the overall path, sometimes dramatically, in
general a path segment that is optimal within the robot’s field of vision says
nothing about the path global optimality.