Page 169 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

144 ACCOUNTING FOR BODY DYNAMICS: THE JOGGER’S PROBLEM

step, in general a path adjustment would be required. We will therefore attempt
to plan only as many steps that immediately follow the current one as is needed
to guarantee nonstop collision-free motion.
The general approach will be as follows: At its current position C i , the robot
will identify a visible intermediate target point, T i , that is guaranteed to lie on
a convergent path and is far enough from the robot—normally at the boundary
of the sensing range. If the direction toward T i differs from the current velocity
vector V i , moving toward T i may require a turn, which may or may not be
possible due to system dynamics.
In the first strategy that we will consider, if the angle between V i and the
direction toward T i is larger than the maximum turn the robot can make in one
step, the robot will attempt a fast smooth maneuver by turning at the maximum
rate until the directions align; hence the name Maximum Turn Strategy.Once a
step is executed, new sensing data appear, a new point T i+1 is sought, and the
process repeats. That is, the actual path and the path that contains points T i will
likely be different paths: With the new sensory data at the next step, the robot
may or may not be passing through point T i .
In the second strategy, at each step, a canonical solution is found which, if no
obstacles are present, would bring the robot from its current position C i to the
intermediate target T i with zero velocity and in minimum time. Hence the name
Minimum Time Strategy. (The minimum time refers of course to the current local
piece of scene.) If the canonical path crosses an obstacle and is thus not feasible, a
near-canonical solution path is found which is collision-free and satisfies the con-
trol constraints. We will see that in this latter case only a small number of options
needs be considered, at least one of which is guaranteed to be collision-free.
The fact that no information is available beyond the sensing range dictates
caution. To guarantee safety, the whole stopping path must not only lie inside
the sensing range, it must also lie in its visible part. No parts of the stopping
path can be occluded by obstacles. Moreover, since the intermediate target T i
is chosen as the farthest point based on the information currently available, the
robot needs a guarantee of stopping at T i , even if it does not intend to do so.
Otherwise, what if an obstacle lurks right beyond the vision range? That is, each
step is to be planned as the first step of a trajectory which, given the current
position, velocity, and control constraints, would bring the robot to a halt at
T i . Within one step, the time to acquire sensory data and to calculate necessary
controls must fit into the step cycle.

4.2 MAXIMUM TURN STRATEGY

4.2.1 The Model
The robot is a point mass,ofmass m. It operates in the plane; the scene may
include a locally finite number of static obstacles. Each obstacle is bounded by
a simple closed curve of arbitrary shape and of finite length, such that a straight
line will cross it in only a finite number of points. Obstacles do not touch each