Page 187 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

162 ACCOUNTING FOR BODY DYNAMICS: THE JOGGER’S PROBLEM

2. Define a farthest visible intermediate target T i on the obstacle boundary in
the direction of motion; make a step toward T i . Iterate Step 2 until detect
M-line. Go to Step 1.

The actual algorithm will include additional mechanisms, such as a finite-time
target reachability test and local path optimization. In the example shown in
Figure 4.1, note that if the robot walked under a kinematic algorithm, at point
P it would make a sharp turn (recall that the algorithm assumes holonomic
motion). In our case, however, such motion is not possible because of the robot
inertia, and so the actual motion beyond point P would be something closer to
the dotted path.

The Effect of Dynamics. Dynamics affects three algorithmic issues: safety
considerations, step planning, and convergence. Consider those separately.

Safety Considerations. Safety considerations refer to collision-free motion. The
robot is not supposed to hit obstacles. Safety considerations appear in a number
of ways. Since at the robot’s current position no information about the scene
is available beyond the distance r v from it, guaranteeing collision-free motion
means guaranteeing at any moment at least one “last resort” stopping path. Oth-
erwise in the following steps new obstacles may appear in the sensing range, and
collision will be imminent no matter what control is used. This dictates a certain
relationship between the velocity V,mass m,radius r v , and controls u = (p, q).
Under a straight-line motion, the range of safe velocities must satisfy

V ≤ 2pd (4.10)

where d is the distance from the robot to the stop point. That is, if the robot
moves with the maximum velocity, the stop point of the stopping path must be
no further than r v from the current position C. In practice, Eq. (4.10) can be
interpreted in a number of ways. Note that the maximum velocity is proportional
to the acceleration due to control, which is in turn directly proportional to the
force applied and inversely proportional to the robot mass m. For example, if mass
m is made larger and other parameters stay the same, the maximum velocity will
decrease. Conversely, if the limits on (p, q) increase (say, due to more powerful
motors), the maximum velocity will increase as well. Or, an increase in the radius
r v (say, due to better sensors) will allow the robot to increase its maximum
velocity, by the virtue of utilizing more information about the environment.
Consider the example in Figure 4.1. When approaching point P along its path,
the robot will see it at distance r v and will designate it as its next intermediate
target T i . Along this path segment, point T i happens to stay at P because no
further point on the obstacle boundary will be visible until the robot arrives at
P . Though there may be an obstacle right around the corner P , the robot needs
not to slow down since at any point of this segment there is a possibility of a
stopping path ending somewhere around point Q. That is, in order to proceed with