Page 165 - Sensing, Intelligence, Motion : How Robots and Humans Move in an Unstructured World

140 ACCOUNTING FOR BODY DYNAMICS: THE JOGGER’S PROBLEM

that it will behave as a holonomic system. Consequently, they deal solely with
the system kinematics and ignore its dynamic properties. One reason for this
state of affairs is that the methods of motion planning tend to rely on tools from
geometry and topology, which are not easily connected to the tools common to
control theory. Although system dynamics and sensor-based motion control are
clearly tightly coupled in many, if not most, real-world systems, little attention
has been paid to this connection in the literature.
The robot is a body; it has a mass and dimensions. Once it starts moving,
it acquires velocity and acceleration. Its dynamics may now prevent it from
making sharp, and sometimes even relatively shallow, turns prescribed by the
planning algorithm. A sharp turn reasonable from the standpoint of reaching the
target position may not be physically realizable because of the robot’s inertia.
In control theory terminology, this is a nonholonomic system [78]. A classical
example of a nonholonomic control problem is the car parallel parking task:
Because the driver does not have enough control means to execute the parking
in one simple translational motion, he has to wiggle the car back and force to
bring it to the desired position.
Given the insufficient information about the surroundings, which is central to
the sensor-based motion planning paradigm, the lack of control means to execute
any desired motion translates into a safety issue: One needs a guarantee of a
stopping path at any time, in case a sudden obstacle makes it impossible to
continue on the intended path.
Theoretically, there is a simple way out: We can make the robot stop every
time it intends to turn, let it turn, and resume the motion as needed. Not many
applications will like such a stop-and-go motion pattern. For a realistic control we
want the robot to make turns on the move, and not stop unless “absolutely neces-
sary,” whatever this means. That is, in addition to the usual problem of “where to
go” and how to guarantee the algorithm convergence in view of incomplete infor-
mation, the robot’s mass and velocity bring about another component of motion
planning, body dynamics. Furthermore, we will see that it will be important to
incorporate the constraints of robot dynamics into the very motion planning algo-
rithm, together with the constraints dictated by collision avoidance and algorithm
convergence requirements.
We call the problem thus formulated the Jogger’s Problem, because it is not
unlike the task a human jogger faces in an urban setting when going for a morn-
ing run. Taking a run involves continuous on-line control and decision-making.
Many decisions will be made during the run; in fact, many decisions are made
within each second of the run. The decision-making apparatus requires a smooth
collaboration of a few mechanisms. First, a global planning mechanism will work
on ensuring arrival at the target location in spite of all deviations and detours
that the environment may require. Unless a “grand plan” is followed, arrival at
the target location—what we like to call convergence—may not be guaranteed.
Second, since an instantaneous stop is impossible due to the jogger’s iner-
tia, in order to maintain a reasonable speed the jogger needs at any moment
an “insurance” option of a safe stopping path. This mechanism will relate the