Chapter 2. Prehension

274 THE PHASES OF PREHENSION
shape of each ellipsoid reflecting the relative force requirement or
motion requirement of the task. A grasp is stable if for every object
wrench, there is a choice of joint torques to balance it, and a grasp is
manipulable if, for every object motion, there exists a choice of joint
velocities that will accommodate that motion without breaking contact.
A grasp is assigned a twist space quality measure, which is the ratio
between the task ellipsoid and the finger joint velocities, and a wrench
space quality measure, which is the ratio between the task ellipsoid
and the joint torques. A grasp is ‘good’, with respect to a given task,
if it has a higher quality measure than other grasps (e.g., precision
tasks need grasps with a high quality measure in the twist space).
Finding a good grasp, then, is solved as an optimization problem.
Once the grasp is found then given a goal, such as moving an object
along a specified trajectory, Li and Sastry formulate a control
algorithm for realizing the trajectory without breaking contact while
regulating the internal forces.
Fearing (1990) discussed how Kobayashi (1985) used a force
control system to control local object motions with fingers in constant
grasping locations. When objects need to be regrasped, for example
in twirling a baton, roboticists have accomplished this through
preprogrammed finger position commands (Okada, 1982) or using a
sequence of applied forces at each finger (Fearing, 1986). To ensure
robust manipulation, tactile sensing and perception are needed to
provide information on contact forces and local shape properties.
Tactile sensors can provide local shape information, including contact
location on the finger, surface normals, principal curvatures and their
direction. From this information, global object properties such as
size, location and orientation are inferred. Fearing (1990, p. 236)
notes that “the reorientation sub-system would command finger force,
stiffness and position. High speed tactile or force sensing can monitor
the grasping operation for unexpected forces, contact slip, and loss of
contact. The reorientation planner may also continuously monitor
object position during reorientation, and develop error recovery
strategies if unexpected object loads are encountered”. He notes that
there are complicated compliance, friction, rolling and slipping effects
that can occur at finger-object interfaces.
Rather than relying on sensors, Mason (1985) discussed how
humans take advantage of task mechanics. In effect, control places us
in the ballpark of the desired locations, forces, torques, motions; then,
we use the intrinsic mechanics of the task environment as a funnel to
eliminate uncertainties about the locations and shapes of objects (like
funneling sand, where the funnel reduces uncertainty in the location of