Chapter 2. Prehension

Chapter 5 - Movement Before Contact 117
Step 1 suggests that the CNS plans movements in hand space, thus
generating a trajectory involving hand positions and speeds along a
path in a body or world coordinate frame. The reason for this is two-
fold. The first has to do with the goal of the task, which is to bring
the hand into contact with the object. If the object is in a world coordi-
nate frame, then planning hand locations in that same coordinate frame
makes the computations easier. The second has to do with the
grasping space of the performer. How can accidental contact with
other objects in the vicinity be avoided, and how can a trajectory be
planned through a cluttered environment? If the objects are in a world
coordinate frame, then planning in the same reference frame is easier.
Transforming this desired trajectory into joint space (step 2) and
generating the motor command (step 3) involves translating from that
coordinate frame into the space within which the actual movement is
being driven. If the control variables are kinematic ones (step 2), this
is an inverse kinematics problem. If the control variables are dynamic
ones (step 3), such as joint torques over time, this is an inverse
dynamic problem.
Such step by step computations, while logical, are inefficient and
most likely, not biological. For one thing, coordinate transformation
computations contain errors, so avoiding re-representations is
advantageous. Alternatively, motor commands can be computed
directly from the desired extrinsically-defined trajectory (step 4) or
even from the goal of the movement (step 5). Another alternative is to
plan directly in joint space (step 1’). While seemingly more
complicated, it is possibly more natural, in the sense that, through
joint and muscle proprioceptors, these are variables that the CNS has
access to. Atkeson & Hollerbach (1985) pointed out that if a trajectory
is determined in an extrinsic coordinate frame (step l), the path of the
hand would follow a straight line (in a world coordinate frame). On
the other hand, if the trajectory generation is computed in joint angles
directly (step l’), the hand would follow a curved path. In behavioral
experiments, both have been observed (see Section 5.3).
5The forward kinematic problem computes endpoint kinematic variables (e.g.,
wrist position) from joint kinematic variables (e.g., shoulder and elbow joint
angles). The inverse kinematic problem computes the shoulder and elbow joint
angles from a given wrist position.