Latash and Gottlieb, 1991).
3.2 Implementation of motor production
strategies
We implemented 14 motor production algorithms.
These included trajectories planned kinematically in
Cartesian world space and joint angle space, dy-
namically simulated virtual trajectories, dynamics
based optimization and hybrid kinematic∕dynamic
methods. The models were either based on or in-
spired by existing motor production theories, and
were intended to generate motions in the form
of joint angle trajectories given specific Carte-
sian hand-point targets and a fixed duration for
the motion. We based our algorithms on a 30
DOF humanoid corresponding to a robot called DB
(Atkeson et al., 2000). A sequence of more than two
target points is unconstrained regarding the pas-
sage time of any internal target points, and the
target points may also be cyclic in which case the
passage times of all but the first target (which is
also the last target) are unconstrained. Four mod-
els, minimum velocity (MV), acceleration (MA), jerk
(MJ) and snap (MS) were based on extrinsic kine-
matic trajectory planning in Cartesian space. The
3D space-line trajectory of the hand was calcu-
lated using a three dimensional piecewise polyno-
mial spline. The coefficients were calculated using
a general derivative minimization strategy of arbi-
trary dimensionality (Hale and Pollick, 2002). The
hand coordinates were then used to derive pos-
tures using the extended Jacobian inverse kinemat-
ics method (Tevatia and Schaal, 2000). Four mod-
els, minimum angular velocity (MAV), angular ac-
celeration (MAA), angular jerk (MAJ) and angu-
lar snap (MAS) were based on intrinsic kinematic
trajectory planning in joint angle space. The joint
angles were represented by 30 dimension piecewise
polynomial splines. The coefficients were calculated
using the same algorithm as above. A minimum
jerk virtual trajectory model (MJVT) was imple-
mented using the MAJ trajectory as a virtual tra-
jectory guiding a dynamic simulation of a 30 DOF
humanoid using spring-dampers acting at each joint.
One model was based on the equilibrium point hy-
pothesis (EPH), and was implemented by calculating
target postures satisfying each hand positioning tar-
get, and then calculating lambda parameters for each
joint by inverting the exponential lambda force equa-
tion. Postures throughout the motion were then gen-
erated by dynamically simulating the motion, and
calculating joint forces using the exponential force
equation with lambda parameters linearly interpo-
lated between the postures. Two models based on
dynamic optimization, minimum torque (MT) and
minimum torque change (MTC) were implemented
using a time consuming gradient descent algorithm.
A minimum jerk trajectory was used as a starting
point for the optimization since minimum jerk is ex-
pected to approximate minimum torque change. Fi-
nally, two algorithms were designed with both opti-
mal dynamics and computational efficiency in mind,
the minimum torque postures (MTP) and minimum
torque postures virtual trajectory (MTPVT). The
MTP model calculated postures satisfying each hand
positioning target with a minimal torque require-
ment to maintain the posture statically and mini-
mum torque change between successive postures. A
minimum angular jerk trajectory through these pos-
tures yielded the final motion. The MTPVT algo-
rithm extended MTP by using the MTP motion as
a virtual trajectory guiding a dynamically simulated
humanoid using spring-dampers and each joint.
3.3 Human motion capture
In addition to implementing synthetic motion pro-
duction models, genuine human motion data was also
recorded. The motion of a human subject was cap-
tured using three Optotrak camera arrays and a total
of 22 strobing infrared markers distributed over the
upper half of the body. The subject was instructed
not to move their feet. Motions were specified using
physical reaching targets and obstacles. The subject
was instructed to perform motions slowly or quickly
and each motion was repeated five times to ensure
good quality capture data was obtained. The marker
locations were logged by the Optotrak system, and
the position of the markers on the body was recorded
in a fixed posture with the arms by the sides. It was
then possible to locate the markers on a synthetic
humanoid of similar kinematic dimensions, and de-
rive joint angles from marker positions using a least-
squares Gaussian optimization algorithm.
3.f. Generation of movement stimuli
Animation clips were generated using the 14 syn-
thetic models and the motion captured human move-
ments (a total of 15 motion models). Two different
motions ((a) & (b)) were performed yielding a total
of 30 clips. The two motion specifications were de-
signed to represent via-point trajectories with fixed
start and end points, and an intermediate passage
point. The motions were slow and fast, performed
in 4.4s and 0.5s. A brief period was included at the
start and end of the clip to facilitate perception of
the onset and termination of motion so that the clip
durations were 5s and 1.5s. The motions were pre-
pared offline and stored as posture (complete joint-
angle) samples taken at 70Hz. Clips showing a com-
puter generated synthetic humanoid were generated
by converting the motion logs to BVH format and
importing the motions into MetaCreation’s Poser