Movement Control Methods for Complex Dynamically Simulated Agents Adonis Dances the Macarena
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Movement Control Methods
for Complex, Dynamically Simulated Agents:
Adonis Dances the Macarena
Maja J. Matari
c Victor B. Zordan Zachary Mason
Computer Science Department College of Computing Computer Science Department
University of Southern California Georgia Institute of Technology Brandeis University
Los Angeles, CA 90089-0781 Atlanta, GA 30332-0280 Waltham, MA 02254-9110
tel: (213) 740-4520 tel: (404) 894-4998 tel: (781) 736-2719
mataric@cs.usc.edu victor@cc.gatech.edu zmason@cs.brandeis.edu
Abstract area in realistic, physically-based animation, where
the control of dynamic simulations of human charac-
We describe and compare two implemented controllers ters, involving realistic physical models, matches the
for Adonis, a physically simulated humanoid torso, complexity of the robotics problem (Pai 1990, Hod-
one based on joint-space torques and the other on gins, Wooten, Brogan & O'Brien 1995, Van de Panne
convergent force-elds applied to the hands. The two & Lamouret 1995).
come from dierent application domains: the former We introduce a novel approach to manipulator
is a common approach in manipulator robotics and control, based on models from neuroscience which
graphics, while the latter is inspired by biological limb employ convergent force-elds at the end-points of
control. Both avoid explicit inverse kinematic calcu- a manipulator. We explore the feasibility of such a
lations found in standard Cartesian control, trading model for complex animation and agent control in
generality of motion for programming eciency. The general, and discuss how it can be generalized to
two approaches are compared on a common sequen- high-level motor tasks and incorporated into a gen-
tial task, the familiar dance \Macarena" and evalu- eral control framework. Furthermore, we compare
ated based on ease of generating new behaviors, exi- the methodology to a standard robotics approach,
bility, and naturalness of movement we also compare which has also been adopted in animation, employ-
them against human performance on the same task. ing joint-space control with torque actuators. Both
Finally, we discuss the tradeos and present a more approaches are appealing because they avoid explicit
general framework for addressing complex motor con- computation of inverse kinematics (IK) found in stan-
trol of simulated agents. dard Cartesian control. The inputs of each controller
are used explicitly, as either positions or orientations,
1 Introduction without IK solvers converting the input data. How-
ever, this presents a tradeo between generality of
Control of humanoid agents, dynamically simulated motion and programming eciency. To compare the
or physical, is an extremely dicult problem due to two approaches, we implemented them on a common
the high dimensionality of the control space, i.e., the motor task: a continuous sequence of smooth move-
many degrees of freedom and the redundancy of the ments. For the purpose of evaluation, a well known,
system. In robotics, standard methods have been de- goal-driven sequence was chosen, the popular dance
veloped for simpler manipulators and have been grad- \Macarena." The dance presents a non-trivial, well-
ually scaled up to more complex arms (Paul 1981, dened task that can be precisely specied and eval-
Brady, Hollerbach, Johnson, Lozano-Perez & Mason uated, both relative to the quantitative specication
1982) and recently to physical human-like arms (Schaal and to qualitative human performance.
1997, Williamson 1996). The problem of anthropo-
morphic control has also found a new application 2 Background
2.1 Control in Robotics and Computer Animation
Computer animation and robotics are two primary
areas of research into motion for articial agents. 3D
animated character motion has traditionally been cre-ated by hand, through a time-consuming process. Re- Our work is inspired by a specic principle derived
cently, physical modeling has been used to generate from evidence in neuroscience. Mussa-Ivaldi & Giszter
motion by minimizing user-specied constraints while (1992), Giszter, Mussa-Ivaldi & Bizzi (1993) and re-
allowing the model constraints to add physical real- lated work on spinalized frogs and rats suggest the ex-
ism. Witkin & Kass (1988) pursue physical modeling istence of force-eld motor primitives that converge
through such a constraint-based approach by choos- to single equilibrium points and produce high-level
ing start and end conditions, they generate anticipa- behaviors such as reaching and wiping. When a par-
tion and determination in the action. Cohen (1992) ticular eld is activated, the frog's leg executes a be-
extended this approach with higher DOF systems and havior and comes to rest at a position that corre-
more complex constraints. Ngo & Marks (1993) in- sponds to the equilibrium point when two or more
troduce a constraint approach of creating behaviors elds are activated, either a linear superposition of
automatically using genetic algorithms. the elds (87% of tested cases), or a \winner-take-all"
Dynamic simulation has been used to generate response (58% of remaining cases) results (Mussa-
graphical motion by applying dynamics to physically- Ivaldi, Giszter & Bizzi 1994). This suggests an el-
based models and using forward integration. Simu- egant organizational principle for motor control, in
lation ensures physically plausible motion by enforc- which entire behaviors are coded with low-level force-
ing the laws of physics. Pai (1990) simulates walk- elds, and may be combined into higher-level, more
ing gaits, drawing strongly from robotics work. His complex behaviors. The idea of supplying an agent
torso and legs use a controller based on high-level with a collection of basis behaviors or primitives rep-
time-varying constraints. Hand-tuned control of sim- resenting force-elds, and combining those into a gen-
ulations has been applied successfully to more com- eral repertoire for complex motion, is very appealing.
plex systems such as full articulated human gures. Our previous work (Mataric 1995, Mataric 1997), in-
Raibert & Hodgins (1991) demonstrate rigid body spired by the same biological results, has already suc-
dynamic simulations of legged creatures. Their hand- cessfully applied the idea of basis behaviors to control
tuned controllers consist of state machines that cy- of planar mobile agents/robots. This paper extends
cle through rule-based constraints to perform dier- the notion to agents with more DOFs.
ent gaits. Hodgins et al. (1995) extend this work Another inspiration comes from psychophysical data
to human characters, suggesting a toolbox of tech- describing what people xate on when observing hu-
niques for controlling articulated human-like systems man movement. Mataric & Pomplun (1997) demon-
to generate athletic behaviors such as 3D running, strate that when presented with videos of human n-
diving, and bicycling. Van de Panne & Lamouret ger, hand, and arm movements, observers focus on
(1995) use search techniques to nd balancing con- the hand, yet when asked to imitate the movements,
trollers for human-like character locomotion, aiming subjects are able to reconstruct complete trajecto-
at more automatic control of simulated agents. ries (even for unnatural movements involving mul-
In robotics, manipulator control has been largely tiple DOFs) in spite of having attended to the end-
addressed for point-to-point reaching, typically by point. This could suggest some form of internal mod-
specifying Cartesian 3D goals and explicitly solving els of complete behaviors or primitives for movement,
the IK for the manipulator's joint angles (Paul 1981, which eectively encapsulate the details of low-level
Brady et al. 1982). Various neural network approaches control. Given an appropriately designed motor con-
to learning IK for simple manipulators have been ex- troller, tasks could be specied largely by end-point
plored and more sophisticated learning methods for positions and a few additional constraints, and the
dynamic tasks and higher DOF systems are being controller could generate the appropriate correspond-
developed (Atkeson 1989, Schaal & Atkeson 1994). ing postures and trajectories. The force-eld approach
The work most similar to the force-eld approach we we describe is a small step toward such an approach.
describe was performed by Williamson (1996), who To compare it with an alternative, we implemented
presented a controller for a 6-DOF robot arm, based both on a common testbed, described next.
on the same biological evidence we describe next. It
consists of four behaviors: three reaching and one 3 The Dynamic Anthropomorphic Simulation: Adonis
resting posture intermediate targets are achieved by
linear interpolation. Adonis is a rigid-body simulation of a human torso,
with static graphical legs (Figure 1), consisting of
2.2 Biological Inspiration eight rigid links connected with revolute joints of one
and three DOFs, totaling 20 DOFs. The dynamic
The exibility and eciency of biological motion pro- model for Adonis was created by methods described
vides a desirable model for complex agent control.meaningful instructions, as opposed to fully describ-
ing the tasks at the simulation level. The Macarena
specication, omitting the hip and whole-body sub-
tasks at the end, is given below:
1. Extend Right Arm straight out, palm down
2. Extend Left Arm straight out, palm down
3. Rotate Right Hand (palm up)
4. Rotate Left Hand (palm up)
5. Touch Right Hand to top of your left shoulder
6. Touch Left Hand to top of your right shoulder
7. Touch Right Hand to the back of your head
8. Touch Left Hand to the back of your head
9. Touch Right Hand to the left side of your ribs
10. Touch Left Hand to the right side of your ribs
11. Move Right Hand to your right hip
12. Move Left Hand to your left hip
No task-planning was necessary because the se-
Figure 1: The Adonis dynamic simulation testbed. quence is provided by the dance specication. How-
ever, the individual subtasks are not specied in the
same frame of reference. The rst four deal with ex-
in Hodgins et al. (1995). Mass and moment-of-inertia tending the arms, best expressed in joint angles, while
information is generated from the graphical body parts the rest are better described in an ego-centric Carte-
and equations of motion are calculated using a com- sian reference frame. This type of heterogeneous task
mercial solver, SD/Fast (SD/Fast User's Manual 1990). specication is common in natural language descrip-
The simulation acts under gravity, accepts other ex- tions, and control systems must satisfy each of the
ternal forces from the environment, and applies low dierent goals regardless of the underlying represen-
level PD-servo control (see Section 6) to keep bal- tation. To address the issue of controller representa-
ance at the waist and neck. No collision detection, tion, we implemented two very dierent alternatives,
with itself or its environment, is used in the described and compared them based on common performance
implementation we are currently implementing this metrics to demonstrate the tradeos involved.
extension.
Adonis is particularly well suited for testing and 5 The Force-Field Approach
comparing dierent motor control strategies the sim-
ulation allows us to apply forces to the end-points We introduce a biologically-inspired control approach
while a physical robot implementation would require based on applying convergent force-elds to end ef-
explicit calculation of the IK of the arms to solve fectors, Adonis' hands. Inspired by the neuroscience
for actuator torques from the desired forces. This, work on motor control in frogs described in Section
in turn, enables us to implement experimental con- 2, this approach aords a more intuitive user inter-
trollers for human-like movement more easily, while face at the expense of motion generality. A number of
having the simulation software handle the issue of IK force elds are used as a set of basis functions for con-
and dynamics. trolling Adonis desired Cartesian goals are reached
by applying forces to the hands to move them to the
4 Task Specication desired destinations. Each eld has a single equilib-
rium point (EP) at a target position where the eld is
Natural, goal-driven movement relies on precise spec- zero. From any point in Adonis' reachable workspace,
ication, coordination, and constraints imposed by the hand will stably move toward the EP, excluding
implementationand evaluation. A test task should be singularities in the kinematics. EPs are chosen em-
challenging to control but familiar enough to evalu- pirically as target positions for the hands in the 12
ate. The Macarena is a popular dance which involves subtasks of the Macarena. Some intermediate pos-
a sequence of coordinated movements that consti- tures were used, as described in Section 7.
tute natural subtasks. We used a verbal description, The force elds used as basis functions depend on
aimed at teaching people the dance (found on the the position and velocity of the hand being controlled.
web at http://www.radiopro.com/macarena.html) to The exerted force is proportional to the dierence
implement controllers according to a common set of between the current and desired velocity, calculatedas a function of the dierence between the current where _actual and _desired correspond to the actual
position and the equilibrium point. Formally: and desired joint velocities, and actual and desired
F = c (vactual ; vdesired ( jx ; xEP j )) correspond to the actual and desired joint angles.
To generate the Macarena controller, the desired
where vdesired is the desired velocity, vactual is the angles used for the feedback error are interpolated
actual velocity and c is the gain constant. The magni- from hand-picked key postures. The postures were
tude of c determines the speed of the complete move- derived directly from the task specication, each cor-
ment. For well-chosen values of c, this model makes responding to one of the 12 subtasks enumerated in
the hand position converge to the EP, following a Section 4. Intermediate postures between subtasks
roughly bell-shaped velocity prole, consistent with help guide the joint trajectories through dicult tran-
human data on regular-speed reaching motions (Flash sitions. For example, an intermediate posture was
& Hogan 1985). Linear combinations of the force- needed for swinging the hands around the head to
elds can produce new elds with convergence points prevent a direct yet unacceptable path through the
in the convex hull of the EPs of the bases. Bases head. The incremental desired angles use a spline
can be combined using vector summation, as in our to smoothly interpolate between the postures. Gains
approach, or using a winner-take-all framework, as for the PD-servo were chosen by hand and remained
used by Williamson (1996) for robot reaching. Our constant throughout the behavior. The joint torque
trajectories are generated by moving the equilibrium approach allows direct control of each actuated joint
point through a set of subgoals or control points. The in the system, giving the user local control of the
EP is computed from a linear weighted composition details of each behavior. However, the controller in
of the bases functions. We use feedback to move turn requires a complete set of desired angles at all
between control points, transitioning when the cur- times. Specifying all of this information can be te-
rent control point is reached. This works well since dious, especially for joints that are less important for
the Macarena is a relatively slow task highly dy- the behavior being generated. Interpolating between
namic behaviors (e.g., ball throwing) are better and key postures is a reasonable method for reducing the
more robustly handled with feedforward control, but required amount of information.
non-trivial arm dynamics make it dicult to predict The control of actuated joints may be individually
proper transition timing. modied using their respective desired angles, giving
The force-eld approach presents a convenient con- localized control over the generated motion. All de-
trol interface because it eectively lowers the dimen- sired key postures are specied as a set of angles in
sionality of the system. This makes the control task joint space. In behaviors such as the Macarena, posi-
easier, although the current implementation limits tion constraints like \hands behind the head", can be
exibility. Several of the joints, including the waist, satised with user-level feedback. However, precise
neck and wrists, use PD-servo controllers (described Cartesian-space constraints, like \nger on the tip
in Section 6) to maintain fairly rigid behavior. Be- of the nose", would be dicult to control by hand-
cause these joints are not explicitly controlled by the tuning using joint-space errors directly. An inverse
user, the range of controllable motion is limited, and kinematics solver could be used to generate desired
the naturalness of the resulting behavior can be re- angles from position constraints, although the con-
duced, as discussed in Section 7. troller has no direct measure of errors in Cartesian
space, currently.
6 The Joint Torque Approach
7 Performance Analysis and Comparisons
Joint-space controllers with torque actuators have been
used successfully to generate behaviors for a variety of Analysis and evaluation of complex behavior is an
systems (Pai 1990, Raibert & Hodgins 1991, Hodgins open research challenge. As synthetic behavior be-
et al. 1995, Van de Panne & Lamouret 1995). In gen- comes more complex, the issue becomes increasingly
eral, these controllers choose a set of torques for all acute in animation, robotics, and AI in general. We
actuated joints. We designed a hand-tuned PD-servo explored several evaluation criteria before deciding on
feedback controller for performing the Macarena on those elaborated below.
Adonis. In this approach, torques are calculated for
each joint as a function of angular position and ve- 7.1 Controller Flexibility
locity errors between the feedback state and desired Behavior constraints come in various forms. Com-
state: plex movements can be broken down into subtasks
T = kd ( _desired ; _actual ) + k ( desired ; actual ) with Cartesian-space or joint-space constraints. ForFigure 2: Adonis performing the Macarena, using the joint-space controller.
example, placing hands behind the head is best rep- straints such as gesturing and free-form movement
resented by a Cartesian constraint while turning the are more easily controlled with this approach, and
hand is better treated as a joint constraint. The issue subtleties, such as head motion and elbow position-
of coordinate and representation transformation has ing, can be controlled (Figure 2). The richness of the
been addressed extensively in manipulator robotics control, however, requires the user to specify joint an-
(Paul 1981, Brady et al. 1982). The two controllers gle information for each DOF in each subtask. In this
implemented favor very dierent representations and approach, the representational transformation from
thus the evaluation of their ability to satisfy all of the Cartesian to joint space is done implicitly by the pro-
various subgoals serves as an eective performance grammer. Consequently, tight Cartesian constraints
metric. are dicult to achieve with the current implementa-
The force-eld controller employs a 3D equilib- tion and may require an IK solver.
rium point as a control handle. This representation A control structure should easily accommodate a
is well suited to subtasks that describe the location variety of tasks and constituent behaviors, and gener-
of the end-points/hands, such as pointing, reaching, ating new behaviors should require a minimal amount
and basic interaction with a 3D environment. How- of user input. The joint-torque approach to control
ever, a Cartesian equilibrium point is an indirect and, is not easily generalizable between behaviors, as lit-
at times, unusable control handle in that complex tle or no knowledge can be transferred timing and
postures, like folding the arms or turning the palms, postures are usually specic and need to be regener-
cannot be naturally achieved. A key advantage of ated with each new controller. In contrast, the force-
this approach is that it limits the amount of infor- eld approach may be used to generate new behaviors
mation required for describing a behavior, reducing more easily due to its reduced control dimensionality.
the dimensionality of the problem. However, it also Also, using its linear additive properties, new behav-
removes access to the individual degrees of freedom iors may be generated by combining existing ones.
for the agent. While specializations of the force-eld
approach are possible, they compromise its simplic- 7.2 Naturalness of Movement: Qualitative
ity.
The joint-space controller uses desired angles as Judging the naturalness of movement is important,
control handles, allowing more complete control of but aesthetic judgment is dicult to quantify. Dy-
the agent's motion. Behaviors that include joint con- namic simulation constrains motion to be physicallycontrollers against the motion of a human performing
Human Data Torque-driven Force-driven the Macarena. We chose this metric over other alter-
T jerk time jerk time jerk time natives, such as minimum torque change, suggested
1 85800 1.00 38500 0.70 1100 2.87 by Uno, Kawato & Suzuki (1989), for its simplicity
2 89000 1.33 63400 0.57 560 1.73 of computation in our domain the hand position was
3 1970 1.33 1010 0.73 * * easily measured for both the simulation and the hu-
4 5060 0.87 1930 0.53 * * man movement. The comparison is performed using
5 18800 0.30 55200 0.57 360 3.40 the metric of total square jerk in 3D Cartesian space
6 21200 1.00 84100 0.47 360 3.27 we added a z position term to the calculation.
7 141000 1.00 105000 0.90 22600 1.60 Motion for 3D hand positions of a human sub-
8 111000 1.57 64000 0.70 7300 1.70 ject performing the Macarena was recorded using a
9 68200 0.90 205000 0.60 14700 1.67 commercial Flock of Birds electro-magnetic tracking
10 65900 1.13 401000 0.67 3200 1.67 system. Each subtask was isolated and calculated
11 71900 0.80 8990 0.30 20 1.67 separately for a ner-grain evaluation. Correspond-
12 12100 1.00 12800 1.00 40 1.73 ing data were collected for the two simulations the
results are presented in Figure 3. The values in the
Figure 3: A comparison of minimum jerk values. table correspond to the square jerk over the length
of the subtask, for the major moving hand in that
subtask (e.g., in subtask one the right arm, in sub-
plausible but it is not necessarily natural. Viewer- task two the left arm, and so on). The units for
based evaluation is one qualitative approach to mea- squared jerk are m2 =sec6 , and the duration of each
suring naturalness. Real-time playbacks of both con- subtask, labeled \time" is given in seconds. Subtasks
trollers we implemented are available from http:// 3 and 4 could not be implemented with the force-eld
www-robotics.usc.edu/ agents/macarena.html approach, since it lacked the ability to control hand
Rigid body simulation imposes limitations that orientation these entries are indicated with . Jerk
cannot be overcome by control. For instance, its is a sensitive measure, susceptible to position error
un-actuated back will necessarily appear sti. Fur- unavoidable in motion capture data collected with
thermore, the controllers have no knowledge of the electro-magnetic trackers. Furthermore, timing has a
body position and avoiding self-collisions was done by signicant eect on the jerk slower movements imply
hand. This results in conservative, unnatural trajec- less jerk, as is shown in the case of the force-control
tories which would be improved with a controller ca- approach. Therefore, the exact values above are less
pable of collision prediction and avoidance. Similarly, signicant than the general trends they indicate.
joint limits would contribute to more natural behav- In this evaluation, there is no correspondence be-
ior. To improve appearance, the force-eld method tween the goal positions and timing for the human
uses strong PD-servos to clamp some joints, avoiding and the simulated agent motions. Therefore, we do
marionette-like unconstrained movement. The joint- not expect correspondence between the controllers
torque method interpolated postures with splines to and the human jerk values, but instead in trends
smooth the resulting motion, and includes small head across each subtask and between the three sets of
and hand movements that result in richer motion. data. Rather than make a one-to-one comparison, we
Head gaze can add much in terms of naturalness of consider where the data are signicantly consistent or
motion and its implementation is straightforward. inconsistent and suggest some reasons for these pat-
terns. The hand jerk calculation is notably noisy and
7.3 Naturalness of Movement: Quantitative varies widely from task to task, so a qualitative analy-
sis is more benecial than an actual numeric compar-
Minimal jerk of hand position has been proposed by ison. It should be noted that the force-eld controller
Flash & Hogan (1985) as a metric for describing hu- explicitly applies forces to the hand and thus directly
man arm movements in the plane, by minimization aects the jerk. Therefore, the magnitude of the jerk
of the following index: is a contrived metric for the force-controlled move-
R
Cj = 0tfinal ( jerkx2 + jerky2 ) dt ment as a whole. However, the relative jerk within
each of the three sets of controllers provides valuable
where jerkx and jerky correspond to the third insight.
derivative of the x and y positions with respect to An important consideration in this comparison is
time. We used jerk as the evaluation metric for com- the amount of environment knowledge available to
paring the simulated motion for the two implemented the controller (human or simulated). Human accessto knowledge about body location and eective means implementation as a metric. Both of the described
of avoiding self-collision allow for generating smooth methods avoid explicit IK computations in favor of
movements of arbitrary complexity. In contrast, sim- simple but less general alternatives. Their relative
ulations have minimal environment knowledge or tra- eciency is dicult to compare, however, due to the
jectory planning capabilities. Consequently, subtasks integral role of the designer in both approaches.
involving complex self-collision avoidance result in
less ecient and less natural behavior. For example, 8 Continuing Work and Conclusion
subtasks 5, 6, and 9, 10 exhibit these characteristic
trajectory planning diculties. We have compared two approaches to anthropomor-
Interestingly, while tasks 7 and 8 are similar in phic agent control, both implemented on a dynamic
nature, and in fact appear most complex in terms of torso simulation, Adonis, and tested on a 12-subgoal
self-collision avoidance, their corresponding jerk val- Macarena task. We introduced a biologically-motivated
ues do not show the same pattern. One interpreta- force-eld approach, which sets up convergent force
tion of this result stems from the subgoals involved elds that operate as a function of the velocity and
in generating the complex movement. While we have position of the hands. We then compared it to a
little understanding of the strategies people use in joint-space controller which manipulates the individ-
reaching this subgoal, we can infer from the behavior ual torques for each DOF of the system allowing com-
that coordinated movement of the head and the arm, plete control over the agent but requiring more intu-
and subsequent contact with the head, is involved. In ition on the behalf of the user. Both approaches avoid
contrast, the simulated behavior proceeds through a explicit IK computation by feeding un-converted user
set of intermediate positions which avoid self-collision inputs to the simulation, making task-specication
and result in the arm behind, but not in contact with, ecient but not fully general. We compare the con-
the head. Not surprisingly, the resulting jerk pattern trollers against each other and to human data on the
is quite dierent. To study this discrepancy further, same task using a minimum jerk computation as a
a less familiar and intuitive set of subtasks could be common metric. The fundamental tradeo between
used that may provide a stronger comparison between believability and control eort still remains, as the
human and simulated motion. two approaches produce dierent results depending
To facilitate an honest comparison, simulated and on subtask specication.
human motion were generated independently. How- The described work is a part of a project aimed
ever, various techniques can be implemented to gen- at developing a biologically-inspired behavior-based
erate a closer t between the data, if that is desired. approach to motor control. We presented implemen-
Specically, human hand positions could be used to tations that employ a single representational method-
select goal positions for the force-eld equilibrium ology, which are a part of an eort toward a system
points. Similarly, an IK solver could nd joint pos- that encapsulates the low-level control details within
tures for the joint-space controller that achieved these primitive parametric behaviors that satisfy various
hand positions. In addition, timing considerations in- motor tasks, including movement to point using a
uence the comparison. As seen from the data, the specic achievement-goal (such as reaching, and most
timing of subtasks was not correlated. Timing taken of the Macarena subtasks) and repetitive and oscil-
from human motion could be used to generate simu- latory movements using maintenance-goals (such as
lated motion that more closely t the human perfor- bouncing, waving, swinging, etc.). Individual behav-
mance. Lastly, minimization techniques could be ap- iors may rely on dierent representations, but their
plied to the controller parameters to nd movements use and performance can be seamlessly integrated
that minimize jerk or other performance metrics. by sequencing and co-activation, as in the biologi-
cal model. In addition to its biological motivation
7.4 Other Evaluation Criteria and potential dimensionality reducing properties, the
behavior-based model for complex motor control pro-
Other criteria were also considered. We explored vides a simple and scalable interface for graphical
evaluating the correctness of the resulting behavior, agents. One of our goals is to develop a control archi-
but without a set of analytical denitions of each tecture that allows for combining various movement
subtask, this proved of little use. Such specic con- primitives (possibly from dierent users) into a ver-
straints could be computed but were rather inconsis- satile and general system. As complex articulated
tent with the graphical environment where the def- agents become more prevalent, such a modular ap-
inition of achieving the task did not rest on precise proach to control would use its \open architecture"
placement as much as on the overall impression of the to combine the advantages of various approaches by
complete movement. We also considered eciency ofencapsulating them into primitives. Mussa-Ivaldi, F. A. & Giszter, S. F. (1992), `Vector
eld approximations: a computational paradigm
Acknowledgments for motor control and learning', Biological Cy-
bernetics 67, 491{500.
This work is supported by the NSF Career Grant IRI-
9624237 to M. Mataric. The authors thank Nancy Mussa-Ivaldi, F. A., Giszter, S. F. & Bizzi, E.
Pollard for help with the jerk calculations, Len Nor- (1994), `Linear combinations of primitives in ver-
ton for help with human motion data, and Stefan tebrate motor control', Proceedings of the Na-
Schaal and Jessica Hodgins for sharing expertise and tional Academy of Sciences 91, 7534{7538.
providing many insightful comments. The Adonis Ngo, J. T. & Marks, J. (1993), Spacetime Constraints
simulation was developed by Jessica Hodgins at Geor- Revisited, in J. T. Kajiya, ed., `Computer
gia Institute of Technology. Graphics (Proceedings, SIGGRAPH '93)', 343{
350.
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