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A bio-inspired limb controller for avatar animation
Ana Lucia Cruz Ruiz, Charles Pontonnier, Georges Dumont
To cite this version:
Ana Lucia Cruz Ruiz, Charles Pontonnier, Georges Dumont. A bio-inspired limb controller for avatar
animation. Computer Methods in Biomechanics and Biomedical Engineering, Taylor & Francis, 2014,
17 (Supplement 1), pp.174-175. �10.1080/10255842.2014.931658�. �hal-01060284�
A bio-inspired limb controller for avatar animation
AL. Cruz Ruiz
a,b
*, C. Pontonnier
a,c
and G. Dumont
a,b
a
IRISA/INRIA MimeTIC, Rennes, France;
b
ENS Rennes, Bruz, France;
c
Ecoles de Saint-Cyr Coëtquidan, Guer,
France
Keywords: motor control; musculoskeletal modeling; human motion synthesis; linearizing feedback
1. Introduction
In the field of computer animation, producing a
realistic procedural avatar animation based on
dynamics remains challenging.
Recent advances in musculoskeletal simulation
have enhanced drastically the limb controllers in
direct dynamics and the final animation by taking
into account the muscular redundancy and the
muscular viscoelasticity in the motion dynamics of
avatars (Geijtenbeek, Van de Panne & Van der
Stappen, 2013). Nevertheless, such optimisation
based animation is costly in terms of computation
time and does not handle the real-time constraint –
mandatory for video-games, serious-games or
virtual reality applications.
In the current abstract, we introduce a new
musculoskeletal-based limb controller including a
linearizing feedback of the musculoskeletal
structure and a PID control of the limb position
with the objective to enhance virtual avatar
animation.
2. Methods
Let us consider a simple 1-dof limb actuated with
two antagonist muscles.
The control inputs of the system are the muscular
neural excitations (
) and the control output is the
angular position of the limb (
q
).
Our control strategy is based on a feedback
linearization of the musculoskeletal dynamics
which will allow us to conceive a joint space
controller. Similarly, to (Bonnet et al., 2009) the
pulling muscle is determined based on the error in
the system.
The classical Hill-type muscle model, force-length
(
l
f
) and force-velocity (
v
f
) relationships featured
in (Rengifo, Aoustin, Plestan & Chevallereau,
2010) were used to determine the total force (
tj
f
) of
muscle j,
tj tj pj mnj j lj mnj vj mnj oj
f l f l a f l f l f
(1)
Where
pj
f
is the passive force,
j
a
is the muscle
activation and
oj
f
is the maximum isometric force
The normalized length (
mnj
l
), tendon length (
tj
l
)
and rate of change in length (
mnj
l
) of both muscles
are dependent on the joint position and joint
velocity.
Consequently, one can represent the dynamics of
this system through the time progression of the joint
position and velocity.
Considering this and the torque imposed at the joint
by the muscles and external forces we obtain the
following state space representation,
1 1 2
2 2 1 t1 t1 2 t2 t2 g
x = q x = x
1
x = q x = r f l + r f l + Γ
I
y = q
(2)
Where
r
1
and
r
2
are the constant muscle moment
arms, I is the inertia of the system and
g
is the
torque produced by gravity.
The relative degree of the system, proves that the
output can be controlled via a feedback
linearization,
(3)
2
1 p1 1 l1 v1 o1 2 p2 2 l2 v2 o2 g
1
y = = r f + a f f f + r f +a f f f +q Γ = v
I
Where,
tt
j j oj
a e a e 1
The initial conditions on the activation are
expressed through the terms
oj
a
,
is the time
constant representing the activation dynamics.
The feedback linearization is done by assigning to
eq.(3) a new control input v.
Inverting the system as in eq.(4), we find an
expression for the neural excitations in terms of the
new control input v,
u A x v b x
1
(4)
(5)
t
tt
o o p p
t
I
e
v a e a e r f r f
II
e
22
1
1 2 1 1 2 2 g
2
22
1
1
Γ
1
Where,
l v o
r f f f
1 1 1 1
and
l v o
r f f f
2 2 2 2
.
The system has been reduced to an integrator chain
that can be easily commanded through the new
control input v. Consequently, classical control
techniques can be used to command the position of
the limb, such as a PID controller.
*Corresponding author. ana-lucia.cruz-ruiz@inria.fr
3. Results and Discussion
The elbow extension task described in (Osu et al.,
2004) was simulated with the parameters in Table
1, taken from (Stroeve, 1999). The limb was
commanded to move from an initial position of 97°
to a desired position of 41°.
Table 1 Parameters
The resulting angular position of the limb, neural
excitations and activations are illustrated in Fig. 1
and Fig. 2.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
30
40
50
60
70
80
90
100
Time (seconds)
Angle (degrees)
Limb Trajectory
Desired Final Value
Figure 1 Limb Extension
Both position and excitations are satisfying in
terms of shape, magnitude, occurrence and are
coherent with a fast extension movement. As in the
experimental measurements presented in (Osu et
al., 2004), the excitation of the extensor muscle is
initially high, decreases as the limb approaches the
goal and achieves a steady state in order to hold the
position. Thanks to the predictive action of the
controller, the flexor muscle is excited to reduce the
velocity of the limb and make final corrections in
position.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
0.5
1
Time (seconds)
Magnitude
Extensor Muscle
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
0.005
0.01
0.015
0.02
Time (seconds)
Flexor Muscle
Magnitude
Figure 2 Excitations/activations
Note that the movement presented above is faster
than those recorded in the experiments and that the
flexor is only activated for preventive or corrective
actions. This difference is due to the fact that other
aspects that are present and controlled during
human motion such as the stiffness and desired
joint velocity were not considered in our model.
4. Conclusions
We have introduced a simple limb controller that
partially reproduces the neural excitation signals
that satisfy a specific kinematic behaviour.
Complex articulated bodies such as those of avatars
could be controlled by assigning a pair of
antagonist muscles and a controller to each degree
of freedom. A finite state machine and a target
generator would then produce desired poses which
the controllers would use for muscle excitation
regulation. In our future work we intend to produce
more realistic, human-like motions through the
consideration of new control variables, such as the
velocity and impedance of the limb. We also intend
to explore optimal control techniques to minimize
external perturbation effects, followed by a model
simplification for real time implementation.
Acknowledgments
This work is supported by the French ANR project
ENTRACTE (Grant agreement: ANR 13-CORD-
002-01).
References
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