arXiv:1411.2276v1 [cs.RO] 9 Nov 2014

Trade-offs in exploiting body morphology
for control: from simple bodies and
model-based control to complex bodies
with model-free distributed control
schemes

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Matej Hoffmann1 and Vincent C. Müller2,3
1
iCub Facility, Istituto Italiano di Tecnologia, Genoa, Italy
matej.hoffmann@iit.it
Division of Humanities & Social Sciences, Anatolia College/ACT,
Pylaia-Thessaloniki, Greece
vmueller@act.edu
3
University of Oxford, UK

Tailoring the design of robot bodies for control purposes is implicitly performed by engineers, however, a methodology or set of tools is largely absent
and optimization of morphology (shape, material properties of robot bodies, etc.) is lagging behind the development of controllers. This has become
even more prominent with the advent of compliant, deformable or "soft"
bodies. These carry substantial potential regarding their exploitation for
control—sometimes referred to as "morphological computation" in the sense
of offloading computation needed for control to the body. Here, we will argue
in favor of a dynamical systems rather than computational perspective on
the problem. Then, we will look at the pros and cons of simple vs. complex
bodies, critically reviewing the attractive notion of "soft" bodies automatically taking over control tasks. We will address another key dimension of
the design space—whether model-based control should be used and to what
extent it is feasible to develop faithful models for different morphologies.

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Introduction
It has become increasingly common to explain the intelligent abilities of natural agents
through reference to their bodily structure, their morphology, and to make extended
use of this morphology for the engineering of intelligent abilities in artificial agents,
e.g. robots–thus "offloading" computational processing from a central controller to the
morphology. These uses of morphology for explanation and engineering are sometimes
referred to as "morphological computation". As we argue in detail elsewhere [21], only
some of the characteristic cases that are embraced by the community as instances of
morphological computation have a truly computational flavor. Instead, many of them are
concerned with exploiting morphological properties to simplify a control task. This has
been labeled "morphological control" in [8]; "mechanical control" could be an alternative
label. Developing controllers that exploit a given morphology is only a first step. The
space of possible solutions to a task increases dramatically once the mechanical design is
included in the design space. At the same time, the dimensionality of the design problem
grows exponentially.
In this work, we want to take a close look at these issues. First, we will borrow the
"trading spaces" landscape from [27] that introduces a number of characteristic examples
and distributes them along a metaphorical axis from "informational computation" to
"morphological computation". Second, we will argue in favor of a dynamical systems
rather than computational perspective on the problem. Third, we will critically look
at the pros and cons of simple vs. complex (highly dimensional, dynamic, nonlinear,
compliant, deformable, "soft") bodies. Fourth, we will address another key dimension
of the design space—whether model-based control should be used and to what extent it
is feasible to develop faithful models for different morphologies. We will close with an
outlook into the future of "soft" robotics.

Design "trading spaces"
Pfeifer et al. [27] offer one possible perspective on the problem in Fig. 1. In traditional robots—as represented by industrial robots and Asimo in the figure—, control is
essentially confined to the software domain where a model of the robot exists and current state of the robot and the environment is continuously being updated in order to
generate appropriate control actions sent to the actuators. In biological organisms, on
the other hand, this does not seem to be the case: the separation between "controllers"
and "controlled" is much less clear and behavior is orchestrated through a distributed
network of interactions of informational (neural) and physical processes. Furthermore,
there is no centralized neural control, but a multitude of recurrent loops from the lowest level (reflexes and pattern generators in the spinal cord) to different subcortical and
cortical areas in the brain. At the same time, the bodies themselves tend to be much
more complex in terms of geometrical as well as dynamical properties. This has motivated the design of compliant, tendon-driven robots like ECCE [36] and soft, deformable
robots like Octopus (e.g., [16]). However, compared to humans or biological octopus, a

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Figure 1: The design trading space. This figure illustrates the degree to which each
system relies on explicit control or self-organization of mechanical dynamics.
On the left-hand side of the spectrum, computer algorithms and commercial
computers rely on physical self-organization at the minimum level, while towards the right-hand side, more embodied, more soft, and smaller-scale systems
require physical interactions as driving forces of behaviors. The design goal
then is to find a proper compromise between efficiency and flexibility, taking
into account that a certain level of flexibility can also be achieved by changing
morphological and material characteristics. (Fig. and caption from [27]).
comparable level of versatility and robustness in the orchestration of behavior has not
yet been achieved in the robotic counterparts. In more restricted settings, the design
and subsequent exploitation of morphology is easier, as the jumping and landing robot
frog [22], the passive dynamic based walker, or the coffee balloon gripper demonstrate.
The passive dynamic walkers [19] are a powerful demonstration that appropriate design
of morphology can generate behavior in complete absence of software control. Yet, there
is only a single behavior and the environmental niche is very narrow. The coffee-balloon
gripper [4] employs a similar strategy, but achieves surprising versatility on the types of
objects that can be grasped. Body designs that follow this guideline were also labeled
"cheap designs" [28].

From computational to dynamical systems perspective on
the control problem
A general formulation of a control problem in control theory is making a dynamical
system follow a desired trajectory. For our purposes, we will consider the cases where
the dynamical system is physical—the body of the agent; in control theory, this is the socalled plant. There are numerous control schemes and branches of control theory and the
reader is referred to abundant literature on the topic (e.g., [3, 7, 15]). The performance of

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the controller can be evaluated on various grounds: precision of a trajectory with respect
to a reference trajectory, or energy expenditure, for example. In addition, performance,
stability and robustness guarantees are required by industry. Control theory typically
deals with the design of controllers that optimize these criteria. Some control schemes
with appropriate cost functions will automatically result in minimal control actions and
thus "optimize the contribution of the morphology". For example, Moore et al. [20]
used Discrete Mechanics and Optimal Control to steer a satellite while exploiting its
dynamics to the maximum. Carbajal [6] developed related methods for reaching, plus
offered a formalization of the concept of "natural dynamics". Nevertheless, the plant is
treated as fixed in these approaches. Yet, the properties of the physical body obviously
have a key influence on the final performance of the whole system (plant + controller),
which calls for including them into the design space. Therefore, including the body into
the design space carries great potential.
We feel that to address the problem of morphology simplifying control, a computational
perspective does not provide the most appropriate framework. Instead, the dynamical
systems description seems more appropriate for the following reasons: (i) It fits the
informational and physical processes equally well; (ii) It copes with continuous (in time)
streams of continuous input and output signals; (iii) It is already used by control theory.
The concept of self-stabilization, for example, which is often cited in the "morphological
computation community" is naturally explained from a dynamical systems standpoint.
In the case of the passive dynamic walker or the jamming-based grippers cited above,
the body is ingeniously contributing to its, perhaps primary, function: enabling physical
behavior in the real world. While this is often interpreted in the "offloading sense"—the
body design takes over computation from the brain (e.g., [25])—we argue that the contribution of the body itself (and the interaction with the environment) is not computational
in any substantial sense. In fact, calling it computation may allude to a much stronger
thesis (at least in the classical notion of computation), namely that what is done by the
interaction here could also be done by a conventional computer. And that is quite the
opposite of what most proponents of the morphological stance want to say. Therefore,
our claim is that exploiting morphology for control should be better handled in a noncomputational context and that the dynamical systems framework is more appropriate
than a classical computational one.

Simple or complex bodies?
The spirit of the morphological computation literature that follows the "offloading" or
"trade-off" perspective, is that complex (highly dimensional, dynamic, nonlinear, compliant, deformable, "soft" ) bodies are advantageous for control because they can take over
the "computation" that a controller would otherwise have to perform (e.g., [9, 10, 25] or
[5] explicitly in Fig. 1). Complex nonlinear bodies give rise to more complex dynamical
landscapes where the location of attractors can facilitate the performance on a given
task.
This view is in stark contrast to the views prevalent in control theory. There, linear

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time-invariant systems are the ideal plants to control. Solutions for nonlinear systems
are much more difficult to obtain and they often involve a linearization of the system of
some sort. In fact, human-like bodies are a nightmare for control engineers ([29] is an
interesting case study) and highly complex models and controllers would be required.
What would be an ideal body then? And, does a complex body imply simple or complex control? Recent attempts at quantifying the amount of morphological computation
shed more light on this issue. Zahedi and Ay [37] propose two concepts for measuring
the amount of morphological computation by calculating the conditional dependence of
future world states (or body state) on previous world states and action taken by the
agent. According to Concept 1, the amount of morphological computation is inversely
proportional to the contribution of the agent’s actions to the overall behavior. Concept
2 equates the amount of morphological computation with the contribution of the world
to the overall behavior. From a robotic perspective, optimizing for morphological computation, Concept 1 is equivalent to systems that cannot be controlled by actions of
the robot; Concept 2 will give rise to systems with strong "body dynamics" or "natural
dynamics" (see e.g., [14] or [6] for a formal definition). A body with strong internal
dynamics (Concept 2), resisting control actions (Concept 1), will not be a product of
typical engineering designs. Yet, if it is possible to design the body to assist in task
performance, it is certainly of advantage. The passive dynamic walker is an extreme
case; however, underactuated designs featuring active and passive degrees of freedom are
also abundant.
Rückert and Neumann [31] study learning of optimal control policies for a simulated
4-link pendulum which needs to maintain balance in the presence of disturbances. The
morphology (link lengths and joint friction and stiffness) is manipulated and controllers
are learned for every new morphology. They show that: (1) for a single controller, the
complexity of the control (as measured by the "variability" of the controller) varies with
the properties of the morphology: certain morphologies can be controlled with simple
controllers; (2) optimal morphology depends on the controller used; (3) more complex
(time-varying) controllers achieve much higher performance than simple control across
morphologies.
In summary, the performance on a task will always depend on a complex interplay of
the controller, body, and environment: taking out the controller is just as big a mistake
as taking out the body was. The tasks that can be completely solved by appropriate
tuning of the body, like passive dynamic walking, are the exception rather than the
rule. A controller will thus be needed too. A complex body may have the potential to
partially solve certain tasks on its own; yet, it may present itself as difficult to control,
model (if the controller is relying on models), design, and manufacture. An optimal
balance thus needs to be found. For that, however, new design methodologies that
would encompass complex cost functions (performance on a task, versatility, robustness,
costs associated with hardware whose parameters can be manipulated etc.) are needed.
Hermans et al. [11] very recently proposed such a method that uses machine learning to
optimize physical systems; an approximate parametric model of the system’s dynamics
and sufficient examples of the desired dynamical behavior need to be available though—
which leads us to the next section.

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With or without a model?
Including the parameters of the body into the design considerations may give rise to better
performance of the whole system; these may be solutions involving a simpler controller,
but also solutions that were previously unattainable when the body was fixed. Following
the dynamical system’s perspective, [8] provide an illustration of the possible goals of the
design process: (1) To design the physical dynamical system such that desired regions of
the state space have attracting properties. Then it is sufficient to use a simple control
signal that will bring the system to the basins of attraction of individual stable points
that correspond to target behaviors. (2) More complicated behavior can be achieved if
the attractor landscape can be manipulated by the control signal.
If a mathematical formulation of the controller and the plant is available, this design
methodology can be directly applied. The first part is demonstrated by McGeer [19]
on the passive dynamic walker: The influence of scale, foot radius, leg inertia, height
of center of mass, hip mass and damping, mass offset, and leg mismatch is evaluated.
In addition, the stability of the walker is calculated. Recently, Jerrold Marsden and his
coworkers presented a method that allows for co-optimization of the controller and plant
by combining an inner loop (with discrete mechanics and optimal control) and an outer
loop (multiscale trend optimization). They applied it to a model of a walker and obtained
the best position of the knee joints ([24] – Ch. 5).
However, typical real-world agents are more complex than simple walkers. Holmes et
al. [12] provide an excellent dynamical systems analysis of the locomotion of rapidly running insects and derive implications for the design of the RHex robot. Yet, they conclude
that "a gulf remains between the performance we can elicit empirically and what mathematical analyses or numerical simulations can explain. Modeling is still too crude to
offer detailed design insights for dynamically stable autonomous machines in physically
interesting settings." Hermans et al. [11] similarly note that applying their method to
robotics, which is known to suffer from lack of accurate models, is a challenge. The modeling and optimization of more complicated morphologies—like compliant structures—is
nevertheless an active research topic (e.g., Wang [35] and other work by the author).
The second point of Füchslin et al. [8]—achieving "morphological programmability" by
constructing a dynamical system with a parametrized attractor landscape—remains even
more challenging though.
One of the merits of exploiting the contributions of body morphology should be that the
physical processes do not need to be modeled, but can be used directly. However, without
a model of the body at hand, several body designs need to be produced and—together
with the controller—tested in the respective task setting. The design space of the joint
controller-body system blows up and we may be facing a curse of dimensionality. This
is presumably the strategy adopted by the evolution of biological organisms that could
cope with the enormous dimensionality of the space. In robotics, this has been taken
up by evolutionary robotics [23]. The simulated agents of Karl Sims [32] demonstrate
that co-evolving brains and bodies together can give rise to unexpected solution to problems. More recently, with the advent of rapid prototyping technologies, physics-based
simulation could be complemented by testing in real hardware [18]. Yet, a "reality gap"

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always remains between simulated and real physics and searching for optimal designs in
hardware directly is very costly (e.g., [13]). The design decisions—which parameters to
optimize—are based on heuristics and a clear methodology is still missing. Furthermore,
with the absence of an analytical model of the controller and plant, no guarantees on the
system’s performance can be given.

Outlook
In terms of applications, the most relevant area where exploitation of morphology is
and will be the key is probably robotics, and in particular soft robotics (see [2, 26,
27, 34] and the first issue of the Soft Robotics Journal [33]). "Soft" robots break the
traditional separation of control and mechanics and exploit the morphology of the body
and properties of materials to assist control as well as perceptual tasks. Pfeifer et al. [26]
even discuss a new industrial revolution. Appropriate, "cheap", designs lead to simpler
control structures, and eventually can lead to technology that is cheap in a monetary
sense and thus more likely to impact on practical applications. Yet, a lot of research in
design, simulation and fabrication is needed (see [17] for a review).
The area of soft robotics and morphological computation seems to be rife with different trading spaces [27]. As we move from the traditional engineering framework with a
central controller that commands a "dumb" body toward delegating more functionality
to the body, some convenient properties will be lost. In particular, the solutions may
not be portable to other platforms anymore, as they will become dependent on the particular morphology and environment (the passive dynamic walker is the extreme case).
The versatility of the solutions is likely to drop as well. To some extent, the morphology
itself can be used to alleviate these issues—if it becomes adaptive. Online changes of
morphology (like changes of stiffness or shape) thus constitute another tough technological challenge (see also project LOCOMORPH [1]). Completely new, distributed control
algorithms that rely on self-organizing properties of complex bodies and local distributed
control units will need to be developed (the tensegrity structure controlled by a spiking
neural network [30] is a step in this direction).

Acknowledgements
M.H. was supported by the Swiss National Science Foundation Fellowship PBZHP2147259. M.H. also thanks Juan Pablo Carbajal for fruitful discussions and pointers to
literature. Both authors thank the EUCogIII project (FP7-ICT 269981) for making us
talk to each other.

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References
[1] Project LOCOMORPH. FP7-ICT-231688.
[2] A. Albu-Schaffer, O. Eiberger, M. Grebenstein, S. Haddadin, C. Ott, T. Wimbock,
S. Wolf, and G. Hirzinger. Soft robotics. Robotics Automation Magazine, IEEE,
15(3):20 –30, september 2008.
[3] K.J. Aström and R. M. Murray. Feedback Systems: An Introduction for Scientists
and Engineers. Princeton University Press, 2008.
[4] Eric Brown, Nicholas Rodenberg, John Amend, Annan Mozeika, Erik Steltz,
Mitchell R Zakin, Hod Lipson, and Heinrich M Jaeger. From the cover: Universal robotic gripper based on the jamming of granular material. Proc Natl Acad Sci
U.S.A., 107(44):18809–18814, Nov 2010.
[5] K. Caluwaerts, M. D’Haene, D. Verstraeten, and B. Schrauwen. Locomotion without a brain: physical reservoir computing in tensegrity structures. Artificial Life,
19(1):35–66, 2013.
[6] J. P. Carbajal. Harnessing Nonlinearities: Behavior Generation from Natural Dynamics. PhD thesis, University of Zurich, 2012.
[7] A. Emami-Naeini, G. F. Franklin, and J. D. Powell. Feedback control of dynamic
systems. Prentice Hall, 2002.
[8] R.M. Füchslin, A. Dzyakanchuk, D. Flumini, H. Hauser, K.J. Hunt, R.H. Luchsinger,
B. Reller, S. Scheidegger, and R. Walker. Morphological computation and morphological control: steps towards a formal theory and applications. Artificial Life,
19(1):9–34, 2013.
[9] H. Hauser, A.J. Ijspeert, R.M. Füchslin, R. Pfeifer, and W. Maass. Towards a theoretical foundation for morphological computation with compliant bodies. Biological
Cybernetics, 105:355–370, 2011.
[10] H. Hauser, A.J. Ijspeert, R.M. Füchslin, R. Pfeifer, and W. Maass. The role of feedback in morphological computation with compliant bodies. Biological Cybernetics,
106:595–613, 2012.
[11] M. Hermans, B. Schrauwen, P. Bienstman, and J. Dambre. Automated design of
complex dynamic systems. PLOS ONE, 9(1):e86696, 2014.
[12] P. Holmes, R. J. Full, D. Koditschek, and J. Guckenheimer. The dynamics of legged
locomotion: Models, analyses and challenges. SIAM Review, 48(2):207–304, 2006.
[13] G.S. Hornby, S. Takamura, J. Yokono, O. Hanagata, T. Yamamoto, and M. Fujita.
Evolving robust gaits with AIBO. In Robotics and Automation, 2000. Proceedings.
ICRA ’00. IEEE International Conference on, volume 3, pages 3040 –3045 vol.3,
2000.

8

[14] F. Iida, G. Gómez, and R. Pfeifer. Exploiting body dynamics for controlling a
running quadruped robot. In Proceedings of the 12th Int. Conf. on Advanced Robotics
(ICAR05)., pages 229–235, Seattle, U.S.A., 2005.
[15] D. Kirk. Optimal control theory: an introduction. Dover Publications, 2004.
[16] C. Laschi, M. Cianchetti, B. Mazzolai, L. Margheri, M. Follador, and P. Dario. Soft
robot arm inspired by the octopus. Advanced Robotics, 26(7):709–727, 2012.
[17] H. Lipson. Challenges and opportunities for design, simulation, and fabrication of
soft robots. Soft Robotics, 1:21–27, 2013.
[18] H. Lipson and J.B. Pollack. Automatic design and manufacture of robotic lifeforms.
Nature, 406(6799):974–978, 2000.
[19] T. McGeer. Passive dynamic walking. The International Journal of Robotics Research, 9(2):62–82, 1990.
[20] A. Moore, S. Ober-Blöbaum, and J.E. Marsden. Trajectory design combining invariant manifolds with discrete mechanics and optimal control. Journal of Guidance,
Control, and Dynamics, 35(5):1507–1525, 2012.
[21] V.C. Müller and M. Hoffmann. Is morphological computation really computation?
Contributions of the body to cognition and control. [submitted].
[22] R. Niiyama, A. Nagakubo, and Y. Kuniyoshi. Mowgli: A bipedal jumping and
landing robot with an artificial musculoskeletal system. In IEEE Int. Conf. Robotics
and Automation (ICRA), pages 2546–2551. IEEE, 2007.
[23] Stefano Nolfi and Dario Floreano. Evolutionary robotics: The biology, intelligence,
and technology of self-organizing machines, volume 26. MIT press Cambridge, 2000.
[24] D.N. Pekarek. Variational methods for control and design of bipedal robot models.
PhD thesis, California Institute of Technology, 2010.
[25] R. Pfeifer and J.C. Bongard. How the body shapes the way we think: a new view of
intelligence. MIT Press, Cambridge, MA, 2007.
[26] R. Pfeifer, M. Lungarella, and F. Iida. The challenges ahead for bio-inspired ’soft’
robotics. Communications of the ACM, 55(11):76–87, 2012.
[27] R. Pfeifer, H.G. Marques, and F. Iida. Soft robotics: the next generation of intelligent machines. In Proc. 23rd Int. Joint Conf. on Artificial Intelligence, pages 5–11.
AAAI Press, 2013.
[28] R. Pfeifer and C. Scheier. Understanding Intelligence. MIT Press, 1999.
[29] V. Potkonjak, B. Svetozarevic, K. Jovanovic, and O. Holland. The puller-follower
control of compliant and noncompliant antagonistic tendon drives in robotic systems.
Int. Journal Advanced Robotic Systems, 8(5):143–155, 2011.

9

[30] J.A. Rieffel, F.J. Valero-Cuevas, and H. Lipson. Morphological communication: exploiting coupled dynamics in a complex mechanical structure to achieve locomotion.
Journal of the Royal Society Interface, 7(45):613–621, 2010.
[31] E. Rückert and G. Neumann. Stochastic optimal control methods for investigating
the power of morphological computation. Artificial Life, 19:115–131, 2013.
[32] K. Sims. Evolving 3D morphology and behavior by competition. Artificial Life,
1(4):353–372, 1994.
[33] B. Trimmer. A journal of soft robotics: Why now? Soft Robotics, 1:1–4, 2013.
[34] D. Trivedi, C.D. Rahn, W.M. Kier, and I.D. Walker. Soft robotics: Biological
inspiration, state of the art, and future research. Applied Bionics and Biomechanics,
5(3):99–117, 2008.
[35] Michael Yu Wang. A kinetoelastic formulation of compliant mechanism optimization. Journal of Mechanisms and Robotics, 1(2):021011, 2009.
[36] S. Wittmeier, C. Alessandro, N. Bascarevic, K. Dalamagkidis, D. Devereux, A. Diamond, M. Jäntsch, K. Jovanovic, R. Knight, H.G. Marques, et al. Toward anthropomimetic robotics: Development, simulation, and control of a musculoskeletal
torso. Artificial life, 19(1):171–193, 2013.
[37] K. Zahedi and N. Ay. Quantifying morphological computation. Entropy, 15(5):1887–
1915, 2013.

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