# Towards a Theoretical Foundation for Morphological Computation with
Compliant Bodies

**H. Hauser, A. J. Ijspeert, R. M. Füchslin, R. Pfeifer, and W. Maass**

### Abstract:

The control of compliant robots is, due to their often nonlinear and complex
dynamics, inherently difficult. The vision of morphological computation
proposes to view these aspects not only as problems, but rather as parts of
the solution. Non-rigid body parts are not seen anymore as imperfect
realizations of rigid body parts, but rather as potential computational
resources. The applicability of this vision has already been demonstrated for
a variety of complex robot control problems. Nevertheless, a theoretical
basis for understanding the capabilities and limitations of morphological
computation has been missing so far.We present a model for morphological
computation with compliant bodies, where a precise mathematical
characterization of the potential computational contribution of a complex
physical body is feasible. The theory suggests that complexity and
nonlinearity, typically unwanted properties of robots, are desired features
in order to provide computational power. We demonstrate that simple generic
models of physical bodies, based on mass-spring systems, can be used to
implement complex nonlinear operators. By adding a simple readout (which is
static and linear) to the morphology, such devices are able to emulate
complex mappings of input to output streams in continuous time. Hence, by
outsourcing parts of the computation to the physical body, the difficult
problem of learning to control a complex body, could be reduced to a simple
and perspicuous learning task, which can not get stuck in local minima of an
error function.

**Reference:** 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(5-6):355-370, 2011.