PhD thesis and preprints: CPGs for lamprey and salamander locomotion

[Auke Ijspeert]

Dear Connectionists,

The following PhD thesis and preprints (see below) may interest
people working on the modeling of central pattern pattern generators for
locomotion. They presents some results in the use of evolutionary
algorithms for completing biological plausible neural circuits modeled as
continuous-time neural networks. In particular, the neural circuits
underlying the swimming of the lamprey and the swimming and trotting of
the salamander are investigated. This work is inspired by Ekeberg's
neuromechanical model of the lamprey swimming (Biol. Cybern. 69, 363-374,
1993), and, similarly, the developed CPGs are incorporated in simple
biomechanical models of a lamprey and a salamander. Animated gifs
illustrating the different gaits developed can be found at:
http://rana.usc.edu:8376/~ijspeert/

The thesis and the papers (title and abstracts below) can be found in
gzipped postscript at:
http://rana.usc.edu:8376/~ijspeert/publications.html
Please tell me if you have any problem downloading them. Comments are most
welcome!

Best regards,

Auke Ijspeert  

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    Dr Auke Jan Ijspeert
    Brain Simulation Lab & Computational Learning and Motor Control Lab
    Department of Computer Science, Hedco Neurosciences building
    U. of Southern California, Los Angeles, CA 90089, USA
    Web:   http://rana.usc.edu:8376/~ijspeert/
    Tel:   +1 213 7401922 or 7406995 (work) +1 310 8238087 (home)
    Fax:   +1 213 7405687
    Email: ijspeert at rana.usc.edu
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_____________________________________________________________________
PhD thesis, A.J. Ijspeert
 
Design of artificial neural oscillatory circuits for the control of
lamprey- and salamander-like locomotion using evolutionary algorithms

Supervisors: John Hallam and David Willshaw

Department of Artificial Intelligence, University of Edinburgh, 1998 
 
Abstract:

This dissertation investigates the evolutionary design of oscillatory
artificial neural networks for the control of animal-like
locomotion. It is inspired by the neural organisation of locomotor
circuitries in vertebrates, and explores in particular the control of
undulatory swimming and walking. The difficulty with designing such
controllers is to find mechanisms which can transform commands
concerning the direction and the speed of motion into the multiple
rhythmic signals sent to the multiple actuators typically involved in
animal-like locomotion. In vertebrates, such control mechanisms are
provided by central pattern generators which are neural circuits
capable of producing the patterns of oscillations necessary for
locomotion without oscillatory input from higher control centres or
from sensory feedback. This thesis explores the space of possible
neural configurations for the control of undulatory locomotion, and
addresses the problem of how biologically plausible neural controllers
can be automatically generated.

Evolutionary algorithms are used to design connectionist models of
central pattern generators for the motion of simulated lampreys and
salamanders. This work is inspired by Ekeberg's neuronal and
mechanical simulation of the lamprey [Ekeberg 93]. The first part of
the thesis consists of developing alternative neural controllers for a
similar mechanical simulation. Using a genetic algorithm and an
incremental approach, a variety of controllers other than the
biological configuration are successfully developed which can control
swimming with at least the same efficiency. The same method is then
used to generate synaptic weights for a controller which has the
observed biological connectivity in order to illustrate how the
genetic algorithm could be used for developing neurobiological
models. Biologically plausible controllers are evolved which better
fit physiological observations than Ekeberg's hand-crafted
model. Finally, in collaboration with Jerome Kodjabachian, swimming
controllers are designed using a developmental encoding scheme, in
which developmental programs are evolved which determine how neurons
divide and get connected to each other on a two-dimensional substrate.

The second part of this dissertation examines the control of
salamander-like swimming and trotting. Salamanders swim like lampreys
but, on the ground, they switch to a trotting gait in which the trunk
performs a standing wave with the nodes at the girdles. Little is
known about the locomotion circuitry of the salamander, but
neurobiologists have hypothesised that it is based on a lamprey-like
organisation. A mechanical simulation of a salamander-like animat is
developed, and neural controllers capable of exhibiting the two types
of gaits are evolved. The controllers are made of two neural
oscillators projecting to the limb motoneurons and to lamprey-like
trunk circuitry. By modulating the tonic input applied to the
networks, the type of gait, the speed and the direction of motion can
be varied.

By developing neural controllers for lamprey- and salamander-like
locomotion, this thesis provides insights into the biological control
of undulatory swimming and walking, and shows how evolutionary
algorithms can be used for developing neurobiological models and for
generating neural controllers for locomotion. Such a method could
potentially be used for designing controllers for swimming or walking
robots, for instance.


_______________________________________________________________________
A.J. Ijspeert, J. Hallam and D. Willshaw: 
Evolving swimming controllers for a simulated lamprey with inspiration
from
neurobiology, 
Adaptive Behavior 7:2, 1999 (in press).

Abstract:
  This paper presents how neural swimming controllers for a simulated
  lamprey can be developed using evolutionary algorithms. A genetic
  algorithm is used for evolving the architecture of a connectionist
  model which determines the muscular activity of a simulated body in
  interaction with water.  This work is inspired by the biological
  model developed by Ekeberg which reproduces the central pattern
  generator observed in the real lamprey \cite{Ekeberg93}. In evolving
  artificial controllers, we demonstrate that a genetic algorithm can
  be an interesting design technique for neural controllers and that
  there exist alternative solutions to the biological connectivity.  A
  variety of neural controllers are evolved which can produce the
  pattern of oscillations necessary for swimming. These patterns can
  be modulated through the external excitation applied to the network
  in order to vary the speed and the direction of swimming.  The best
  evolved controllers cover larger ranges of frequencies, phase lags
  and speeds of swimming than Ekeberg's model.  We also show that the
  same techniques for evolving artificial solutions can be interesting
  tools for developing neurobiological models. In particular,
  biologically plausible controllers can be developed with ranges of
  oscillation frequency much closer to those observed in the real
  lamprey than Ekeberg's hand-crafted model.

  Keywords: Neural control; genetic algorithm; simulation;
  central pattern generator; swimming; lamprey.

_______________________________________________________________________
A.J. Ijspeert, J. Kodjabachian: 
Evolution and development of a central pattern generator for the swimming 
of a lamprey, 
Artificial Life 5:3, 1999 (in press). 

Abstract:

  This paper describes the design of neural control architectures for
  locomotion using an evolutionary approach. Inspired by the central
  pattern generators found in animals, we develop neural controllers
  which can produce the patterns of oscillations necessary for the
  swimming of a simulated lamprey.
  
  This work is inspired by Ekeberg's neuronal and mechanical model of
  a lamprey \cite{Ekeberg93}, and follows experiments in which
  swimming controllers were evolved using a simple encoding scheme
  \cite{Ijspeert99_ab,Ijspeert98_sab}.  Here, controllers are developed
  using an evolutionary algorithm based on the SGOCE encoding
  \cite{Kodjabachian98a,Kodjabachian98b} in which a genetic
  programming approach is used to evolve developmental programs which
  encode the growing of a dynamical neural network.  The developmental
  programs determine how neurons located on a 2D substrate produce new
  cells through cellular division and how they form efferent or
  afferent interconnections.  Swimming controllers are generated when
  the growing networks eventually create connections to the muscles
  located on both sides of the rectangular substrate.  These muscles
  are part of a 2D mechanical simulation of the body of the lamprey in
  interaction with water.

  The motivation of this paper is to develop a method for the design
  of control mechanisms for animal-like locomotion. Such a locomotion
  is characterised by a large number of actuators, a rhythmic
  activity, and the fact that efficient motion is only obtained when
  the actuators are well coordinated. The task of the control
  mechanism is therefore to transform commands concerning the speed
  and direction of motion into the signals sent to the multiple
  actuators. We define a fitness function, based on several
  simulations of the controller with different commands settings,
  which rewards the capacity of modulating the speed and the direction
  of swimming in response to simple, varying input signals. Central
  pattern generators are thus evolved capable of producing the
  relatively complex patterns of oscillations necessary for
  swimming. The best solutions generate travelling waves of neural
  activity, and propagate, similarly to the swimming of a real
  lamprey, undulations of the body from head to tail propelling the
  lamprey forward through water.  By simply varying the amplitude of
  two input signals, the speed and the direction of swimming can be
  modulated.

  Keywords: Neural control; genetic programming; developmental
  encoding; SGOCE; simulation; central pattern generator; swimming;
  lamprey.



________________________________________________________________________
Preliminary results on CPGs for salamander locomotion can be found in:

A.J. Ijspeert: 
Evolution of neural controllers for salamander-like locomotion, 
in McKee, G.T. and Schenker, P.S., Editors, Proceedings of Sensor 
Fusion and Decentralised Control in Robotics Systems II, 
SPIE Proceeding Vol. 3839, September 1999, pp. 168-179. 

Abstract:
This paper presents an experiment in which evolutionary algorithms are
used for the development of neural controllers for salamander
locomotion. The aim of the experiment is to investigate which kind
of neural circuitry can produce the typical swimming and trotting
gaits of the salamander, and to develop a synthetic approach to
neurobiology by using genetic algorithms as design tool. 

A 2D bio-mechanical simulation of the salamander's body is
developed whose muscle contraction is determined by the locomotion
controller simulated as continuous-time neural networks.  While the
connectivity of the neural circuitry underlying locomotion in the
salamander has not been decoded for the moment, the general
organization of the designed neural circuits corresponds to that
hypothesized by neurobiologists for the real animal. In particular,
the locomotion controllers are based on a body {\it central pattern
generator} (CPG) corresponding to a lamprey-like swimming controller
as developed by Ekeberg~\cite{Ekeberg93}, and are extended with a limb
CPG for controlling the salamander's body.  A genetic algorithm is
used to instantiate synaptic weights of the connections within the
limb CPG and from the limb CPG to the body CPG given a high level
description of the desired gaits.  A set of biologically plausible
controllers are thus developed which can produce a neural activity and
locomotion gaits very similar to those observed in the real
salamander. By simply varying the external excitation applied to the
network, the speed, direction and type of gait can be varied.