Examples of evolved center-crossing recurrent synaptic delay based NN controllers
The biped is controlled by a recurrent synaptic delay based NN . The bias of each node is defined according to the center-crossing condition . Thus, all the nodes will be near the maximum sensitivity regions to induce activation changes.
The evolutionary robotics methodology  was used to obtain the neural controllers. A standard genetic algorithm was employed, using a mutation operator and a rank-based method as selection operator. Each synaptic delay based NN is codified by a vector that includes the connection weights, the temporal delays and the biases of the output neurons.
Example of locomotion behaviors on a flat surface and obtained by means of the GA, showing the effect of selecting different intervals for the time constants of the output nodes. In all the videos the original speed was divided by 4.
Example 1: Locomotion behavior using time constants in the output nodes between 0.5 and 2.5, whereas the time delays of the NN connections are in the range [0,25]:
Example 2: Locomotion behavior using time constants in the output nodes between 2.5 and 5.0, whereas the time delays of the NN connections are in the range [0,50]:
Example 3: Locomotion behavior obtained with the robot on a slope. Time constants in the output nodes are in the range [0.5,5], time delays of the NN connections are in the range [0,50]:
<![if !supportLists]> <![endif]>Beer, R. (1995), "On the Dynamics of Small Continuous Time Recurrent Neural Networks", Adaptive Behaviour 3(4): 469-509.
<![if !supportLists]> <![endif]>Duro, R.J. and Santos, J. (1999), “Discrete time backpropagation for training synaptic delay based artificial neural networks”, IEEE Transactions on Neural Networks 10(4): 779-789.
<![if !supportLists]> <![endif]>Mathayomchan, B., and Beer, R. (2002), "Center-Crossing Recurrent Neural Networks for the Evolution of Rhythmic Behavior", Neural Computation 14: 2043-2051.
<![if !supportLists]> <![endif]>Floreano , D. and Mattiussi, C. (2008), Bio-Inspired Artificial Intelligence, MIT Press.
<![if !supportLists]> <![endif]>Nolfi, S. and Floreano, D. (2000), Evolutionary Robotics, MIT Press.
<![if !supportLists]> <![endif]>Santos, J. and Duro, R.J. (2001), “Influence of noise on discrete time backpropagation trained networks”, NeuroComputing 41(1-4): 67-89.
More information in:
Santos, J. (2014), “Evolutionary algorithms to automatically obtain central pattern generators for biped and hexapod robotic structures”, Workshop on Nature-Inspired Techniques for Robotics, Parallel Problem Solving form Nature - PPSN 2014.
Santos, J. (2013), “Evolved center-crossing recurrent synaptic delay based neural networks for biped locomotion control”, Proceedings IEEE Congress on Evolutionary Computation - IEEE-CEC 2013, 142-148.
Santos, J. and A. Campo, A. (2012), “Biped locomotion control with evolved adaptive center-crossing continuous time recurrent neural networks”, Neurocomputing 86(1):86-96.