Examples of evolved biped controllers using adaptive center-crossing continuous time recurrent neural networks
The biped is controlled by a CTRNN. The bias of each node is adjusted, in each iteration of the recurrent network, to the value that defines the center-crossing condition , as it is moved towards the negative value of the incoming activation at time t. Thereby, all the nodes will be near the maximum sensitivity regions to induce activation changes.
We have used the evolutionary robotics methodology  to obtain the neural controllers. We used a standard genetic algorithm, using a mutation operator and a rank-based method as selection operator. Each CTRNN is codified by a vector that includes the connection weights and the bias and time constants associated to each neuron. With the use of the run-time adaptive biases all the individuals of the genetic population present a rhythmic behavior, so the genetic algorithm has more NNs to fine-tune, obtaining higher fitness controllers in fewer generations.
Example of a locomotion behavior obtained by means of the GA (displayed with two different speeds):
In addition, the coefficient for bias adaptation determines how fast each node is moved to the center-crossing condition. So, higher values in the coefficient can force cyclic behaviors with shorter periods, and vice-versa. Hence, the rhythmic of the locomotion behavior can be adjusted dynamically, providing a form of external control. The next videos correspond to different biped behaviors with such control of the coefficient.
The figures show several runs obtained training the CTRNN with different adaptation coefficients. We can observe the differences of the gait between them, with lower coefficient we appreciate a longest step and, as we increase the coefficient, the period of the rhythmic behavior decreases showing a more human walking behavior.
More information in:
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.
Campo, A. and Santos, J. (2010), “Evolution of adaptive center-crossing continuous time recurrent neural networks for biped robot control”, Procc. European Symposium on Artificial Neural Networks (ESANN 2010), pp. 535-540.