Evolution of synaptic delay based neural controllers for implementing central pattern generators in hexapod robotic structures.


Examples of evolved controllers:


The hexapod is controlled by a recurrent synaptic delay based NN (SDBNN) [2][6]. The bias of each node is defined according to the center-crossing condition [1][3]. Thus, all the nodes will be near the maximum sensitivity regions to induce activation changes.

Example 1: Example of a best evolved SDBNN controller for the hexapod structure when the robot has to climb stairs.



Example 2: Trajectories followed by a hexapod structure when one of the front-most legs has a malfunctioning after t=8 seconds from the beginning. After that time instant the leg ignores the velocity imposed by the corresponding neural controller. The fitness function was the distance traveled in a straight line (in 35 seconds), penalizing it when the robot does not follow a straight trajectory.


(a)  Trajectory using the best evolved CTRNN controller:










(b)  Trajectory using the best evolved synaptic delay based neural network as controller:








Example 3: One of the central legs is fixed and without touching the ground, so the neural controller must automatically reconfigure the activation pattern so that the robot travels using five legs. The imbalance in the number of supporting legs in both sides makes the task more difficult. The video shows the trajectory followed by the hexapod when the right central leg is fixed and raised, between t = 5 and t = 9 seconds from the beginning. The two videos show the same neural controller (SDBNN) with two different camera positions:


FrameInicialPataCentralFijadaDTB frameInicialHexapodoPataCentralFijaVista2


[1]       Beer, R. (1995), "On the Dynamics of Small Continuous Time Recurrent Neural Networks", Adaptive Behaviour 3(4): 469-509.


[2]       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.


[3]       Mathayomchan, B., and Beer, R. (2002), "Center-Crossing Recurrent Neural Networks for the Evolution of Rhythmic Behavior", Neural Computation 14: 2043-2051.


[4]       Floreano , D. and Mattiussi, C. (2008), Bio-Inspired Artificial Intelligence, MIT Press.


[5]       Nolfi, S. and Floreano, D. (2000), Evolutionary Robotics, MIT Press.


[6]       Santos, J. and Duro, R.J. (2001), “Influence of noise on discrete time backpropagation trained networks”, NeuroComputing 41(1-4): 67-89.