Modeling Hydra Behavior Using Methods Founded in Behavior-Based Robotics

Appendix BRecurrent neural networksANNs are, as the name implies, networks of computational units, called neurons. Anartificial neuron has three basic properties: (1) A number of synaptic weights (weightedlinks) which connects input signals (and bias) to the neuron. (2) An adder that sumsthe weighted inputs. (3) An activation function that limits the output amplitude of theneuron. The activation function can also serve to add non-linearity to the neuron. A modelof an artificial neuron is shown in Fig. B.1.ANNs have been used in various application fields, including image recognition, timeseries prediction, non-linear control problems, and as robotic brains [67]. In cases whereinput-output data is available, specifically in cases where it is difficult to arrive at ananalytical model for the problem, or when such a model simply does not exist, ANNs canbe advantageous, and is then used as a black-box model of the system. RNNs is one kindof ANNs, that make use also of feedback connections between neurons (as opposed tofeedforward neural networks, FFNNs). While FFNNs always generate the same outputfor any given input, the feedback connections provide RNNs with some memory, allowingits output to depend also on previous inputs. ANNs can operate in continuous time orin discrete time. In this project only continuous time RNNs were used, and the relevantequations for these networks will now be presented. For a more thorough review of ANNs,see e.g. [23].B.1 Network equationsAs previously mentioned, the RNNs used in this project operate in continuous time. Thearchitecture of the RNN is such that the neurons are not arranged in layers (as is the57