Analysis

Fig. 8 attempts to represent one of the wall-avoiders in state-transition format. This particular individual used an evolved clock frequency of 9Hz (about twice the sonar pulse repetition rate). Both sonar inputs evolved to be asynchronous, and both motor outputs clocked, but the internal state variable that was clocked to become the left motor output was free-running (asynchronous), whereas that which became the right output was clocked. In the diagram, the dotted state transitions occur as soon as their input combination is present, but the solid transitions only happen when their input combinations are present at the same time as a rising clock edge. Since both motor outputs are synchronous, the state can be thought of as being sampled by the clock to become the motor outputs.

This state-transition representation is misleadingly simple in appearance, because when this DSM is coupled to the input waveforms from the sonars and its environment, its dynamics are subtle, and the strategy being used is not obvious. It is possible to convince oneself that the diagram is consistent with the behaviour, but it would have been very difficult to predict the behaviour from the diagram because of the rich feedback through the environment and sensorimotor systems on which this machine relies. The behaviour even involves a stochastic component, arising from the probabilities of certain combinations of the machine's mixed synchronous/asynchronous state, at the arrival of pulses from the clock and the asynchronous sonars.

Figure 8: A representation of one of the wall-avoiding DSMs. Asynchronous transitions are shown dotted, and synchronous transitions solid. The transitions are labelled with (left, right) sonar input combinations, and those causing no change of state are not shown. There is more to the behaviour than is seen immediately in this state-transition diagram, because it is not entirely a discrete-time system, and its dynamics are tightly coupled to those of the sonars and the rest of the environment.

The DSM underlies a non-trivial robot behaviour, using minimal resources [46], by means of the circuit's rich dynamics and exploitation of the hardware (an idea dating back to 1949 [47]). After relaxing the temporal constraints necessary to support the designers' digital abstraction, a tiny amount of hardware has been able to display rather surprising abilities. As a control experiment, three GA runs were performed under identical conditions, but with all of the optional latches set to `clocked' irrespective of the genotype. All three runs failed completely, confirming that new capabilities had been released from the architecture when the dynamical constraints were relaxed. In another set of three control runs, all the optional latches were set to `unclocked.' These runs succeeded but the behaviour was not so reliable: from time to time the robot would head straight for a wall and crash into it.

In three repetitions of the main experiment, the clock allowed the mixed synchronous/asynchronous controllers to move with a slight `waggle' (just visible in the bottom-right picture in Fig. 7), and this prevented them from being disastrously fooled by specular sonar reflections. The sonars were effectively scanning the walls slightly because of the waggling movement of the robot body. This suggests that while removing an enforced clock can widen the repertoire of dynamical behaviours, providing an optional clock of evolvable frequency, to be used at points in the circuit determined by evolution, can expand the repertoire of dynamics still further. The clock becomes a resource, not a dynamical constraint.