Hierarchical Organization of Robots
The testbed model represents the environment by a digit string s of arbitrary length s and arbitrary number base. There is also a digit string a of arbitrary length a but the same number base as the environment string which represents actions. The digits of the action string can be either positive or negative. The digits of the environment string are non-negative.
There is an as matrix S, the elements of which are of the same number base and can be positive or negative such that the {i,j}th element is the effect on the jth digit of the environment string of a unit value of the ith digit of the action string. An ss matrix T is the matrix of elements sjk, the change in the kth digit of the state string as a result of a unit change in the jth digit. In simulation experiments, we have also allowed for a small probability of mutation in any of the state-string digits.
All matrices are generated at random at the start of each simulation. The probability of non-zero elements in each matrix is user-determined for each run. A higher probability of a non-zero element in the matrix S implies a greater degree of interconnectivity between an action and different aspects of the environment since more state-string digits are affected by some actions. Similarly, a higher probability of elements taking non-zero values in the matrix T implies greater interconnectivity among the different aspects of the environment. Consequently, actions change one or more aspects of the environment which then affect one another.
At the start of each simulation, either a state string is generated at random or specified by the model operator. In either case, that initial value is taken as the target value which all agents seek to maintain.
In the simulation models, the agents are able to observe a subset of the state digits the size of which is determined by the user and is, typically, less than the length of the state string. The change each task cycle in the state string is
(1)
Substituting recursively into the second term on the right,
(2)
At period 0, the change from the "previous" period is 0 and so at period T, the change in the state string is
(3)
For number bases greater than 2, it frequently happens that the smallest change in the value of a state string digit consequent upon a unit change in any action is greater than the deviation of the value of that digit from its target value. Agents therefore have to find a sequence of actions which, taking account of interactions among state digits, re-establish the target values or, at least, achieve some minimal difference between the target and the observed values. Since some of the state digits are not observable by the agents, their responses to environmental changes necessarily take place in conditions of limited understanding of the environmental processes involved.
The simulations were implemented in SDML, a logic-based language optimized for the implementation of multi-agent models in structured environments and communicating with one another. In this model, agents were organized into one or more hierarchically structured groups. Some agents were assigned to observe particular digits and to plan and undertake actions to correct any discrepancies between the target values and the observed values of those digits. Initial domain knowledge included knowledge of the actions which would directly (but not indirectly) change the values of the digits they observed.
Every group of agents had a chief executive whose sole responsibility was to set the organizational structure of the group by assigning some individuals to observe-and-act and others to supervise two or more other agents. Both the organizational structure and the task assignments could be changed at each "date" comprised of four task cycles each.
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