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Evolutionary Robotics and Open-Ended Design Automation 139

How could a tree representation be used to describe robot morphologies? Top-down construc-
tion of a mechanism starts with an embryonic kinematic basis with the desired number of DoFs,
such as the four-bar mechanism shown in Figure 4.5c. A tree of operators then recursively modifies
that mechanism by replacing single links (DoF ¼ 1, i.e., over-constrained) with assemblies of
links with an equivalent DoF, so that the total number of DoF remains unchanged. Two such
transformations are shown in Figure 4.5c: the D and T operators. The D operator creates a new node
and connects it to both the endpoints of a given link, essentially creating a rigid triangular

Figure 4.5 A language to represent kinematic machines: (a) Top-down and bottom-up trees used to represent
structure, (b) a tree used to represent a kinematic machine; this machine traces a nearly-exact straight line.
These mechanisms can be represented as top-down trees (c), or as bottom-up trees (d). (From Lipson, 2006. With
permission.)