272 CATALYZING INQUIRY
For example, variation in a species results from mutations (involving random changes to a genome)
and crossovers (involving exchanges of different parts of existing genomes). One hypothesis is that
crossovers result in changes that are much more rapid than those driven by mutation. The argument in
favor of this is that genomic exchange is in some sense enabling an organism to build on stable substruc-
tures. On the other hand, it may be that evolutionary solutions cannot make good use of existing
substructures or that crossover is incapable of integrating existing substructures.
If it is true that evolutionary change is more rapid with crossovers than with mutations, this
suggests that programs designed to evolve genetic programs may wish to emphasize crossover in their
processes for introducing variation.
8.3.2 Robotics 3: Energy and Compliance Management,
Biological systems provide an existence proof that self-effected motion is possible. Furthermore,
compared to the locomotion made possible by human engineering, biological mechanisms capable of
locomotion appear to be energetically efficient, possible in a wide variety of physical environments, and
often small in size.
Given these characteristics, it is not unreasonable to ask what lessons biology might hold for the
design of engineered systems for locomotion. For example, one reason that biological systems are
energetically efficient is that they are not rigid, but rather compliant, and often have mechanisms for
energy recovery. That is, these mechanisms store kinetic energy that might otherwise be dissipated,
much as a braking electric car can store in batteries the kinetic energy associated with slowing down. A
kangaroo employs such a mechanism in its tail, which acts as a spring that compresses as the kangaroo
lands from one jump and then assists the kangaroo in pushing off for the next jump. Full has argued that
leg locomotion can be described as a point mass attached to a spring and finds that the ratio of relative
leg stiffness^67 to body mass is more or less constant across legged animals spanning a wide range of
size.^68 In this context, leg musculature functions not just as a source of power but also as an actuator, a
springy “strut” that participates in energy absorption, storage, and return.
A second example is that many-legged animals demonstrate an inherent dynamic stability. Con-
trary to expectations that locomotion would require complex neural control feedback mechanisms, the
structure of the leg itself and its inherent multifunctionality provide a key aspect of the control of the
system and the combination of stability and forward momentum needed for locomotion. Indeed, analy-
sis of many-legged animals reveals that this inherent stability arises from the production of large lateral
and opposing leg forces when the legs are moving. Modeling these forces as a spring between opposing
legs reveals that the system is highly stable against perturbations—and the leg assembly is capable of
stabilizing itself without any equivalent of neural reflexes at all. Thus, the animal does not need to
devote expensive neurological processing to the supervision of locomotive tasks.
Raibert was one of the pioneers of robotics engineering based on physics-inspired control laws—
one for height, one for pitch, and one for speed. A fundamental insight was that running animals make
use of dynamic stability—a running animal moving forward is out of balance, but legs move forward in
rhythm to break its fall. To model this phenomenon, a one-legged “animal” (the “Planar One-legged
Hopper”) was created. It consisted of a mechanized pogo stick with a three-part control system—one
controlling forward running speed, one controlling body attitude, and one controlling hopping height.
Stepping motion was not programmed explicitly, but rather emerged under the constraints of balance
(^67) Relative leg stiffness is the weight-normalized, size-normalized spring constant of the leg.
(^68) R. Blickhan and R.J. Full, “Similarity in Multilegged Locomotion: Bouncing Like a Monopode,” Journal of Comparative Physi-
ology 173:509-517, 1993; T.M. Kubow and R.J. Full, “The Role of the Mechanical System in Control: A Hypothesis of Self-stabiliza-
tion in Hexapedal Runners,” Philosophical Transactions of the Royal Society of London B 354:849-862, 1999; A. Altendorfer et al.,
“RHex: A Biologically Inspired Hexapod Runner,” Journal of Autonomous Robots 11:207-213, 2002.