  Multisection continuum arms offer complementary characteristics to those of
traditional rigid-bodied robots. Inspired by biological appendages, such as
elephant trunks and octopus arms, these robots trade rigidity for compliance,
accuracy for safety, and therefore exhibit strong potential for applications in
human-occupied spaces. Prior work has demonstrated their superiority in
operation in congested spaces and manipulation of irregularly-shaped objects.
However, they are yet to be widely applied outside laboratory spaces. One key
reason is that, due to compliance, they are difficult to control. Sophisticated
and numerically efficient dynamic models are a necessity to implement dynamic
control. In this paper, we propose a novel, numerically stable, center of
gravity-based dynamic model for variable-length multisection continuum arms.
The model can accommodate continuum robots having any number of sections with
varying physical dimensions. The dynamic algorithm is of O(n2) complexity, runs
at 9.5 kHz, simulates 6-8 times faster than real-time for a three-section
continuum robot, and therefore is ideally suited for real-time control
implementations. The model accuracy is validated numerically against an
integral-dynamic model proposed by the authors and experimentally for a
three-section, pneumatically actuated variable-length multisection continuum
arm. This is the first sub real-time dynamic model based on a smooth continuous
deformation model for variable-length multisection continuum arms.
