Center of Gravity-based Approach for Modeling Dynamics of Multisection Continuum Arms

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.