| In the effort to simulate the biologically inspired continuum robot's dynamic capabilities, researchers have been faced with the daunting task of simulating---in real-time---the complete three dimensional dynamics of the "beam-like" structure which includes the three "stiff" degrees-of-freedom transverse and dilational shear. Therefore, researchers have traditionally limited the difficulty of the problem with simplifying assumptions. This study, however, puts forward a solution which makes no simplifying assumptions and trades off only the real-time requirement of the desired solution.;The solution is a Finite Difference Time Domain method employing an explicit single step method with cheap right hands sides. The cheap right hand sides are the result of a rather ingenious formulation of the classical beam called the Cosserat rod by, first, the Cosserat brothers and, later, Stuart S. Antman which results in five nonlinear but uncoupled equations that require only multiplication and addition. The method is therefore suitable for hardware implementation thus moving the real-time requirement from a software solution to a hardware solution. |
