Real-Time Dynamics of Cable-Driven Continuum Robots Considering the Cable Constraint and Friction Effect

In this letter, a novel dynamic model of a cable-driven continuum robot is established based on the principle of virtual power, in which the dynamically centralized length of the driving cable is used to simulate the driving process. This loading model implicitly represents the driving loads and explicitly describes the geometrical constraint of cables on the system. The distribution law for friction forces of actuated cables is demonstrated, which can be handily represented by the derived relationship between the tension of the cables and the Lagrange multiplier. This dynamic model is applicable for continuum robots with a single/multi-tandem arm driven by any number of cables. Furthermore, an average stress strategy is developed so that the high-frequency components of the dynamic model can be reasonably controlled in a simple but effective manner, which can strikingly reduce the stiffness of the differential equations. Simulation results show that this strategy significantly improves the simulation efficiency with sound and reasonable precision. A comparison of the results from the numerical simulations and experiments for a cable-driven continuum structure verifies the validity of the proposed model, and the average percentage error for the trajectory between the simulation and experimental results is 1.92%. Moreover, the numerical simulations for the dynamic equations of the cable-driven continuum robot with twenty segments can be run in real-time.