Rapid Computation of Optimally Safe Tension Distributions for Parallel Cable-Driven Robots

In this paper, we present a novel linear-program formulation that yields optimally safe (OS) tension distributions in parallel cable-driven robots by the introduction of a slack variable. The slack variable also enables explicit computation of a near-optimal, feasible starting point. This, in turn, enables rapid computation of the OS tension distributions. The formulation also contains a parameter that can be used to steer cable tensions toward desired regions of operation. We present static results from two simulated robotic systems that demonstrate the ability of our formulation to avoid tension limits. Simulated execution of highly dynamic trajectories on both systems demonstrates rapid-computation abilities. Furthermore, we present experimental results from a real robotic system that further validate the importance of safe tension distributions.