On the Use of Tension Transition Zones for Kinematic and Compliance Performance Analysis of Wire-actuated Continuum Robots

Wire-actuated/tendon-actuated mechanisms suffer from discontinuity in their performance measures stemming from the limitation of unilateral actuation due to tendon actuation (pull-only actuation). Using traditional Jacobian-based performance measures ignores these limitations and can under-estimate the expected position/orientation (pose) uncertainty for a given design. In this paper, we put forth the notion of wire-tension transition zones, and we illustrate how these tension transition zones can be used to modify the definition of the traditional Jacobian when calculating the expected robot performance in terms of dexterity, end-effector pose uncertainty, and compliance. We use wire-actuated continuum robots as an illustrative robot architecture. We compare the expected performance of three-wire vs. four-wire designs while considering somewhat realistic design parameters drawn from surgical robotics as an application domain. The results of our simulation studies emphasize the importance of carefully using the reduced Jacobin with tension transition zones to capture the performance measure discontinuities due to wires/tendons going slack. Furthermore, the results show that the traditional approach underestimates the uncertainty in the position of the end-effector by as much as 50% (effects of joint-level uncertainty) and 206% (compliance performance analysis) in the case of a three-wire design alternative. We believe that this contribution supports medical robotic system designers in architecture selection and comparative design performance analysis while avoiding unpleasant surprises that would otherwise be encountered if traditional performance measures were used.