A Combined Planning Method Based on Biarc Curve and Bézier Curve for Concentric Cable-Driven Manipulators Working in Confined Environments

The concentric cable-driven manipulator is becoming increasingly important in minimally invasive surgery. Obviously, one of the basic requirements is to track trajectory and avoid collision at the same time. However, the unavoidable difficulty is to choose an inverse kinematics solution that fits inside the confined environment from infinitely many solutions due to its redundancy. This article proposes a combined planning method based on biarc curve and Bézier curve for the concentric cable-driven manipulator tracking desired trajectory in confined 2-D and 3-D. First, the new proposed structure and the nomenclature are introduced. Then, the kinematic modeling of the concentric cable-driven manipulator in actuator space, configuration space, and task space is detailed. Thereafter, using the proposed biarc curve, the relationship between the end direction and bending angles is comprehensively analyzed. The Bézier curve is then adopted to plan the desired path for the concentric cable-driven manipulator moving in confined 2-D and 3-D environments. Finally, the proposed combined planning method based on biarc curve and Bézier curve is experimentally verified in a trajectory tracking task simulating a large intestine examination in both the typical “C” configuration (2-D environment) and the “S” configuration (3-D environment). The results prove that the combined planning method based on biarc curve and Bézier curve can be applied to generate a reasonable solution for concentric cable-driven manipulators that are confined both 2-D and 3-D environments.