Durability-Aware Trajectory Planning and Quasi-Static Control of a Continuum Parallel Robot for Industrial Applications

This paper addresses durability-aware trajectory planning and tracking strategies for the motion of the platform in an extensible planar tendon-actuated continuum parallel robot (CPR). The proposed planning approach combines the A* algorithm with the Geometric Variable Strain (GVS) static Cosserat rod model, incorporating a durability-related cost alongside Euclidean distance to enhance the durability of the robot's legs in pick-and-place applications. Simulation results demonstrate a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$23\%$</tex-math></inline-formula> reduction in the durability-related cost compared to the shortest-path trajectory. Additionally, the same GVS static model is used to extend the classical Jacobian-based controller to the CPR case, with multiple legs geometrically constrained, for precise and robust quasi-static tracking of the planned trajectories. Experimental validation is conducted under nominal conditions and in the presence of external disturbances, including end-effector loading and temporary manual perturbations, demonstrating the effectiveness and robustness of the proposed strategies, achieving a mean tracking error below <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$0.84\%$</tex-math></inline-formula> and a maximum error below <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$4.2\%$</tex-math></inline-formula>, with respect to the length of the CPR leg.