White Shark Optimizer Based Time-optimal Trajectory Planning for Supernumerary Robotic Limbs

This paper presents an improved time-optimal trajectory planning algorithm leveraging the White Shark Optimizer (WSO), specifically designed for 6-degree-of-freedom (DOF) Supernumerary Robotic Limbs (SRL). This approach effectively addresses prevalent issues in trajectory planning, including low efficiency, premature convergence, and unstable operation. Beginning with an examination of the SRL's structural peculiarities, an auxiliary joint is incorporated to rectify the coordinate offset, facilitating subsequent inverse kinematics analysis. By utilizing the WSO algorithm, we develop a time- optimal trajectory optimization method within the joint space of the SRL. Moreover, to address the continuity challenges in the terminal movements of the SRL, we introduce a 3-5-3 piecewise polynomial trajectory planning method that integrates both 3degree and 5-degree polynomials. Building on this foundational work, we present an optimization algorithm rooted in WSO to identify the most efficient time trajectory optimization strategy, considering multiple constraints. The effectiveness of the proposed optimization strategy is demonstrated through comprehensive co-simulation. A comparative analysis with current optimization algorithms highlights the advantages of the proposed time-optimal trajectory planning algorithm.