DYNAMIC-SENSITIVITY-GUIDED TRAJECTORY OPTIMIZATION OF A REDUNDANT 7-DOF MANIPULATOR UNDER DYNAMIC-PARAMETER UNCERTAINTY

Abstract

Dynamic-parameter uncertainty can significantly affect the torque response and robustness of redundant robotic manipulators, particularly when trajectory generation does not account for variations in inertial properties. This study proposes a dynamic-sensitivity-guided trajectory optimization framework for a redundant 7-DOF Franka Emika Panda manipulator. The proposed method first evaluates the sensitivity of the manipulator torque response to 49 dynamic parameters, comprising seven link masses and 42 inertia terms. The sensitivity analysis identifies five dominant link masses that account for 98.67% of the total mean sensitivity and are subsequently used to construct a Dynamic Uncertainty Sensitivity Index (DUSI). Redundancy is exploited through a null-space coordinate represented by a cubic B-spline, allowing the joint trajectory to be modified while maintaining the desired Cartesian motion. The trajectory is optimized using a constrained nonlinear programming formulation that minimizes the normalized mean DUSI and jerk, while imposing limits on the DUSI upper tail, mechanical work, joint motion, and Cartesian position error. For the nominal 5-s trajectory, the optimized solution reduces the mean DUSI by 0.129% and RMS jerk by 3.34%, with a 3.36% increase in absolute mechanical work. The DUSI 95th percentile increases by only 0.007%, remaining within the imposed tolerance. Monte Carlo validation using 1000 paired realizations of ±5% dynamic-parameter uncertainty shows a 0.197% reduction in mean RMS relative torque deviation, with the optimized trajectory performing better in 91.7% of paired trials. The results demonstrate that dynamic sensitivity can provide a quantitative basis for exploiting redundancy to obtain small but statistically consistent improvements in trajectory robustness.