Joint-Angle Invariance of Jacobian-Based Performance Indices for Serial Robotic Manipulators

This paper introduces a twist decomposition framework for serial manipulators performing lower mobility tasks. Rather than relying on Jacobian null-space projections, the method separates the end-effector twist into task and redundant components using geometrically defined twist projectors. This formulation provides a direct and intuitive distinction between task-relevant and task-irrelevant motions in operational space, enabling a compact inverse kinematics scheme that naturally handles both manipulator and task redundancy.

Yoshikawa's Manipulability Index is generally used as a classical measure to define an optimal morphology of a manipulator. However, any such optimization is almost always studied as a purely kinematic quantity in simulation and is rarely validated on hardware. We present a reinforcement-learning framework with RSL-RL PPO that optimizes the morphology of a 2R SCARA-type manipulator arm with Yoshikawa's kinematic manipulability index as a core reward, and the analytically derived closed-form optimum for the circular task is used to verify that our method recovers it. Then the same method is applied to custom elliptical and rectangular paths having no analytical optimum. The RL-optimized morphologies are then transferred to a 2R hardware manipulator to validate its effect in reduction of joint load in the hardware. Compared to the worst morphology, the optimum morphology delivered by our method reduces second joint load by 38.4 +/- 0.6% for the ellipse path and 41.3 +/- 0.3% for the rectangle, and first joint load by 15%.

Traditional robotic hand metrics focus on static properties such as workspace, manipulability, and grasp stability. However, these metrics do not directly measure dexterity under the standard definition in robotic manipulation: the ability to continuously change an object's pose within the hand while maintaining contact from an initial grasp. We introduce Kinematic Rolling Manipulation Ability (KaRMA), a kinematic-only metric for fine manipulation that quantifies reachable in-hand translation and reorientation of a spherical test object within a two-finger precision pinch through feasible rolling motions. KaRMA enforces joint limits, collision constraints, rolling contact, and antipodal force feasibility, then investigates reachable in-hand object poses via breadth-first search over translation and rotation primitives. KaRMA reports three scores: translational coverage (KaRMA-T), rotational coverage (KaRMA-R), and sensitivity to the initial grasp (KaRMA-S). We evaluate KaRMA on 16 widely used robotic hands and compare against static baselines, showing that KaRMA separates hands that rank identically under static proxies, reveals translation-rotation tradeoffs invisible to existing baselines, and is qualitatively consistent with selected published task benchmarks where Jacobian-based metrics can be misleading.