ファイバー正規化可操作性と行列式代理指標：タスクファイバー間および内での内在的冗長性最適化

原文アブストラクト

This work establishes that determinant-based manipulability is an exact objective for fixed-task redundancy optimization, despite its dependence on task coordinates and the choice of task-space metric used for volume measurement. On every regular task fiber, the determinant proxy, its representation in any task chart, and every metric-completed manipulability differ only by positive constants. They consequently induce the same complete ordering, constrained extrema, gradient directions, critical points, and local optimality classifications. For comparisons and trajectory optimization across task fibers, this work introduces fiber-normalized manipulability: the capability attained at an internal state divided by the best capability available on the same fiber. The resulting dimensionless scalar is invariant under coordinate changes on the internal-state and task manifolds and independent of the task-space metric. Its associated loss provides an intrinsic objective for physically admissible cross-fiber trajectories, including problems with prescribed or free task evolution and temporal coupling. Planar-manipulator and redundant aerodynamic-allocation examples demonstrate fixed-fiber equivalence, task-dependent cross-fiber differences, and invariant fiber-normalized trajectory optimization.