Advanced Robotics: Redundancy and Optimization
Authors: Yoshihiko Nakamura · Year: 1991 · Venue: Addison-Wesley (ISBN 0-201-15198-7; Consulting Editor J. J. Craig) · Raw: md (full book) · pdf
Summary
A graduate monograph on kinematically and actuation-redundant manipulators: differential kinematics, local and global optimization of the redundant DOF, multirobot coordination, and — its most-cited contribution — the singularity-robust (SR) inverse of the Jacobian (Ch. 9). In this corpus it is the provenance for Arc 7 (the 7-DOF arm): the canonical reference for redundancy resolution and for the damped-least-squares inverse used to cross kinematic singularities.
Key Claims
- Singularity-robust inverse (Ch. 9). Replacing with the damped least-squares inverse trades exact task tracking for bounded joint rates through a singularity — the standard tool for singularity-robust redundancy resolution.
- Redundancy as optimization. The self-motion (null-space) freedom of a redundant arm is resolved by local (instantaneous) and global (variational) optimization of a secondary criterion — manipulability, joint-limit avoidance, etc.
- Manipulability. Redundancy and singularity are quantified through the manipulability measure and the Jacobian’s singular values.
Method
Textbook + research monograph: differential-kinematic derivations, pseudoinverse/weighted-inverse algebra, variational optimization, and worked manipulator examples.
Regime note. Classical fixed-base manipulator theory, but the redundancy-resolution and SR-inverse tools are regime-agnostic and carry directly to the free-flying arm (used with the generalized Jacobian in the FFSM setting).
Relevance to thesis
Arc 7 (SevenDof) rests on redundancy resolution for the 7-DOF arm; Nakamura is the textbook root for the null-space / SR-inverse machinery and the manipulability geometry that arc reasons about. This page supplies the resolving bibkey so the arc/lean pages cite the book rather than a plain-text mention.
Connections
Topics: singularity-robust inverse · damped least squares · kinematic redundancy resolution · generalized Jacobian · manipulability measure · reaction null space Sources: chiaverini1994review · umetani1989resolved
Key Equations / Quotes
The author’s own preferred citation, printed on the copyright page:
“Yoshihiko Nakamura. Advanced Robotics: Redundancy and Optimization, Addison-Wesley, 1991.”
Preface (statement of intent):
“This book is intended as a second-level graduate course textbook in robotics and as a research monograph.”
Open Questions
- The corpus PDF is the author’s 2020 re-release (original TeX text + scanned figures). Prose extracts cleanly, but the math is substantially mangled by CID/old-font glyph failures — e.g. σ →
(cid:190), ∈ →2, × →£, Σ →§, ≥ →‚, with flattened super/subscripts (the same failure mode as seibert / khalil per the ctrllib OCR triage). Text-for-search is sound, but equations are not faithful — read them from the PDF. Per corpus policy (reference text) this is flagged, not escalated to VLM OCR.