terminology

Terminology & Acronyms

Canonical definitions for terms and acronyms used across the wiki. One line each. Coined terms go
here too. Keep consistent with notation.md. review: draft — verify and flip.

Acronyms

Acronym	Expansion	One-line meaning
FFSM	Free-Flying Space Manipulator	a manipulator on a fully-actuated 6-DOF base — distinct from free-floating
GJM	Generalized Jacobian Matrix	maps joint rates to EE motion accounting for base reaction (Umetani & Yoshida 1989); a free-floating construct
RNS	Reaction Null-Space	joint motions producing zero reaction on the base
RMRC	Resolved Motion Rate Control	velocity-level inverse-kinematics control
NBV	Next-Best-View	choosing the next sensor viewpoint to maximize information
OOS	On-Orbit Servicing	—
CVaR	Conditional Value-at-Risk	expected loss in the worst $(1-\alpha )$ tail; a coherent risk measure
OCP	Optimal Control Problem	—
NMPC	Nonlinear Model Predictive Control	—
SVD	Singular Value Decomposition	$\mathbf{\Gamma }={\sum }_i{s}_i{\mathbf{u}}_i{\mathbf{v}}_i^{\top }$; conditioning diagnosis
SLERP	Spherical Linear intERPolation	geodesic interpolation between two rotations

Terms

Term	Definition
Free-flying	base is fully actuated (6-DOF); the regime of this thesis
Free-floating	base is uncontrolled; arm motion is compensated by reaction on the base (contrast with free-flying)
Circumcentroidal	describing motion of the end-effector about the system CoM $\mathcal{C}$ (the $\oplus$ quantities); Giordano’s coordinate split that decouples the CoM from the attitude+EE dynamics
Dynamic singularity	configuration where the generalized Jacobian loses rank (depends on dynamics/inertia), unlike a kinematic singularity
Dynamic coupling	the interaction by which arm motion disturbs base pose/attitude (and vice versa)
Hat vs breve matrices	$\widehat{(\cdot )}$ = full $12\times 12$ transformed ($\hat{\mathbf{M}}={\mathbf{\Gamma }}^{-T}\mathbf{M}{\mathbf{\Gamma }}^{-1}$); $\breve{(\cdot )}$ = the reduced $9\times 9$ attitude+EE block after the $3\times 3$ CoM decouples — see circumcentroidal_decoupling
POSE mode	camera looks directly at the scheduled surface point (default; achieves complete coverage)
ANCHOR mode	the scorer chooses the final aim point (retained for risk-aware planning)
Tikhonov regularization	damped least-squares inverse $({\mathbf{\Gamma }}^{\top }\mathbf{\Gamma }+\lambda \mathbf{I}{)}^{-1}{\mathbf{\Gamma }}^{\top }$; here with Chiaverini variable damping
Impedance derate	scaling the control gains (${\mathbf{K}}_e,{\mathbf{D}}_e,{\mathbf{\tau }}_b^{\oplus }$) by $\gamma ({\sigma }_G)$ near singularity — yields an emergent slowdown; distinct from a literal speed derate (throttling the command), which cannot beat the amplification bound
Cruise-lag / error floor	the standing steady-state pose error ${\tilde{\mathbf{x}}}_{ss}$ the outer loop must hold while cruising — see steady_state_error_floor
Threshold cascade	the three singularity thresholds ${\sigma }_{\mathrm{crit},1/2/3}$ threaded from one velocity budget — see singularity_threshold_cascade
Hold-last (freeze)	below ${\sigma }_{\mathrm{crit},3}$, freeze the ${\mathbf{J}}^{\oplus }$/$\mathbf{\Gamma }$ inverse at its last good value
Self-motion (null-space)	the redundant-DOF reconstruction in the 7-DOF case; frozen below $\sim 10^{-3}$ where it swings violently
Standoff	the camera offset $r_{\mathrm{cam}}$ along $\hat{\mathbf{r}}$ from the aim point
Versine pointing error	pointing error reported as $1-\cos \theta =1-\hat{\mathbf{z}}\cdot {\hat{\mathbf{z}}}_{\mathrm{des}}$ (an angle), never a raw vector difference

Add terms as they arise during ingestion. Coined terms also propagate to the thesis glossary.