Technical Controllability

Definition

Technical controllability is a design-level necessary condition on a free-flying space manipulation robot (FSMR): each generalized coordinate $q_i$ must be drivable in the commanded direction and at a prescribed rate by its own bounded actuator, irrespective of the other control actions. Formally (Rutkovskii & Glumov 2023, after Glumov et al. 2001), starting from rest at a configuration $q=q^{\ast }$, applying the maximum control $|M_i|=M_i^{\max }$ to coordinate $i$ (with all $M_j=0,j\ne i$) must produce an acceleration $\Delta {\ddot{q}}_i$ of the same sign as $M_i$ and bounded away from zero. The source proves that whether this holds in a neighborhood of $q^{\ast }$ depends only on the design parameters (mass–inertia geometry) of the mechanical system — not on the control-bound vector $M^{\max }$. This source is genuinely free-flying: the body is actively oriented by gas-jet and electromechanical actuators, so the property concerns both body angular motion and joint motion, not a reactive free-floating base.

Key Equations

Symbols per notation.md.

The robot’s angular motion, linearized about a reference configuration $q^{\ast }$, is
$\mathbf{A}(q^{\ast })\Delta \ddot{\mathbf{q}}=\mathbf{P}(q^{\ast })\mathbf{M}(q),$
where $\mathbf{A}(q^{\ast })\succ 0$ is the configuration inertia (the source’s $A$; the inertia symbol in notation.md is $\mathbf{M}$, so beware the clash — here $\mathbf{M}(q)$ is the source’s control-force vector, not inertia) and $\mathbf{P}(q^{\ast })$ maps controls to generalized forces.

Technical controllability at $q^{\ast }$ requires, for each $i=\overline{1,6}$, from zero initial conditions,
$|M_i(t)|=M_i^{\max }\forall t\ge t_0⟹\mathrm{sign}(\Delta {\ddot{q}}_i(t))=\mathrm{sign}(M_i(t)),\Delta {\ddot{q}}_i(t)\ge {\eta }_i\ne 0,$
independent of $M_j(j\ne i)$, where ${\eta }_i$ are characteristic acceleration values fixed by the mechanism. (The symbol ${\eta }_i$ here is the source’s characteristic acceleration; do not confuse it with the quaternion scalar part $\eta$ in notation.md.) When this condition holds over the whole working domain, the joint-block coupling is negligible and the manipulator inertia block ${\mathbf{A}}_{22}$ may be treated as diagonal.

Source Support

• rutkovskii2023control — defines technical controllability as a necessary performance condition for an FSMR, gives the linearized model (Eq. 3) and the per-coordinate sign/acceleration test (Eq. via ref [18], Glumov et al. 2001), and uses it to justify neglecting inter-joint coupling (diagonal ${\mathbf{A}}_{22}$) during soft installation.

Related Topics

• ffsm_dynamics — technical controllability is a property of the coupled FSMR equations of motion $\mathbf{A}(q)\ddot{\mathbf{q}}=\mathbf{M}(q,u)+\mathbf{F}(q,\dot{\mathbf{q}})$; it certifies that the dynamics are drivable per-coordinate.
• dynamic_coupling — the condition is exactly a guarantee that the off-diagonal (body↔arm, joint↔joint) coupling terms do not overpower a coordinate’s own actuator, so coupling can be neglected where it holds.
• coordinated_control — it underwrites the joint use of gas-jet body actuators and electromechanical joint actuators for angular stabilization (motion exchange between body and links).
• free_floating_dynamics — contrast regime: the source notes the free-floating mode (body orientation control disabled) brings narrowing of the working area and dynamic singularities; technical controllability is asserted for the actuated free-flying mode.
• generalized_jacobian — the free-floating Generalized Jacobian Matrix (GJM) is the kinematic-rank object whose loss of rank is a dynamic singularity; technical controllability is a distinct, dynamics/design-level drivability condition rather than a Jacobian-rank test.
• configuration_dependent_stability_domain — the source pairs technical controllability with a stability domain in joint-angle space used to pick the initial configuration and admissible range during installation.

Open Questions

• The source’s per-coordinate test is built on a simplified angular motion model with small joint rates (Coriolis/centrifugal products ${\dot{q}}_i{\dot{q}}_j$ neglected). How tight is the condition for our fast-cruise inspection trajectories where those terms are not negligible?
• The proof (ref [18]) ties controllability to design parameters alone, not to $M^{\max }$. Does this design-only criterion transfer cleanly to our circumcentroidal coordinate formulation, where the relevant inertia is $\breve{\mathbf{M}}$ rather than the raw ${\mathbf{A}}_{22}$ block?
• Treating ${\mathbf{A}}_{22}$ as diagonal once the condition holds is justified for soft, low-rate installation; is the decoupling assumption safe for our coordinated base+arm tracking, or only for quasi-static placement?