system_diagram

System Diagram: Free-Flying Space Manipulator

The FFSM structural reference — coordinate frames + system layout. The “what is the system” node of the
wiki, linked from index.md and the GNC orientation rule’s “read these first”. Based on Giordano 2019
RA-L (circumcentroidal coordinated control).

Coordinate Frames

Frame	Body	Role
B	Base spacecraft (large body)	Free-floating ellipsoidal body; origin of position vectors p_bc, p_bj
C	System center of mass	Floats near spacecraft; shifts when arm joints move (reaction coupling)
J	Joint j frame	Intermediate joint frame on the arm; p_bj = vector from B to joint j
E	End effector	Camera mount at arm tip; inspection point
T	Target satellite	Small target body; defines coverage objective

System Layout

graph LR
    subgraph system ["Free-Flying Space Manipulator (Giordano 2019)"]
        B["B — Base Spacecraft\nlarge free-floating body\n(origin of p_bc, p_bj)"]
        C(["C — System COM\np_bc = B→C\nshifts with arm joints"])
        J["J₁…Jₙ — Arm Joints\nn joints, configs q\np_bj = B→joint j"]
        E["E — End Effector\ncamera at arm tip"]

        B -- "arm base\n(joint 1)" --> J
        J -- "joint n → tip" --> E
        B -. "p_bc" .-> C
    end

    T["T — Target Satellite\ncoverage objective"]

    E <-. "inspection orbit\nhelical sweep\nmin Δν_e · max coverage" .-> T

ASCII Fallback (faithful to paper figure)

                         J (joint j frame)
                        /  \
           Joint 2    /      \  Joint j+1 … Joint n
            /        /                            \
  Joint 1  /      p_bj (B→J)                      E (end effector, camera)
   |      /                                              ↕  inspection orbit
   |     C (system COM)  ←— p_bc (B→C)             T (target satellite)
   |    /
  [B] Base Spacecraft
      (origin of all p_b* vectors)

Control Objective

Minimize control effort (joint torques + base thrust) and tracking error (Δν_e)
while maximizing area coverage via a helical inspection orbit around T.

• Coordinated control (Giordano 2019) couples base attitude (B) with arm joints (q)
  through the centroidal frame (C), so arm motion does not disturb base pointing.
• The end effector (E) follows a helical waypoint sequence around T.
• Coverage is marked per FOV-to-surface intersection at each timestep.