Free-Floating Space Robot Arm: Reaction-Coupled Control Simulator

Free-Floating Manipulator

Base inertia (mass ratio) 25

Control gain 4.0

Base drift angle

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True EE error

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Believed EE error

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Status

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Drag the yellow grapple marker to set a target. The arm always mounts on a free-floating spacecraft bus — there is nothing to react against but itself.

How it works

The spacecraft base and its arm form one isolated mechanical system: with no external torques, their total angular momentum about the origin stays exactly zero. Any joint velocity q̇ the arm commands must be balanced by an opposite base spin ω_base, weighted by how the base's inertia compares with each link's:

ω_base = −Σ a_k·q̇_k
a_k = (I_k + I_k+1 + … + I_N) / (I_base + ΣI_i)

That reaction is physical — it happens identically in both controller modes, and you can see the whole spacecraft (bus + solar panels) rotate as the arm moves. The two modes differ only in what the controller assumes:

Naive (fixed-base IK) — solves joint rates from a Jacobian that assumes the base never rotates, exactly like an Earth-mounted arm. It reaches its own believed end-effector position perfectly (dashed ghost arm) — but the real arm, riding a base that actually spun underneath it, ends up somewhere else. The believed error converges to ~0 while the true error stays offset.
Coupled (momentum-aware) — uses the generalized Jacobian J_g = J_std + ω_base-term, which folds the same reaction law directly into the velocity mapping. It drives the real, sensed error to zero, so even though the base drifts by the same physical amount, the arm still lands exactly on target.
Base inertia — a heavier bus reacts less per unit of joint motion (smaller a_k); a light bus drifts dramatically for the same command.

This is the same idea behind the Generalized Jacobian Matrix used for real satellite-servicing and orbital-assembly manipulators (Umetani & Yoshida, 1989): control law must know its own recoil.

Spacecraft base Arm — true position Arm — controller's belief Grapple target (drag)

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