Momentum dumping is the active extraction of linear and angular momentum that a space
manipulator has accumulated — typically from contact with a target — by switching on the base’s external actuators and driving the stored momentum back to zero. In Giordano et
al.’s formulation the system is operated free-floating (fuel-free, base actuators off) for
all contact-free motion; external actuators are turned on only when an impulse leaves a
residual momentum, and they are used solely to bleed it off so the inertial drift is arrested
and the system re-settles at rest (zero residual momentum). Note that momentum dumping alone
does not fix the inertial location: the source reports that after each impulse the system
re-settles at a position farther from the target, and stabilizing the inertial workspace
location requires the separately added CoM-regulation task (eq. 19, fc), not
the dumping law itself (giordano2018workspace). Because
dumping is realized through actuated base force/torque, it presupposes a base that can produce
external wrench — exactly the free-flying capability our system has permanently, rather than
intermittently. Exploiting the triangular CoM/momentum/end-effector dynamics, momentum dumping
and end-effector control run simultaneously, avoiding the controller switching that a pure
free-floating-to-base-position handoff would require.
The angular momentum about the system centroid obeys a pure integrator (eq. 13b), whose input is
the net centroidal torque τc supplied by the base actuators:
L˙=τc.
Momentum dumping is the feedback law that drives the accumulated angular momentum to zero
(eq. 20):
\;\Longrightarrow\; \dot{\boldsymbol{L}} = -\boldsymbol{D}_{L}\,\boldsymbol{L},$$
an asymptotically stable closed loop that extracts the residual momentum after each contact.
> **Notation flags.** The source writes the centroidal angular momentum as $\boldsymbol{h}_r$;
> [notation.md](../notation.md) canonicalizes angular momentum as $\boldsymbol{L}$ (used here).
> The momentum-gain matrix $\boldsymbol{D}_{L}$ (source: $\boldsymbol{D}_{hr}$) is **not** in
> notation.md — coined locally, flagged for central registration. The net centroidal torque
> $\boldsymbol{\tau}_c$ is the actuated dual of $\boldsymbol{L}$ ($\boldsymbol{a}_r=\boldsymbol{I}_\mathcal{C}^{-1}\boldsymbol{\tau}_c$);
> it is realized physically through the base torque $\boldsymbol{\tau}_b$ via the triangular
> actuation map (eq. 27) and is **not** the bare $\boldsymbol{\tau}_b^{\oplus}$ row of notation.md.
## Source Support
- [giordano2018workspace](../sources/giordano2018workspace.md) — derives the triangular
CoM/momentum/end-effector dynamics and the dumping law $\boldsymbol{\tau}_c=-\boldsymbol{D}_{L}\boldsymbol{L}$;
validates on the DLR OOS-Sim that repeated end-effector impulses are each dumped to zero
momentum, and extends the prior momentum-dumping work with simultaneous CoM regulation.
## Related Topics
- [momentum_conservation](momentum_conservation.md) — dumping is its complement: conservation
holds while base actuators are off (free-floating, eqs. 13a–13b homogeneous), and dumping is
the deliberate violation of that invariant once contact injects momentum.
- [reaction_null_space](reaction_null_space.md) — RNS reorients/maneuvers the arm **without**
disturbing base momentum (zero reaction); momentum dumping instead **removes** momentum that
has already accumulated. Complementary tools for the same base-momentum budget.
- [base_disturbance_rejection](base_disturbance_rejection.md) — dumping is one mechanism of base
disturbance management: it rejects the persistent inertial drift a contact would otherwise
leave on the base.
- [coordinated_control](coordinated_control.md) — the triangular structure lets dumping,
CoM regulation, and end-effector tracking be commanded as one coordinated cascade rather than
by switching controllers.
- [momentum_exchange_attitude_control](momentum_exchange_attitude_control.md) — internal
momentum-exchange actuators (wheels/CMGs) saturate as they absorb momentum and themselves need
desaturation; momentum dumping here is the external-actuator counterpart that empties the
whole-system momentum store.
## Open Questions
- Giordano keeps the base actuators **off** in nominal motion and dumps momentum only after
contact (an intermittently-actuated, mostly free-floating policy). For our permanently
free-*flying* base, is intermittent dumping still preferable to continuous momentum
regulation, given that we already pay for an actuated base?
- The dumping experiment shows the CoM drifting farther from its start after each impulse,
driving the arm toward a (near-)singular, low-manipulability configuration around
$t_{\mathrm{sing}}$. How should momentum dumping be co-designed with
[dynamic_singularity](dynamic_singularity.md)-avoidance and CoM regulation so that bleeding
momentum does not push the workspace into a singular pose?
- Residual base **attitude** can accumulate or cancel across impulses (the source notes a
reorientation maneuver may be needed). Can the dumping law be augmented to bound attitude
drift directly rather than leaving it as an after-the-fact reorientation?