rutkovskii2023control

Control of a Free-Flying Space Manipulation Robot with a Payload

Authors: Rutkovskii, Glumov · Year: 2023 · Venue: Automation and Remote Control (Avtomatika i Telemekhanika), DOI 10.1134/S0005117923100090
Raw: md

Summary

The paper treats a free-FLYING space manipulation robot (FSMR: actuated platform with gas-jet engines plus an electromechanically driven multi-link arm) that transports and installs a heavy building element on a large space structure (LSS). Its central contribution is twofold: (i) a “cost-efficient” angular-stabilization scheme that conserves gas-jet working fluid by exchanging momentum between the body and the manipulator links via the arm’s electromechanical actuators (with an unloading mode that resets the arm using the jets), and (ii) a stability analysis for the soft-installation phase that yields an explicit stability domain in the joint-angle space $({\alpha }_1,{\alpha }_2)$ used to pick the initial manipulator configuration and admissible joint excursions.

Key Claims

• Body angular stabilization can be achieved by torquing the manipulator links (motion exchange between body and arm) instead of firing the gas-jet nozzles, recovering electrical energy and saving working fluid; the jets are only needed during the “unloading mode” that returns the arm to its initial configuration ${\alpha }_i(t)\to {\alpha }_i^{\ast }$ when joint limits are reached.
• For the linearized soft-installation model, the endpoint-error dynamics $({\ddot{X}}_{\epsilon },{\ddot{Y}}_{\epsilon })$ are governed by a configuration-dependent coupling matrix $d_{ij}(q)$; certain link positions make $d_{ij}(q)\le 0$, causing instability of $X_{\epsilon },Y_{\epsilon }$.
• A necessary stability condition for the PD-controlled installation is $\Delta d=k_{0x}{k}_{0y}(d_{11}{d}_{22}-d_{12}{d}_{21})>0$ together with sign conditions $\mathrm{sgn}{d}_{11}\ne \mathrm{sgn}{k}_{0x}$ and $\mathrm{sgn}{d}_{22}\ne \mathrm{sgn}{k}_{0y}$; $\Delta d>0$ is independent of the gains and depends only on the sign/magnitude relations among the $d_{ij}$ (Eq. 14).
• Increasing the positive body-attitude angle $\vartheta$ shrinks the stability domain ($\Delta d>0$), reducing the admissible range of ${\alpha }_1,{\alpha }_2$ during installation; the gripper angle ${\alpha }_3$ has a comparatively small effect on the domain boundaries.
• Controllability (“technical controllability”) of the FSMR near a configuration $q=q^{\ast }$ is determined only by the robot’s mechanical design parameters, not by the control-magnitude constraints $M^{\max }$ (citing the authors’ earlier theorem).

Method

A planar FSMR with one three-link manipulator is modeled. Body generalized coordinates $q_K=(X_0,Y_0,\vartheta {)}^T$ and joint angles $q_{\alpha }=({\alpha }_1,{\alpha }_2,{\alpha }_3{)}^T$ assemble into $q=(q_K,q_{\alpha }{)}^T$. The full dynamics are

A(q)\ddot q = M(q,u) + F(q,\dot q) \tag{1}

with $A(q)\in {\mathbb{R}}^{6\times 6}$ partitioned into body block $A_{11}$, arm block $A_{22}$, and the body-arm dynamic-coupling blocks $A_{12}=A_{21}$; $M=(M_K,M_{\alpha }{)}^T$ split into jet/body actions $M_K$ and joint torques $M_{\alpha }$; $F=(f_K,f_{\alpha }{)}^T$ the Coriolis/centrifugal terms. DC-motor actuator dynamics (Eq. 2) and self-braking gears (which delete an arm equation, reducing system order by $2r$) are included.

Regime — this is free-FLYING, not free-floating. The platform attitude is actively controlled. The authors explicitly contrast their approach with the free-FLOATING mode (body attitude control disabled), which they note suffers from a narrowed workspace and dynamic singularities [their refs 10, 11 = Yoshida/Umetani, Papadopoulos/Dubowsky]. The paper deliberately keeps the base actuated and uses arm-body momentum exchange to economize jet fuel — a hybrid that is neither pure free-flying-by-jets nor free-floating.

For trajectory motion, with cost-efficient control driven first by the shoulder torque $M_{\alpha 1}$ only, a reduced model (Eq. 4) gives the attitude scalar dynamics

\ddot\vartheta = k_0\big(k_\alpha M_{\alpha1} + k_d M_\vartheta^d + k_y F_y\big), \tag{5}

with $k_0=(\det [A_1(q)]{)}^{-1}$ and the $k$-coefficients defined as algebraic cofactors of $A_1(q)$. A PD-like stabilizing law $M_{\alpha 1}=-{\tilde{k}}_0{k}_A(\vartheta +k_{\dot{\vartheta }}\dot{\vartheta })$ (Eq. 6) yields a closed loop (Eq. 7) made constant-coefficient by the stationarity condition ${\tilde{k}}_0(t){\overline{k}}_{\alpha }({\alpha }_1,\lambda )=K$ (Eq. 8). The implementing voltage law (Eq. 9) feeds the shoulder actuator. The unloading mode is analyzed on the $(\vartheta ,\dot{\vartheta })$ phase plane via limit cycles ${\Gamma }_0\to {\Gamma }_1\to {\Gamma }_0$ (Fig. 1).

For installation (working area), neglecting small-velocity nonlinear terms and using self-braking so $A_{r,21}=0$, the model reduces to $A_r(q)\ddot{q}=M(q,u)$ (Eq. 11), giving the endpoint-error dynamics (Eq. 12) with coupling coefficients $d_{ij}(q)$ (transcribed below). PD laws (Eq. 13) close the loop and the quartic characteristic polynomial ${\sum }_{j=0}^4{c}_j{\lambda }^j=0$ provides the stability domain (Eq. 14).

Relevance to thesis

Directly on-target: this is a genuinely free-FLYING (fully-actuated-base) manipulator, the same regime as our thesis, and it tackles guidance/control during a contact-adjacent installation task with a massive payload. The momentum-exchange idea — using the arm to stabilize attitude and reserve jet fuel — is a concrete coordinated-control strategy worth comparing against. The configuration-dependent coupling matrix $d_{ij}(q)$ and its sign-based stability domain $\Delta d>0$ give a clean, transcribable criterion for safe joint excursions, which maps naturally onto our risk/feasibility layer (admissible-region planning). The explicit observation that body attitude $\vartheta$ contracts the stability domain is a useful coupling fact. Caveats for our use: planar, single 3-link arm, linearized small-velocity regime, and reliance on the authors’ own “technical controllability” framework rather than standard generalized-Jacobian formulations.

Connections

Topics: free_flying_vs_free_floating, dynamic_coupling, momentum_exchange_attitude_control, configuration_dependent_stability_domain, technical_controllability

Key Equations / Quotes

“When controlling an FSMR in its working area in the free-floating mode (i.e., the angular position control system of the robot body is disabled), the challenges include the narrowing of the working area and the presence of dynamic singularities.” (Sec. 1)

“It is proposed to save the working fluid of the gas-jet engines of the robot body when moving along the trajectory by using the mobility of a manipulator with electromechanical drives for the angular stabilization of the mechanical ‘robot–transported element’ system.” (Abstract)

Endpoint-error dynamics in the installation mode (Eq. 12):

${\ddot{X}}_{\epsilon }=d_{11}(q)M_{\alpha 1}+d_{12}(q)M_{\alpha 2},{\ddot{Y}}_{\epsilon }=d_{21}(q)M_{\alpha 1}+d_{22}(q)M_{\alpha 2}.$

Stability conditions for the gain-independent factor $\Delta d>0$ (Eq. 14):

$(\mathrm{sgn}{d}_{11}\ne \mathrm{sgn}{d}_{22}\wedge \mathrm{sgn}{d}_{12}=\mathrm{sgn}{d}_{21})\vee (\mathrm{sgn}{d}_{11}=\mathrm{sgn}{d}_{22}\wedge \mathrm{sgn}{d}_{12}\ne \mathrm{sgn}{d}_{21});$
$(\mathrm{sgn}{d}_{11}=\mathrm{sgn}{d}_{22}\wedge \mathrm{sgn}{d}_{12}=\mathrm{sgn}{d}_{21}\wedge |d_{11}{d}_{22}|>|d_{12}{d}_{21}|)$
$\vee (\mathrm{sgn}{d}_{11}\ne \mathrm{sgn}{d}_{22}\wedge \mathrm{sgn}{d}_{12}\ne \mathrm{sgn}{d}_{21}\wedge |d_{11}{d}_{22}|<|d_{12}{d}_{21}|).$

Open Questions

• The development is planar with a single 3-link arm; how do the $d_{ij}(q)$ sign conditions and the body-attitude/stability-domain coupling generalize to a spatial 6-DOF base with a 6/7-DOF arm?
• The “technical controllability” theorem (ref 18) underpins the diagonal-$A_{22}$ approximation and the cofactor coefficients but is not reproduced here — what are its precise hypotheses relative to standard controllability/Jacobian-rank conditions?
• Contact/impact during “soft installation” of a payload heavier than the manipulator is asserted but the contact model is not given; how is contact force regulated, and is the linearized small-velocity model valid through contact transients?
• Energy recovery from the electromechanical drives is claimed as the fuel-saving mechanism, but no quantitative fuel-vs-energy budget is provided.