Coordination of thrusters, reaction wheels, and arm in orbital robots
Authors: Giordano, Dietrich, Ott, Albu-Schäffer · Year: 2020 · Venue: Robotics and Autonomous Systems (Elsevier)
Raw: md
Summary
The paper develops a fuel-efficient, continuous coordinated controller for a spacecraft-mounted manipulator equipped with three heterogeneous actuator sets: thrusters, reaction wheels (RWs), and arm joint drives. A dynamics transformation decouples the external (momentum/center-of-mass) motion from the internal (end-effector and base-attitude) motion and produces a triangular control-allocation structure in which thrusters are commanded only to regulate the position of the center of mass (CoM) of the whole robot and to dump angular momentum, never to perform end-effector or attitude tasks. Consequently the strategy ideally consumes zero fuel during contact-free maneuvering, activating thrusters automatically only after contact, and the closed loop is proven asymptotically stable. The method is validated on DLR’s OOS-Sim hardware-in-the-loop facility (7-DOF arm on a 6-DOF simulated spacecraft) and in numerical simulation with 24 discrete PWM thrusters.
Key Claims
- A CoM-control strategy (regulating the CoM of the whole robot) yields ideally zero thruster firing during the pre-contact phase, because the CoM is naturally conserved when momentum is zero; this is contrasted with base-control strategies (e.g. [31]) that must continuously fire thrusters to hold base translation.
- The dynamics transformation Γ̌ produces a triangular actuator-allocation matrix (Eq. 36) in which the thruster wrench F_b appears only in the column multiplying the centroidal control F_c; the end-effector and attitude inputs are realized solely by the (fast) wheel and joint torques τ_w, τ_m.
- Using internal velocities v_e^int and ω̌_b^int inertially decouples the momentum from the rest, and a dynamically-consistent null-space projection (Eq. 15-17) additionally decouples the internal end-effector and base inertial blocks, giving a fully block-decoupled inertia matrix (Eq. 21).
- Asymptotic stability of the equilibrium χ₀ = 0 (state χ ∈ ℝ²⁷) is proven via conditional/hierarchical Lyapunov analysis over nested invariant sets A₂ ⊂ A₁ ⊂ Ω, valid in a region Ω that excludes singularities of Ť(q_m).
- Experimentally, contact-free end-effector maneuvers consumed exactly zero fuel; RW torque stayed within the 0.3 N·m limit and RW speed returned to zero at rest, supporting the “mutual momentum exchange between arm and wheels” interpretation.
- With discrete thrusters (T_sat = 300 ms), only the momentum/CoM loop bandwidth had to be reduced (≥20× below sampling frequency); the end-effector and attitude gains were unchanged precisely because those tasks are not actuated by the slow thruster channel.
Method
Regime: free-FLYING. The spacecraft base is fully actuated (thrusters provide external force f_b ∈ ℝ³ and torque τ_b ∈ ℝ³). This contrasts with the free-floating literature ([6-10], generalized-Jacobian control [7], transposed-Jacobian dynamics [8]) where the base actuators are off. The authors explicitly motivate moving beyond free-floating: a single accidental contact drifts a free-floating arm toward singularity within short time, and spacecraft-mounted relative sensors may require attitude pointing — both demanding base actuation.
System: spacecraft + serial arm with n_m revolute joints + n_w fixed-gimbal RWs; total DOF = 6 + n, n = n_w + n_m. Assumptions: (1) each RW is a rotationally symmetric rigid body; (2) RWs nonredundant and nonsingular, n_w = 3; (3) arm nonredundant, n_m = 6 (so n = 9). Redundancy resolution is deferred to future work. No orbital/environmental forces are modeled (small vs. control forces).
Dynamics (Eq. 3) partition velocities into base 6-DOF twist v_b, wheel rates q̇_w, joint rates q̇_m with a structured inertia matrix M and Coriolis matrix C; the off-diagonal blocks M_w↔m and C_w↔m vanish (no direct wheel-arm coupling), but wheels couple to the arm indirectly through the base.
Generalized momentum about CoM frame C (Eq. 4): h = A_cb^{-T}(M_b v_b + M_bw q̇_w + M_bm q̇_m), with CoM velocity v_c = (1/m) Q_c h (Eq. 5).
The generalized Jacobian J*_em = J_em − A_eb M_b^{-1} M_bm (Eq. 7) recovers the free-floating notion of [7,8]. The internal velocity v_x^int is defined as the frame velocity when momentum is zero (Eq. 6); with RWs present, v_e^int depends on both q̇_m and q̇_w (Eq. 8a), unlike the no-wheel case. The transformation Γ̌ (Eq. 19) maps (v_b, q̇_w, q̇_m) → (h, v_e^int, ω̌_b^int); it is rank-deficient exactly when Ť(q_m) is singular (singularity depends only on joint angles, not on R_b). Forces transform by Γ̌^T (Eq. 20), giving the triangular allocation (Eq. 36).
Decoupled control (Eq. 25): centroidal F_c = −Q_c^T K_c x̃_c − D_h h; end-effector F̌_e^int = −J_{x̃e}^T K_e x̃_e − D_e v_e − C*be^T ω̌_b^int (the last term compensates base→EE Coriolis coupling, required for the proof); base τ̌_b^int = −J{x̃b}^T K_b x̃_b − D_b ω_b. All gains symmetric positive definite. Orientation errors use the vector part of the error quaternion.
Relevance to thesis
This is a direct, rigorous template for our free-flying (fully-actuated 6-DOF base) manipulator. The central insight — allocate the expensive/slow/non-renewable thruster channel only to tasks no internal actuator can perform (inertial CoM placement and momentum dumping), while delegating end-effector and attitude tasks to fast renewable actuators — is exactly the kind of nominal-algorithm structure we want before layering risk. The triangular allocation and the cascaded external/internal stability proof give a clean baseline whose decoupling could be stress-tested under uncertainty (e.g., thruster deadzone/discretization, model error in M_b, contact wrench), and the explicit singularity region Ω of Ť(q_m) is a natural place to attach chance constraints or CVaR margins. The deferred redundant-arm case and absent null-space control are open seams our work could fill.
Connections
Topics: coordinated_control · generalized_jacobian · internal_velocity · reaction_null_space · free_flying_vs_free_floating
Key Equations / Quotes
“the thrusters shall only stabilize the angular momentum of the system and regulate the position of CoM of the whole space robot.” (p. 2, Sect. 2.1)
Generalized Jacobian (Eq. 7):
J*_em = J_em − A_eb M_b^{-1} M_bm ∈ ℝ
Decoupled / simplified transformed dynamics (Eq. 22):
ḣ = F_c
[M_e 0; 0 M_b][v̇_e^int; ω̇̌_b^int] + [C_e −C_be^T; C_be C_b][v_e^int; ω̌_b^int] + [C_eh; C_bh] h = [F̌_e^int; τ̌_b
Triangular actuator allocation (Eq. 36):
[F_b; τ_w; τ_m] = [A_cb^T 0 0; M_bw^T M_b^{-1} A_cb^T T_ew^T Ť_bw^T; M_bm^T M_b^{-1} A_cb^T T_em^T Ť_bm^T] [F_c; F̌_e^int; τ̌_b
“during the entire time of robot maneuvers that do not involve contact … it will remain x̃_c = 0, h = 0, and in turn F_b = 0. Hence … all end-effector or base attitude maneuvers that do not involve contact will require no thrusters.” (p. 6, Sect. 4.2)
Open Questions
- How does the method extend to a redundant arm (n_m > 6) and redundant RW sets? The paper defers redundancy resolution and notes uncontrolled null-space motion caused longer attitude oscillations (only dissipated by joint friction).
- Stability and impedance matching during the contact phase itself (not just pre/post) are not treated; the proof assumes no applied contact wrench.
- Behavior near and through singularities of Ť(q_m): loss of controllability along the singular direction is acknowledged but only mitigated by pre-planned trajectories / singularity avoidance, not analyzed.
- Robustness to a moving/tumbling target (frame T assumed stationary) and to genuine measurement/estimation uncertainty in CoM and momentum reconstruction.