An engineering approach to the dynamic control of space robotic on-orbit servicers
Authors: Ellery · Year: 2004 · Venue: Proc. IMechE Part G: J. Aerospace Engineering, Vol. 218
Raw: md
Summary
Ellery argues that the standard free-floating generalized-Jacobian machinery (with its dynamic singularities, non-holonomy and O(n^2) cost) is the wrong tool for an on-orbit servicer, and that a far simpler “engineering approach” follows from giving the platform a dedicated attitude control system (reaction/momentum wheels or CMGs). With attitude actively held (R_0 = I_3, w_0 = w_0_dot = 0), the angular non-holonomic constraint is removed and only the holonomic linear-momentum constraint must be folded into the kinematics. The reaction forces/moments the arm exerts on the bus are computed as a byproduct of the recursive Newton-Euler arm dynamics and fed forward to the attitude controller, so terrestrial DH/RCCL algorithms can be reused with only a “lumped parameter” substitution. Simulation of the ATLAS servicer grappling a 200 kg ORU shows force-control reaction torques of ~1-10 kN m, beyond reaction wheels but within CMG capability.
Key Claims
- A 6-DOF arm on a 6-DOF bus is a 12-DOF system driven by 6 joint inputs (assuming no independent attitude actuation): kinematically redundant, non-square Jacobian, no closed-form inverse kinematics. Generalized-position control of even a 3-DOF arm on a satellite has infinitely many inverse-kinematics solutions, dependent on motion history, not joint configuration alone.
- For free-floating systems the platform attitude is non-holonomic: angular-momentum conservation is not integrable, so a given end-effector orientation maps to many possible bus attitudes. This produces dynamic singularities that are functions of mass/inertia AND path history, cannot be predicted from kinematics alone, and at which inverse-generalized-Jacobian control becomes unstable.
- The path-independent workspace (no dynamic singularities) is much smaller than the path-dependent workspace of an uncontrolled-attitude platform; the path-independent workspace attains its maximum extent (coinciding with the constrained workspace) precisely when attitude control is employed.
- Decoupling linear (holonomic) from angular (non-holonomic) motion matches how spacecraft are actually built (separate orbit and attitude subsystems) and collapses the problem to terrestrial complexity. Linear momentum is integrated to an equilibrium-of-moments constraint; angular reaction is handled by feedforward to the attitude controller.
- When dedicated attitude control is used, the complex generalized Jacobian J* reduces to a “freeflyer Jacobian” J-bar obtained by replacing kinematic link parameters l_i with lumped kinematic-dynamic parameters lambda_i; this is invertible like a terrestrial Jacobian and the constants differentiate to zero.
- Reaction wheels (~0.1-1 N m) cannot compensate manipulator reaction torques; CMGs (e.g. ISS CMGs at ~27 kN m) are required, especially during force-controlled capture. Pre-acquisition position-control torques are <5 N m; force-control/impact torques reach ~1-10 kN m.
- ETS-VII (1998) flight experience: leaving attitude uncontrolled during manipulation led to large attitude error (asymmetric inertia -> non-negligible gravity-gradient torque from products of inertia), corroborating that active dedicated attitude control is essential.
Method
Model: spacecraft bus = rigid link i=0, manipulator links i=1..n, payload = link i=n+1, treated as an open kinematic chain (branched for multiple arms). Environmental disturbance torques (~10^-6 N m) neglected. Inertial frame taken at the system centre of mass (assumed quasi-inertial over short task times; orbital pitch drift ~10^-3 rad/s decoupled).
Regime — explicitly FREE-FLYING. The entire contribution rests on a fully actuated, attitude-controlled base. The paper carefully contrasts this with free-floating systems (no dedicated attitude control, which suffer dynamic singularities and non-holonomy). This is exactly the thesis regime.
Conservation laws as the two constraints:
- Linear momentum P = sum_{i=0}^{n+1} m_i r_i_dot = 0 (Eq. 4), a holonomic constraint, integrable to the equilibrium-of-moments form sum m_i r_i = const (Eq. 5).
- Angular momentum L = sum (I_i w_i + m_i r_i_dot x r_i) = 0 (Eq. 6), a non-holonomic constraint, NOT integrable (non-commutativity of finite rotations).
Kinematics: inertial end-effector position p* = r_c0 + R_0 s_0 + sum_{i=1}^n R_i l_i (Eq. 7), with R_0 = I_3 for an attitude-controlled platform. After locating the system CoM p*_cm (Eqs. 8-13) and substituting, the end-effector position is reorganized into terrestrial form (Eq. 15):
p* = p*cm + (m_0/m_T) s_0 + sum{i=1}^n R_i lambda_i - (m_{n+1}/m_T) R_{n+1} r_{n+1}
with the lumped kinematic parameter lambda_i = (1/m_T) sum_{j=0}^i (m_j l_i - m_i r_i). Because p*cm, s_0 and the payload term are constant, this has the terrestrial form p = sum R_i l_i plus constants; r{n+1} is the “virtual stick” from grasp point to payload CoM (the POR).
Freeflyer Jacobian by direct differentiation (Eq. 18): J-bar = sum_{i=1}^n sum_{k=1}^i (dR_i/dtheta_k) lambda_i, since pcm_dot = s_0_dot = R{n+1}_dot = 0. Compared to the generalized Jacobian J = (J_m - J_0 I_0^{-1} D_ik) for free-floating systems, J-bar simply swaps kinematic link parameters for kinematic-dynamic ones.
Dynamics / reaction feedforward: reaction moment on the bus from the NE formulation, N_r = N_T + (p*_cm - r_c0 - s_0) x F_T (Eq. 30), with F_T = sum m_i v_ci_dot and N_T = sum (I_i w_i_dot + w_i x I_i w_i). The bus attitude controller then enforces the Euler equation N_r = I_0 w_0_dot + w_0 x I_0 w_0 (Eq. 31). Feedforward alone is unstable (model-dependent); the attitude loop supplies the feedback component. N_0, F_0 fall out of the NE pass for free.
Control laws used in simulation: computed-torque PD inverse-dynamics for position (Eq. 32) and a PI scheme for force control; bang-bang knot-point trajectory; plastic/elastic impact model with 10^-3 s impact duration.
Notation flag: the markdown shows several OCR artifacts in the notation table and intermediate algebra (stray symbols like “λī”, “n l l”, a malformed strain-energy integral on p. 4, and an apparent index typo in Eq. 13’s L_i where the summed mass should be the outboard m_j). The boxed final results (Eqs. 7, 13, 15, 18, 30, 31) are internally consistent and used here as authoritative.
Relevance to thesis
This is close to a charter document for the thesis regime: it makes the free-flying (fully-actuated, attitude-controlled base) case the design choice and shows that doing so dissolves the free-floating pathologies (dynamic singularities, non-holonomic path dependence, costly generalized Jacobian) that dominate the older literature. The lumped-parameter freeflyer Jacobian and the NE reaction-feedforward-to-attitude-controller architecture are directly reusable as the nominal guidance/control layer before risk is added. The CMG-vs-reaction-wheel actuator-sizing result and the ETS-VII corroboration give concrete, citable numbers for the coupled bus/arm control budget.
Connections
Topics: dynamic_singularity · generalized_jacobian · dynamic_coupling · free_flying_vs_free_floating
Key Equations / Quotes
“For a spacecraft-mounted manipulator, singularities are no longer purely kinematic. Dynamic singularities are a function of both robotic kinematics and the dynamic properties of both the manipulator and the spacecraft.” (p. 6)
“All such schemes which leave spacecraft attitude uncontrolled cannot cope with the input dynamics of target acquisition in real time using present-day and near-future space-rated computational hardware.” (p. 7)
Freeflyer end-effector position (Eq. 15):
p* = p*cm + (m_0/m_T) s_0 + sum{i=1}^n R_i lambda_i - (m_{n+1}/m_T) R_{n+1} r_{n+1}, lambda_i = (1/m_T) sum_{j=0}^i (m_j l_i - m_i r_i)
Reaction moment fed to the attitude controller (Eqs. 30-31):
N_r = N_T + (p*_cm - r_c0 - s_0) x F_T; N_r = I_0 w_0_dot + w_0 x I_0 w_0
Generalized vs freeflyer Jacobian:
J* = (J_m - J_0 I_0^{-1} D_ik) [free-floating]; J-bar = sum_{i=1}^n sum_{k=1}^i (dR_i/dtheta_k) lambda_i [free-flying]
Open Questions
- The feedforward reaction model is “highly dependent on the accuracy of the predictive model” — how is stability/robustness preserved under the unknown/variable payload inertias the paper itself flags? (This is the natural seam for the risk-aware layer.)
- Sizing depends on knowing m_{n+1}, payload CoM and inertia; the virtual-stick r_{n+1} is treated as known. How are estimation errors in these propagated into the required CMG torque margin?
- Force-control torques of ~1-10 kN m are stated as within CMG capability via the ISS example, but no closed-loop demonstration that a CMG cluster on a small servicer can actually track them during impact is given.
- Extension to closed-chain dual-arm grasping (grasp matrix J-bar^T) is asserted but not derived or simulated here.