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Nomenclature a = positive parameter a tx a ty a tz T = linear acceleration due to the tether tension, m · s −2 a x a y a z T = linear acceleration of the gripper's thruster force, m · s −2 Ck = matrix in coordinated desaturation controller d = position vector of the capture position, m F l = tether tension, N I = inertia matrix of the combination, kg · m 2 I 0 = nominal value of combination's inertia matrix, kg · m 2 K ξ = positive-definite design matrix k 2 = positive-definite design matrix m = mass of tethered space robot-target combination, kg Ox l y l z l = space tether frame Ox p y p z p = space platform orbital frame Ox t y t z t = combination orbital frame Ox 0 t y 0 t z 0 t = combination body frame P = positive-definite design matrix R = transformation matrix from platform orbital frame to combination body frame Sk = constant positive weighting matrix T l = tether control torque, Nm x y z T = centroid position of the combination in the platform orbital frame, m ΔI = inertia matrix uncertainty, kg · m 2 ε = positive parameter λk = Lagrange multiplier λ L = upper bound of disturbancê λ L = estimation values of disturbance μ = positive design parameter ξ = state of the auxiliary design system σ = modified Rodrigues parameters σ d = desired modified Rodrigues parameters τk = vector of optimal thruster force and tether tension τ c = control torque of the combination, N · m τ d = disturbing torques, N · m τ t = control torque of the thruster, N · m τ l = control torque of the tether, N · m ω = absolute angular velocity of the combination, rad · s −1 ω d = desired angular velocity of the combination, rad · s −1