Singularity-robust full-pose workspace control of space manipulators with non-zero momentum

Adaptive Fuzzy Integral Sliding Mode Cooperative Control Based on Time-Delay Estimation for Free-Floating Close-Chain Manipulators

“…For free-floating close-chain manipulator system, which satisfies the law of conservation of momentum, according to assumption 2, the Equations ( 1a ) and ( 1b ) may be rewritten as By substituting Equation ( 7 ) into Equation ( 6 ), one can obtain where the left of Equation ( 8 ) represents the velocity of the end effectors, is the GJM. GJM directly relates the joints’ velocity to the end effectors’ velocity, and this brings convenience to mission trajectory planning [ 31 ], the controller design [ 32 ] of space robots, and learning impact dynamics when capturing a floating target in space [ 33 ]. The velocity of the base can be written as where is used to represent the velocity mapping of the space manipulators to the common base.…”

“…where the left of Equation ( 8) represents the velocity of the end effectors, J g = J m − J o H −1 1 H 2 is the GJM. GJM directly relates the joints' velocity to the end effectors' velocity, and this brings convenience to mission trajectory planning [31], the controller design [32] of space robots, and learning impact dynamics when capturing a floating target in space [33]. The velocity of the base can be written as…”