An analysis of the kinematics and dynamics of underactuated manipulators. Jain, A. & Rodriguez, G. IEEE Transactions on Robotics and Automation, 9(4):411–422, August, 1993.
doi  abstract   bibtex   
The dynamics and kinematics of manipulators that have fewer actuators than degrees of freedom are studied. These underactuated manipulators arise in a number of important applications such as free-flying space robots, hyperredundant manipulators, manipulators with structural flexibility, etc. In the analysis such underactuated manipulators are decomposed into component active and passive arms. This decomposition allows techniques previously developed for regular (fully actuated) manipulators to be applied to underactuated systems. Spatial operator identities are used to develop closed-form expressions for the generalized accelerations for the system. These expressions form the basis for a recursive O(N) dynamics algorithm. The structure of this algorithm is a hybrid of known forward and inverse dynamics algorithms for regular manipulators. Expressions and computational algorithms are also developed for the generalized and disturbance Jacobians for underactuated manipulators. The application of the results in the paper to space manipulators is also described
@article{jain_analysis_1993,
	title = {An analysis of the kinematics and dynamics of underactuated manipulators},
	volume = {9},
	issn = {1042-296X},
	doi = {10.1109/70.246052},
	abstract = {The dynamics and kinematics of manipulators that have fewer actuators than degrees of freedom are studied. These underactuated manipulators arise in a number of important applications such as free-flying space robots, hyperredundant manipulators, manipulators with structural flexibility, etc. In the analysis such underactuated manipulators are decomposed into component active and passive arms. This decomposition allows techniques previously developed for regular (fully actuated) manipulators to be applied to underactuated systems. Spatial operator identities are used to develop closed-form expressions for the generalized accelerations for the system. These expressions form the basis for a recursive O(N) dynamics algorithm. The structure of this algorithm is a hybrid of known forward and inverse dynamics algorithms for regular manipulators. Expressions and computational algorithms are also developed for the generalized and disturbance Jacobians for underactuated manipulators. The application of the results in the paper to space manipulators is also described},
	number = {4},
	journal = {IEEE Transactions on Robotics and Automation},
	author = {Jain, A. and Rodriguez, G.},
	month = aug,
	year = {1993},
	keywords = {Acceleration, Actuators, Arm, Fasteners, Force control, Heuristic algorithms, Jacobian matrices, Manipulator dynamics, Orbital robotics, Robot kinematics, active arm, aerospace control, closed-form expressions, control system analysis, decomposition, disturbance Jacobians, dynamics, forward dynamics, free-flying space robots, hyperredundant manipulators, inverse dynamics, kinematics, passive arm, recursive O(N) dynamics, robots, space manipulators, underactuated manipulators},
	pages = {411--422}
}

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