Abstract
A mobile-based robot, a robot with an actuator failure, a manipulator with structural flexibility, and robots grasping an articulated object are systems with unactuated or "passive" joints. The dynamics and control of these robot systems is more complex than fully-actuated systems because unactuated joints may lead to uncontrollability. Based on a recursive formulation of the inverse dynamics for manipulators with some unactuated joints, control laws are developed for joint space control and task space control. Important in the task space control law for underactuated systems is the inversion of the generalized Jacobian. Spatial operator algebra techniques are used to develop computationally efficient algorithms for the inverse generalized Jacobian and the control laws.
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