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A case study of inverse dynamics control of manipulators with passive joints

Blajer W., Kołodziejczyk K.

Journal of Theoretical and Applied Mechanics

2014

Vol. 52 nr 3

793--801

Manipulators with both active and passive joints are examples of underactuated systems, featured by less control inputs than degrees of freedom. Due to the underactuation, in the trajectory tracking (servo-constraint) problem, the feed-forward control obtained from an inverse model is influenced by internal dynamics of the system, leading to a more involved control design than in the fully actuated case. It is demonstrated that a convenient approach to the problem solution is to formulate the underactuated system dynamics in the input-output normal form, with the arising governing equations formulated either as ODEs (ordinary differential equations) or DAEs (differential-algebraic equations). The interrelationship between the inverse dynamics control and the associated internal dynamics is then studied and illustrated using a planar manipulator with two active and one passive joint. Some simulation results for the sample case study are reported.

Motion planning of the underactuated manipulators with friction in constrained state space

Ratajczak A., Janiak M.

Journal of Automation Mobile Robotics and Intelligent Systems

2011

Vol. 5, No. 3

33-40

This paper addresses the constrained motion planning problem for passive joint manipulators with friction. Constraints are imposed on a system state space vector. The dynamics of underactuated manipulators are described by a control-affine system with a drift term. In order to solve the constrained motion planning problem the imbalanced Jacobian algorithm derived from an endogenous configuration space approach is used. The state space constraints are included into the system representation of the manipulator dynamics. The extended system is subject to regularisation because of the Jacobian singularities, then the unconstrained motion planning problem is solved for the regularised system. The solution of the motion planning problem for this system is equivalent to the solution of the constrained motion planning problem for an original system. Performance of the imbalanced Jacobian algorithm has been demonstrated with series of simulation for the two kinds of manipulators with and without friction.