In this paper inverse dynamics of redundant multibody systems using a
minimum number of control forces is formulated. It is shown that the c
ontrol forces and the task accelerations may become noncausal at certa
in configurations, yielding the dynamical equation set of the system t
o be singular. For a given set of tasks, each different set of actuato
rs leads to a different system motion and also to different singular c
onfigurations. To avoid the singularities in the numerical solution, t
he dynamical equations are modified in the neighborhoods of the singul
ar configurations by utilizing higher order derivative information. Th
e modification is made easier by transforming the equations of motion
to the null space of the control force direction matrix. The condition
s for the existence of solution are also discussed. A redundant planar
manipulator is analyzed to illustrate the methods proposed.