STABILITY OF CONTROL FORCES IN REDUNDANT MULTIBODY SYSTEMS

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.