INVERSE DYNAMICS OF UNDERACTUATED MULTIBODY SYSTEMS USING A DAE OPTIMAL CONTROL APPROACH

The inverse dynamics analysis of underactuated multibody systems aims at determining
the control inputs in order to track a prescribed trajectory. This paper studies the inverse dynamics
of non-minimum phase underactuated multibody systems, e.g. for end-effector control of
flexible manipulators or manipulators with passive joints. Unlike for minimum phase systems,
the inverse dynamics of non-minimum phase systems cannot be solved by adding trajectory
constraints to the equations of motion and by applying a forward time integration. Indeed, the
inverse dynamics of a non-minimum phase system is known to be non-causal, which means that
the control forces and torques should start before the beginning of the trajectory (pre-actuation
phase) and continue after the end-point is reached (post-actuation phase). The existing stable
inversion method proposed for general nonlinear non-minimum phase systems requires to
derive explicitly the equations of the internal dynamics and to solve a boundary value problem.
This paper proposes an alternative solution strategy which is based on an optimal control
approach. The method is illustrated for the inverse dynamics of a planar underactuated manipulator
with rigid links and four degrees-of-freedom. An important advantage of the proposed
approach is that it can be applied directly to the standard equations of motion of multibody
systems either in ODE or in DAE form. Therefore, it is easier to implement this method in a
general purpose simulation software.