The present work deals with the application of a class of passivity-based control schemes to the flexible gantry robots domain. These controllers, which also include an adaptive version, effectively exploit the passivity property satisfied by a suitably defined input and output for the system in con junction with an approximate model of the payload-dominated dynamics. Simulations as well as hardware implementation on an experimental flexible gantry robot demonstrate the efficacy of the schemes, which combine end-point tracking of prescribed trajectories together with active vibrations suppression.

The robotic control problem is considered from the passivity– based control point of view and a modified version of the computed torque method for rigid robots is briefly reviewed. A control strategy suitable for flexible–link robots manipulating large payloads is also presented, which effectively exploits the passivity property satisfied by a suitably defined set of inputs and outputs for the system in conjunction with an approximate model of the dynamics. Both of the above control schemes are experimentally implemented on a flexible– link, multi-joint arm in order to investigate their characteristics and provide useful insight into the control problem for flexible robots.

This paper first outlines the generally accepted procedures for model validation. Four dynamics models are then described which represent the full range of nonlinear complexity for modeling structural flexibility in robotic manipulators. Test manoeuvres are performed on a 2-DOF flexible-link direct-drive manipulator. The natural frequencies and mode shapes are captured very well by the finite element model when damping is incorporated. The performance of the four dynamics models with and without damping is also compared to one another and to the experiment. High order nonlinearities and model damping are shown to be less important for slow manoeuvres by close agreement between the simple and complex models. The importance of the high order terms is also shown to decrease for fast manoeuvres in the presence of damping. Results for the exact nonlinear model are inconclusive because of its poor convergence characteristics.

A derivation is presented of an approximate form of the dynamics governing a structurally flexible manipulator carrying a massive payload at its end-effector. An output called the /spl mu/-tip rate which incorporates end-effector and elastic motions is introduced. The input-output mapping relating a transformed version of the joint torques to the /spl mu/-tip rates is shown to be passive for large payloads. A feedforward torque strategy is developed which preserves the passivity property in the error dynamics and a suitable Lyapunov function is used to demonstrate global asymptotic stability of the tracking provided by a PD law. Implementation of the controllers without measurements of the elastic coordinates and rates is shown to be possible. Simulation studies of a six DOF manipulator with flexible links, modeled after the Shuttle Remote Manipulator System, demonstrate excellent tracking in all six Cartesian end-effector coordinates, even for payloads with modest mass properties. A major conclusion is that some of the problems normally associated with lack of collocation in flexible manipulators can be surmounted when large (massive) payloads are involved.

Two important issues relevant to modeling of flexible-link robotic manipulators are addressed. The authors examine the question of which terms should be included in the equations of motion for purposes of simulation. A complete model incorporating all nonlinearities that couple rigid-body and elastic motions is presented, along with a rational scheme for classifying their inclusion. The issue of basis function selection for spatial discretization of the elastic displacements is discussed. The finite element method and an eigenfunction expansion techniques are presented and compared. Both issues are examined numerically in the context of the Space Shuttle remote manipulator system. It is shown that certain key nonlinear elastic terms are required if numerical instability of the simulation is to be averted. Simulation results for two discretization schemes are included.>

A recursive algorithm, based on a Newton-Euler formulation, is developed for the solution of the simulation-dynamics problem for a chain of rigid bodies. Arbitrary joint constraints are permitted, that is, joints may allow translational and/or rotational degrees of freedom. The recursive procedure is shown to be identical to that encountered in a discrete-time optimal-control problem. For each relevant quantity in the multibody-dynamics problem, there exists an analog in the context of optimal control. The performance index that is minimized in the control problem is identified as Gibbs' function for the chain of bodies.>