Friction models and compensation methods are applied to harmonic drive motors used with flexible robotic linkages. In the absence of output torque measurements and output shaft encoder data nearly complete friction compensation is achieved allowing the application of a passivity based controller. Simulation and experimental results are given.

A mathematical model of a uniform Bernoulli-Euler beam with a single discrete arbitrarily oriented rotor located at the tip of the beam is presented. The rotor is assumed to rotate at a constant angular velocity about its axis of inertial symmetry; that axis is not necessarily coincident with the neutral axis of the beam. The governing equations of motion are derived when the system is subject to a compressive conservative external load. It is shown that these systems can display both static instabilities (divergence) and dynamic instabilities (flutter), that the structure of the stability regions depends on the distribution of stiffness and that gyroscopic stabilization is sometimes possible.

To design and test large flexible manipulators, dynamically equivalent scale model manipulators can be built which will fit inside a conventional research lab. By constructing dynamically equivalent prototypes, all the dynamic properties of the manipulator are scaled, including gravity and flexibility effects. Dimensional analysis is used to determine the nondimensional groups which define the dynamic equivalence conditions for general flexible-link manipulators. The scaling laws for natural frequencies, mode shapes, and friction effects are also presented. An example illustrates how two physically different flexible-link manipulators with two degrees of vibration can be constructed to be dynamically equivalent. The example also illustrates how, with the application of scaled PD controllers, the responses of the two systems can be scaled versions of one another.

Dimensional analysis is used to determine the nondimensional groups which define the dynamic equivalence conditions for rigid-link manipulators. Scaling laws for general actuators and nonlinear controllers are also presented. As an example, simulation results are presented which illustrate how a large two-link elbow manipulator operating on the Moon can be designed by constructing a dynamically equivalent prototype in Earth gravity, and also, how a sliding mode controller designed for the prototype Earth robot can be scaled for implementation on the Moon-based manipulator.

When constructing large robotic manipulators or space structures, it is advisable to begin with a small-scale prototype on which to perform the design, analysis, and debugging. To ensure that the results obtained on the scale-model apply directly to the actual manipulator, it is necessary that the prototype and the original robot are dynamically equivalent. This paper examines the single flexible link (SFL) manipulator. Dimensional analysis is used to identify the nondimensional groups for the SFL. These groups are present in the corresponding nondimensional equations of motion, which are also derived. To account for inherent manufacturing imprecision, tolerances are developed for the nondimensional groups. Scaling laws for continuous-time and discrete-time controllers are developed for dynamically equivalent SFL systems. These theoretical scaling laws are verified experimentally for an H/sub /spl infin// and a PD control strategy.

The effect of rotating speed on the transverse vibration of a flexible Timoshenko beam with a load at the tip is investigated. The governing equations of motion are derived using the extended Hamilton's principle and an approximate solution is determined using the Rayleigh-Ritz method. The results indicate an increasing frequency, and decreasing vibration amplitude with increasing rotating speed. These are attributable to centrifugal stiffening and there is a threshold rotating speed for a given configuration below which the centrifugal stiffening effect is negligible.

The nondimensional groups which characterize a group of dynamically equivalent single flexible link (SFL) manipulators are determined. A scaling law for linear rational controllers is developed for dynamically equivalent SFL systems. As an example of the applicability of this theoretical scaling law to even sophisticated control techniques, it is verified experimentally for an H/sub /spl infin// control strategy.

A mathematical model of a Euler-Bernoulli beam with a discrete gyroscopic element, consisting of a single rotor located at the tip of the beam, is presented. The rotor is assumed to have a constant angular velocity and an axis of inertial symmetry which is coincident with the neutral axis of the beam. The governing equations of motion and corresponding boundary conditions are derived when the system is subject to conservative external loads. It is shown that these systems can display both static instabilities (divergence) and dynamic instabilities (flutter), that the structure of the stability regions depends on the distribution of stiffness and that gyroscopic stabilization is sometimes possible.

An idealized mathematical model of a uniform Bernoulli-Euler beam with a single discrete rotor located at the tip of the beam is presented. The rotor is assumed to rotate at a constant angular velocity and to have an axis of inertial symmetry which is coincident with the neutral axis of the beam. The governing equations of motion are derived when, the system is subject to a compressive conservative external load. It is shown that these systems can display both static instabilities (divergence) and dynamic instabilities (flutter), that the structure of the stability regions depends on the distribution of stiffness and that gyroscopic stabilization is sometimes possible.>

An open-loop control system is designed using frequency-domain techniques to compute a desired hub torque profile. The motion of the arm after tip impact, including hub actuation, is simulated. Simulation results are compared to experimental data. It is shown that the controller damps vibration caused by the impact and allows the steady-state tip deflection to be predetermined.>

Resource allocation in a flexible manufacturing system (FMS), such as assignment of resources to tasks, can be solved efficiently using graph matching methods. The FMS is modeled as a graph: the vertices are resources and tasks, and the edges ar relationships between the resources and tasks. Resources are allocated by finding a match in the graph. The general matching problem is reviewed as an optimization problem; the more specific maximum cardinality 1-matching problem is discussed in detail. A direct parallelization of an algorithm is described which may be regarded as an archetype for implementation on a distributed network of computers in a large FMS. In such an FMS, planning activities such as resource allocation are decentralized, allowing for quicker and more detailed planning.>

A finite-element model for a single-link flexible robotic arm including the effects of beam damping, hub inertia and both Coulomb and viscous hub friction is derived. The initial conditions required to represent impact loading are determined, and the motion of the arm under impact loading is simulated. Simulation results are compared to experimental data. From the experimental results it is concluded that this model provides an accurate representation of the physical process. It also provides a vehicle for investigating the effects of parameters of the process model, in particular, frictional effects and load profiles. Impact loading has been effectively represented in terms of initial conditions and can be applied to a range of finite-element models.>

A finite-element model of a single-link flexible robotic arm is derived, and the initial conditions required to represent impact loading are determined. An open-loop control system is designed using frequency-domain techniques to compute a desired hub torque profile. The motion of the arm after tip impact and including hub actuation is simulated. Simulation results are compared to experimental data. It is shown that the controller damps vibration caused by the impact and allows the steady-state tip deflection to be predetermined.>