James B. Dabney

Modeling, identification, and compensation of friction in harmonic drives

Harmonic drives are increasingly used in precision positioning applications such as military radars, wafer handling machines, and satellite cameras. Precision tracking performance of these drives is deteriorated by nonlinear transmission attributes including kinematic error, flexibility, hysteresis and friction. Hence characterization and compensation of these nonlinear attributes is crucial to improve the precision in tracking and regulation. This paper focuses on modeling, identification, and compensation of nonlinear friction in harmonic drives. Harmonic drive friction models presented in the literature are found to be a combination of Coulomb and viscous friction. However, a dynamic friction phenomenon exhibits, in addition to Coulomb and viscous frictions, other nonlinear phenomena including the Dahl effect, and the Stribeck effect which must be considered in an accurate friction model. In addition, in this research, harmonic drive friction is discovered to be dependent on the motor position. Complete characterization of friction in harmonic drives is carried out in this paper by using a recently developed LuGre (Lund-Grenobel) friction model superimposed with a new position-dependent part. Parameters of the proposed model are identified using linear and nonlinear identification tools. Experimental implementation of a friction compensation scheme based on the proposed model demonstrates the effectiveness of the model.

Modeling and Control of a Shape Memory Alloy Actuator

In this paper, we present a complete mathematical model of a spring-biased shape memory alloy (SMA) wire actuator driven by an electric current. The working of the SMA actuator is based on diverse physical phenomena, viz., heat convection, phase transformation, stress-strain variations and electrical resistance variation accompanying the phase transformation. The proposed model decomposes the operation of the actuator into these phenomena and comprises modules which represent each of these phenomena independently. The phase transformation involves significant temperature hysteresis. We model this hysteresis by a differential hysteresis model, which can conveniently represent both major and minor loops. We also propose a differential inverse of the hysteresis model, whereby, we obtain the differential inverse of the complete SMA actuator model. We propose a feedback control scheme with inverse compensation based on the inverse SMA model. Simulation results are presented, which demonstrate the effectiveness of the proposed control technique

Optimal control of a ship for collision avoidance maneuvers

We consider a ship subject to kinematic, dynamic, and moment equations and steered via rudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. We formulate and solve four Chebyshev problems of optimal control, the optimization criterion being the maximization with respect to the state and control history of the minimum value with respect to time of the distance between two identical ships, one maneuvering and one moving in a predetermined way.Problems P1 and P2 deal with collision avoidance maneuvers without cooperation, while Problems P3 and P4 deal with collision avoidance maneuvers with cooperation. In Problems P1 and P3, the maneuvering ship must reach the final point with a given lateral distance, zero yaw angle, and zero yaw angle time rate. In Problems P2 and P4, the additional requirement of quasi-steady state is imposed at the final point.The above Chebyshev problems, transformed into Bolza problems via suitable transformations, are solved via the sequential gradient-restoration algorithm in conjunction with a new singularity avoiding transformation which accounts automatically for the bounds on rudder angle and rudder angle time rate.The optimal control histories involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values. In problems where quasi-steady state is imposed at the final point, there is a higher number of subarcs than in problems where quasi-steady state is not imposed; the higher number of subarcs is due to the additional requirement that the lateral velocity and rudder angle vanish at the final point.

Verification and validation (panel session): what impact should project size and complexity have on attendant V&V activities and supporting infrastructure?

The size and complexity of modeling and simulation (MS and recognizing the necessity and benefits of tailoring V&V activities commensurate with the size of the project, i.e., one size does not fit all. We provide six questions and four sets of responses to those questions. These questions and responses are intended to foster additional thought and discussion on topics crucial to the synthesis of quality M&S applications.

Optimal control of a ship for course change and sidestep maneuvers

We consider a ship subject to kinematic, dynamic, and moment equations and steered via rudder under the assumptions that the rudder angle and rudder angle time rate are subject to upper and lower bounds. We formulate and solve four Mayer problems of optimal control, the optimization criterion being the minimum time.Problems P1 and P2 deal with course change maneuvers. In Problem P1, a ship initially in quasi-steady state must reach the final point with a given yaw angle and zero yaw angle time rate. Problem P2 differs from Problem P1 in that the additional requirement of quasi-steady state is imposed at the final point.Problems P3 and P4 deal with sidestep maneuvers. In Problem P3, a ship initially in quasi-steady state must reach the final point with a given lateral distance, zero yaw angle, and zero yaw angle time rate. Problem P4 differs from Problem P3 in that the additional requirement of quasi-steady state is imposed at the final point.The above Mayer problems are solved via the sequential gradient-restoration algorithm in conjunction with a new singularity avoiding transformation which accounts automatically for the bounds on rudder angle and rudder angle time rate.The optimal control histories involve multiple subarcs along which either the rudder angle is kept at one of the extreme positions or the rudder angle time rate is held at one of the extreme values. In problems where quasi-steady state is imposed at the final point, there is a higher number of subarcs than in problems where quasi-steady state is not imposed; the higher number of subarcs is due to the additional requirement that the lateral velocity and rudder angle vanish at the final point.

A spherical pendulum system to teach key concepts in kinematics, dynamics, control, and simulation

The Rice Spherical PENDUlum Laboratory APparatus (SPENDULAP) is a rich teaching aid for senior and first year graduate courses in kinematics, dynamics, control and simulation. It consists of a free-swinging (unactuated) rigid pendulum mounted in a rotating frame. The frame rotates about an axis perpendicular to the pendulum swing axis and is driven by an electric motor. The SPENDULAP is attractive as a teaching tool because it is easy to visualize the motion of the pendulum, but somewhat challenging to model kinematically and dynamically. In particular, the three-dimensional nature of the pendulum motion allows students to gain proficiency and confidence not possible with a planar apparatus. Additionally, nonlinearities in the dynamics present interesting, but tenable, control challenges. In this paper, the authors illustrate each step in the process of kinematic and dynamic modeling, simulation and control of the SPENDULAP. They start with the kinematic analysis and then develop the equations of motion using both Newtonian and Lagrangian approaches. The spherical pendulum is sufficiently complex to demonstrate the advantages of the Lagrangian approach, and it also offers an excellent illustration of the benefits of the Newtonian formulation. Next, they illustrate the development of a numerical simulation of the SPENDULAP dynamics, and provide examples of uses of simulation and animation using MATLAB. Finally, they show the development of linear and nonlinear control laws, and illustrate testing them using simulation.

Nanomanipulation Modeling and Simulation

A novel approach to better model nanomanipulation of a nanosphere laying on a stage via a pushing scheme is presented. Besides its amenability to nonlinear analysis and simulation, the proposed model is also effective in reproducing experimental behaviors commonly observed during AFM-type nanomanipulation. The proposed nanomanipulation model consists of integrated subsystems that are identified in a modular fashion. The subsystems consistently define the dynamics of the nanomanipulator tip and nanosphere, interaction forces between the tip and the nanosphere, friction between the nanosphere and the stage, and the contact deformation between the nanomanipulator tip and the nanosphere. The main feature of the proposed nanomanipulation model is the Lund-Grenoble (LuGre) dynamic friction model that reliably represents the stick-slip behavior of atomic friction experienced by the nanosphere. The LuGre friction model introduces a new friction state and has desirable mathematical properties making it a well-posed dynamical model that characterizes friction with fidelity. The proposed nanomanipulation model facilitates further improvement and extension of each subsystem to accommodate other physical phenomena that characterize the physics and mechanics of nanomanipulation. Finally, the versatility and effectiveness of the proposed model is simulated and compared to existing models in the literature.Copyright

An AFM-Based Nanomanipulation Model Describing the Atomic Two Dimensional Stick-Slip Behavior

A new AFM-based nanomanipulation model describing the relevant physics and dynamics at the nanoscale is presented. The nanomanipulation scheme consists of integrated subsystems that are identified in a modular approach. The model subsystems define the AFM cantilever-sample dynamics, the AFM tip-sample interactions, the contact mechanics and the friction between the sample and the substrate. The coupling between these different subsystems is emphasized. The main contribution of the proposed nanomanipulation model is the use of a new 2D dynamic friction model based on a generalized bristle interpretation of one asperity contact. The efficacy of the proposed model to reproduce experimental data is demonstrated via numerical simulations. In fact, the model is shown to describe the 2D stick-slip behavior with the substrate lattice periodicity. The proposed nanomanipulation model facilitates the improvement and extension of each subsystem to further take into account the complex interactions at the nanoscale.Copyright

Adhesion and Friction Coupling in Atomic Force Microscope-Based Nanopushing

The use of the atomic force microscope (AFM) as a tool to manipulate matter at the nanoscale has received a large amount of research interest in the last decade. Experimental and theoretical investigations have showed that the AFM cantilever can be used to push, cut, or pull nanosamples. However, AFM-based nanomanipulation suffers a lack of repeatability and controllability because of the complex mechanics in tip-sample interactions and the limitations in AFM visual sensing capabilities. In this paper, we will investigate the effects of the tip-sample interactions on nanopushing manipulation. We propose the use of an interaction model based on the Maugis–Dugdale contact mechanics. The efficacy of the proposed model to reproduce experimental observations is demonstrated via numerical simulations. In addition, the coupling between adhesion and friction at the nanoscale is analyzed.

Modeling closed kinematic chains via singular perturbations

Closed kinematic chains (CKC) are constrained multibody systems the dynamics of which are characterized by differential-algebraic equations. In this paper we present a novel approach to modeling CKC that supports model-based control. The approach is based on a singular perturbation formulation with attractive properties including (i) the number of slow second-order differential equations is the same as the number of degrees of freedom of the system, (ii) the domain of definition of the singularly perturbed system is the entire singularity-free workspace of the CKC. We illustrate the effectiveness of our approach by simulating the dynamics of the parallel Rice Planar Delta Robot.