Inna Sharf

Literature survey of contact dynamics modelling

Abstract Impact is a complex phenomenon that occurs when two or more bodies undergo a collision. This phenomenon is important in many different areas––machine design, robotics, multi-body analysis are just a few examples. The purpose of this manuscript is to provide an overview of the state of the art on impact and contact modelling methodologies, taking into account their different aspects, specifically, the energy loss, the influence of the friction model, solution approaches, the multi-contact problem and the experimental verification. The paper is intended to provide a review of results presented in literature and some additional insights into existing models, their interrelationship and the use of these models for impact/contact scenarios encountered in space robotic applications.

Contact Stiffness and Damping Estimation for Robotic Systems

In this paper, we review and compare four algorithms for the identification of contact stiffness and damping during robot constrained motion. The intended application is dynamics modeling and simulation of robotic assembly operations in space. Accurate simulation of these tasks requires contact dynamics models, which in turn use contact stiffness and damping to calculate contact forces. Hence, our primary interest in identifying contact parameters stems from their use as inputs to simulation software with contact dynamics capability. Estimates of environmental stiffness and damping are also valuable for force tracking and stability of impedance controllers. The algorithms considered in this work include: a signal processing method, an indirect adaptive controller with modifications to identify environment damping, a model reference adaptive controller and a recursive least-squares estimation technique. The last three methods have been proposed for real-time implementation in impedance and force-tracking controllers. The signal processing scheme uses a frequency estimate calculated with fast Fourier transform of the force signal and is an off-line method. The algorithms are first evaluated using numerical simulation of a benchmark test. Experiments conducted with a robotic arm contacting a flexible wall provide a further demonstration of their performance. Our results indicate that the indirect adaptive controller has the best combination of performance and ease of use. In addition, the effect of persistently exciting signals is discussed.

Parallel O(log N) algorithms for the computation of manipulator forward dynamics

In this paper, two parallel O(log N) algorithms for the computation of manipulator forward dynamics are presented. They are based on a new O(N) algorithm for the problem which is developed from a new factorization of mass matrix M. Specifically, a factorization of the inverse M/sup -1/ in the form of a Schur complement is derived. The new O(N) algorithm is then developed as a recursive implementation of this factorization. It is shown that the resulting algorithm is strictly parallel, that is, it is less efficient than other algorithms for serial computation of the problem. However, to our knowledge, it is the only algorithm that can be parallelized to derive both a time-optimal O(logN) - and processor-optimal - O(N) - parallel algorithm for the problem. A more efficient parallel O(logN) algorithm based on a multilevel exploitation of parallelism is also briefly described. In addition to their theoretical significance, these parallel algorithms allow a practical implementation due to their simple architectural requirements. >

Simulation of Flexible-Link Manipulators With Inertial and Geometric Nonlinearities

Several important issues relevant to modeling of flexible-link robotic manipulators are addressed in this paper. First, we examine the question of which inertial nonlinearities should be included in the equations of motion for purposes of simulation. A complete model incorporating all inertial terms that couple rigid-body and elastic motions is presented along with a rational scheme for classifying them. Second, the issue of geometric nonlinearities is discussed. These are terms whose origin is the geometrically nonlinear theory of elasticity, as well as the terms arising from the interbody coupling due to the elastic deformation at the link tip. Accordingly, a general way of incorporating the well-known geometric stiffening effect is presented along with several schemes for treating the elastic kinematics at the joint interconnections. In addition, the question of basis function selection for spatial discretization of the elastic displacements is also addressed. The finite element method and an eigenfunction expansion techniques are presented and compared. All issues are examined numerically in the context of a simple beam example and the Space Shuttle Remote Manipulator System. Unlike a single-link system, the results for the latter show that all terms are required for accurate simulation of faster maneuvers. Hence, the conclusions of the paper are contrary to some of the previous findings on the validity of various models for dynamics simulation of flexible-body systems

PAW: a hybrid wheeled-leg robot

This paper discusses current wheeled mobility work on a hybrid wheeled-leg robot called PAW. In addition to providing design details, controllers are proposed for inclined turning and sprawled braking which take advantage of the hybrid nature of the platform and improve stability. Power consumption values for a number of its basic behaviours are given, as is the range of the robot

Dynamics Modeling and Simulation of Flexible Airships

A new dynamics modeling approach is proposed for flexible airships, which integrates the flight dynamics, structural dynamics, aerostatics, and aerodynamics. In particular, a comprehensive aerodynamic computation is presented, including the potential-flow aerodynamics, the viscous effects, the forces on the fins, the forces on the hull due to the fins, and the axial drag. The coupling between flexibility and aerodynamics is incorporated through the local velocity of the deformed airship. The resulting dynamics model is represented by a single set of nonlinear ordinary differential equations, describing the rigid-body motion, the elastic deformation, and the coupling between them. This model has been implemented and used to simulate the Skyship-500 airship. Simulation results demonstrate the effects of structural flexibility on the aerodynamic and dynamic characteristics of the vehicle. These results reveal that strong coupling exists between the roll rotation and the bending deflection in the lateral plane, and that the natural frequencies of the airship in air are much lower than those in vacuum. In addition, the nonlinear dynamics model is numerically linearized to investigate the aeroelastic stability of the airship.

Adaptive Reactionless Motion and Parameter Identification in Postcapture of Space Debris

This paper presents a new control scheme for the problem of a space manipulator after capturing an unknown target, such as space debris. The changes in the dynamics parameters of the system, as a result of capturing an unknown target, must be accommodated because they may lead to poor performance of the trajectory control and attitude stabilization system. To address this issue in the postcapture scenario, the adaptive reactionless control algorithm to produce the arm motions with minimum disturbance to the base is proposed in this study. In addition, the online momentum-based estimation method is developed for inertia-parameter identification after the space manipulator grasps an unknown tumbling target with unknown angular momentum. This control scheme is intended for use in the transition phase from the instant of capture until the unknown parameters are identified and/or the available stabilization methods can be applied properly. To verify the validity and feasibility of the proposed concept, MSC.Ada...

Validation of Nonlinear Viscoelastic Contact Force Models for Low Speed Impact

Compliant contact force modeling has become a popular approach for contact and impact dynamics simulation of multibody systems. In this area, the nonlinear viscoelastic contact force model developed by Hunt and Crossley (1975, “Coefficient of Restitution Interpreted as Damping in Vibroimpact,” ASME J. Appl. Mech., 42, pp. 440–445) over 2 decades ago has become a trademark with applications of the model ranging from intermittent dynamics of mechanisms to engagement dynamics of helicopter rotors and implementations in commercial multibody dynamics simulators. The distinguishing feature of this model is that it employs a nonlinear damping term to model the energy dissipation during contact, where the damping coefficient is related to the coefficient of restitution. Since its conception, the model prompted several investigations on how to evaluate the damping coefficient, in turn resulting in several variations on the original Hunt–Crossley model. In this paper, the authors aim to experimentally validate the Hunt–Crossley type of contact force models and furthermore to compare the experimental results to the model predictions obtained with different values of the damping coefficient. This paper reports our findings from the sphere to flat impact experiments, conducted for a range of initial impacting velocities using a pendulum test rig. The unique features of this investigation are that the impact forces are deduced from the acceleration measurements of the impacting body, and the experiments are conducted with specimens of different yield strengths. The experimental forces are compared with those predicted from the contact dynamics simulation of the experimental scenario. The experiments, in addition to generating novel impact measurements, provide a number of insights into both the study of impact and the impact response.

Nonlinear Strain Measures, Shape Functions and Beam Elements for Dynamics of Flexible Beams

In this paper, we examine several aspects of the development of an explicit geometrically nonlinear beam element. These are: (i) linearization of the displacement field; (ii) the effect of a commonly adopted approximation for the nonlinear Lagrangian strain; and (iii) use of different-order shape functions for discretization. The issue of rigid-body check for a nonlinear beam element is also considered. An approximate check is introduced for an element based on an (approximate) intermediate strain measure. Several numerical examples are presented to support the analysis. The paper concludes with a discussion on the use of explicit nonlinear beam elements for multibody dynamics simulation.

Experimental Validation of Contact Dynamics Simulation of Constrained Robotic Tasks

Dynamics simulation plays a key role in the design, verification, and operation planning of space manipulator systems because of the difficulties of ground-based physical tests with large, flexible robotic systems. Modeling of contact dynamics has increasingly become an essential step in dynamics simulation of space station robotic operations (such as the assembly and maintenance of the station). This role requires the modeling tool to have very high fidelity. This paper describes a research project aimed at experimentally validating a general contact dynamics simulation software developed by McDonald Dettwiler Space and Advanced Robotics Ltd (previously Spar Aerospace Ltd). The experimental tests were carried out in the robotics laboratory at the University of Victoria. The validation results demonstrated that the software is capable of predicting realistic contact behavior.