Energy conserving schemes for the simulation of musical instrument contact dynamics

Collisions are an innate part of the function of many musical instruments. Due to the nonlinear nature of contact forces, special care has to be taken in the construction of numerical schemes for simulation and sound synthesis. Finite difference schemes and other time-stepping algorithms used for musical instrument modelling purposes are normally arrived at by discretising a Newtonian description of the system. However because impact forces are non-analytic functions of the phase space variables, algorithm stability can rarely be established this way. This paper presents a systematic approach to deriving energy conserving schemes for frictionless impact modelling. The proposed numerical formulations follow from discretising Hamilton's equations of motion, generally leading to an implicit system of nonlinear equations that can be solved with Newton's method. The approach is first outlined for point mass collisions and then extended to distributed settings, such as vibrating strings and beams colliding with rigid obstacles. Stability and other relevant properties of the proposed approach are discussed and further demonstrated with simulation examples. The methodology is exemplified through a case study on tanpura string vibration, with the results confirming the main findings of previous studies on the role of the bridge in sound generation with this type of string instrument

Simulation of the impact response of a sliotar core with linear and non-linear contact models

Static and dynamic models of the characteristic responses of sliotar cores made of both cork and polyurethane were studied in this work in order to understand their constitutive behaviour. Data from quasi-static tests at 10 mm/s and from dynamic impacts at speeds from 5 to 25 m/s were used to develop and evaluate the models. The quasi-static response was described well by Hertzian theory. A non-linear HunteCrossley model and a modified linear KelvineVoigt model were used to predict the dynamic response with set mass and shape coefficient parameters. The HunteCrossley model predicted well both the maximum force and maximum deflection for each ball type. The HunteCrossley model generally captured the experimental contact times well with a mean difference between experimental and model contact times of 8.3%. The mean difference between the KelvineVoigt model and experimental contact times was 7.6%, while the corresponding mean difference for the coefficient of restitution was 13.1%. Overall, the modified KelvineVoigt model predicted the parameters of contact time and coefficient of restitution well. Contact time and coefficient of restitution prediction in this linear model were not particularly sensitive to the strain rate

Contact Force Modeling Between Non Convex Objects Using a Nonlinear Damping Model

At Sandia National Laboratories, the authors are developing the ability to accurately predict motions for arbitrary numbers of bodies of arbitrary shapes experiencing multiple applied forces and intermittent contacts. In particular, they are concerned with the simulation of systems such as part feeders or mobile robots operating in realistic environments. Preliminary investigation of commercial dynamics software packages led us to the conclude that they could use a commercial code to provide everything they needed except for the contact model. They found that ADAMS best fit the needs for a simulation package. To simulate intermittent contacts, they need collision detection software that can efficiently compute the distances between non-convex objects and return the associated witness features. They also require a computationally efficient contact model for rapid simulation of impact, sustained contact under load, and transition to and from contact conditions. This paper provides a technical review of a custom hierarchical distance computation engine developed at Sandia, called the C-Space Toolkit (CSTk). In addition, the authors describe an efficient contact model using a non-linear damping term developed at Ohio State. Both the CSTk and the non-linear damper have been incorporated in a simplified two-body testbed code, which is used to investigate how to correctly model the contact using these two utilities. They have incorporated this model into ADAMS SOLVER using the callable function interface. An example that illustrate the capabilities of the 9.02 release of ADAMS with the extensions is provided

Modeling, system identication, and control for dynamic locomotion of the LittleDog robot on rough terrain

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 76-80).In this thesis, I present a framework for achieving a stable bounding gait on the LittleDog robot over rough terrain. The framework relies on an accurate planar model of the dynamics, which I assembled from a model of the motors, a rigid body model, and a novel physically-inspired ground interaction model, and then identied using a series of physical measurements and experiments. I then used the RG-RRT algorithm on the model to generate bounding trajectories of LittleDog over a number of sets of rough terrain in simulation. Despite signicant research in the field, there has been little success in combining motion planning and feedback control for a problem that is as kinematically and dynamically challenging as LittleDog. I have constructed a controller based on transverse linearization and used it to stabilize the planned LittleDog trajectories in simulation. The resulting controller reliably stabilized the planned bounding motions and was relatively robust to signicant amounts of time delays in estimation, process and estimation noise, as well as small model errors. In order to estimate the state of the system in real time, I modified the EKF algorithm to compensate for varying delays between the sensors. The EKF-based filter works reasonably well, but when combined with feedback control, simulated delays, and the model it produces unstable behavior, which I was not able to correct. However, the close loop simulation closely resembles the behavior of the control and estimation on the real robot, including the failure modes, which suggests that improving the feedback loop might result in bounding on the real LittleDog. The control framework and many of the methods developed in this thesis are applicable to other walking systems, particularly when operating in the underactuated regime.by Michael Yurievich Levashov.S.M

Kraftsensorlose Manipulator Kraftsteuerung zur Abtastung unbekannter, harter Oberflächen

Die vorliegende Arbeit zeigt ein Verfahren zur kraftgesteuerten Kontaktierung unbekannter harter Freiformflächen mit einem Standard–6DOF-Industriemanipulator (z.B. Manutec R2). Die bisher entwickelten Verfahren auf dem Gebiet der Manipulatorkraftregelung waren auf teure, fragile, mehrdimensionale Kraft-/Momentensensoren am Manipulator-Endeffektor angewiesen, die bei dem in dieser Arbeit entwickelten Ansatz der sensorlosen Kraft-/Geschwindigkeitsregelung überflüssig werden. Die Einstellung der gewünschten Kontaktkraft zu der unbekannten Umgebung erfolgt ausschließlich über eine robuste, beobachtergestützte Regelung der Motorströme der Gelenkantriebe. In freien Bewegungsphasen garantierte eine kaskadierte Kraft-/Geschwindigkeitsregelung vordefinierte Heranfahrgeschwindigkeiten an die unbekannte Kontaktoberfläche. Hierdurch eröffnen sich vollkommen neue Einsatzszenarien für die kraftkontrollierte Kontaktierung und Bearbeitung unbekannter Oberflächen oder Werkstücke beliebiger Härte und Steifigkeit