Simulation of Mechanical Systems With Multiple Frictional Contacts

There are several applications in robotics and manufacturing in which nominally rigid objects are subject to multiple frictional contacts with other objects. In most previous work, rigid body models have been used to analyze such systems. There are two fundamental problems with such an approach. Firstly, the use of frictional laws, such as Coulomb\u27s law, introduce inconsistencies and ambiguities when used in conjunction with the principles of rigid body dynamics. Secondly, hypotheses traditionally used to model frictional impacts can lead to solutions which violate principles of energy conservation. In this paper these problems are explained with the help of examples. A new approach to the simulation of mechanical systems with multiple, frictional constraints is proposed which is free of inconsistencies

Dynamics of Rigid Bodies Undergoing Multiple Frictional Contacts

There are several applications in robotics and manufacturing in which nominally rigid objects are subject to multiple frictional contacts with other objects. In most previous work, rigid body models have been used to analyze such systems. There are two fundamental problems with such an approach. Firstly, the use of frictional laws, such as Coulomb\u27s law, introduce inconsistencies and ambiguities when used in conjunction with the principles of rigid body dynamics. Secondly, hypotheses traditionally used to model frictional impacts can lead to solutions which violate principles of energy conservation. In this paper these problems are explained with the help of examples. A new approach to the simulation of mechanical systems with multiple, frictional constraints is proposed which is free of inconsistencies

Oblique Frictional Impact of a Bar: Analysis and Comparison of Different Impact Laws

In this paper a basic, easily to multi-contact problems extendable, non-smooth approach is applied to analyze a bar striking an inelastic half-space. Coulomb contact is assumed and modeled by using set-valued Newtonian impact laws in normal as well as in tangential direction. The resulting linear complementarity problem contains all possible impact states and provides an instantaneous collision operator that respects all inequality constraints. This operator depends on the orientation of the bar and determines uniquely the post-impact velocities as functions of the pre-impact state. Different types of solutions may occur, including "stick'' and "slip''. In this context, stick and slip have to be understood as the two cases characterized by the tangential impulsive force as an element of either the set-valued or of the single-valued domain of the friction law. Depending on the choice of parameters, sign reversal of the tangential contact velocity is possible. For certain inertia properties and initial conditions, the collision operator yields an impact, even for initially vanishing normal contact velocity. This phenomenon is well known as the Painlevé paradox. The results obtained by this fully non-smooth rigid body approach are compared with those of other impact models, such as a lumped mass model with compliance elements, and a collision operator used for particle interactions in flow

Impact mitigation using kinematic constraints and the full space parameterization method

A new method for mitigating unexpected impact of a redundant manipulator with an object in its environment is presented. Kinematic constraints are utilized with the recently developed method known as Full Space Parameterization (FSP). System performance criterion and constraints are changed at impact to return the end effector to the point of impact and halt the arm. Since large joint accelerations could occur as the manipulator is halted, joint acceleration bounds are imposed to simulate physical actuator limitations. Simulation results are presented for the case of a simple redundant planar manipulator

Distributed compliant model for efficient dynamic simulation of systems with frictional contacts.

ABSTRACT The use of Coulomb's friction law with the principles of classical rigid body dynamics introduces mathematical inconsistencies. Specifically, the forward dynamics problem can have no solutions or multiple solutions. In these situations an explicit model of the contact compliance at the contact point can resolve these difficulties. In this paper, we introduce a distributed compliant model for dynamic simulation. In contrast to the rigid body model and the lumped model, our approach models each contact as a finite patch and uses half space approximation to derive solutions for the small deformations and force distributions in the contact patch. This approach leads to a linear complementarity problem formulation for the contact dynamics. The existence of an unique solution can be proved for both the lumped model in the point contact case and the more accurate, distributed model. Simulation algorithm that incorporates compliant contact models and linear complementarity theory are created and demonstrated through numerical examples

A Hybrid Systems Model for Simple Manipulation and Self-Manipulation Systems

Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs individually. In concert, it is well known that the interaction of such idealized approximations can lead to conflicting and even paradoxical results. As robotics modeling moves from the consideration of isolated behaviors to the analysis of tasks requiring their composition, a mathematically tractable framework for building models that combine these simple approximations yet achieve reliable results is overdue. In this paper we present a formal hybrid dynamical system model that introduces suitably restricted compositions of these familiar abstractions with the guarantee of consistency analogous to global existence and uniqueness in classical dynamical systems. The hybrid system developed here provides a discontinuous but self-consistent approximation to the continuous (though possibly very stiff and fast) dynamics of a physical robot undergoing intermittent impacts. The modeling choices sacrifice some quantitative numerical efficiencies while maintaining qualitatively correct and analytically tractable results with consistency guarantees promoting their use in formal reasoning about mechanism, feedback control, and behavior design in robots that make and break contact with their environment. For more information: Kod*La

An Adaptive Tool-Based Telerobot Control System

Modern telerobotics concepts seek to improve the work efficiency and quality of remote operations. The unstructured nature of typical remote operational environments makes autonomous operation of telerobotic systems difficult to achieve. Thus, human operators must always remain in the control loop for safety reasons. Remote operations involve tooling interactions with task environment. These interactions can be strong enough to promote unstable operation sometimes leading to system failures. Interestingly, manipulator/tooling dynamic interactions have not been studied in detail. This dissertation introduces a human-machine cooperative telerobotic (HMCTR) system architecture that has the ability to incorporate tooling interaction control and other computer assistance functions into the overall control system. A universal tooling interaction force prediction model has been created and implemented using grey system theory. Finally, a grey prediction force/position parallel fuzzy controller has been developed that compensates for the tooling interaction forces. Detailed experiments using a full-scale telerobotics testbed indicate: (i) the feasibility of the developed methodologies, and (ii) dramatic improvements in the stability of manipulator – based on band saw cutting operations. These results are foundational toward the further enhancement and development of telerobot

Computational modeling of impact and deformation

This thesis tackles several problems arising in robotics and mechanics: analysis and computation of two- and muti-body impacts, planning a contact velocity for robotic batting, impact of an elastic rod onto a fixed foundation, robotic pickup of soft three-dimensional objects, and recovery of their gravity-free shapes. Impact is an event that lasts a very short period of time but generates a very large interaction force. Assuming Stronge’s energy-based restitution, a formal impulse-based analysis is presented for the collision of two rigid bodies at single contact point under Coulomb friction in three dimensions (3D). Based on this analysis, we describe a complete algorithm to take advantage of fast numerical integration and closed-form evaluation. For a simultaneous collision involving more than two bodies, we describe a general computational model for predicting its outcome. Based on the impact model, we then look into the task of planning an initial contact velocity between a bat and an in-flight object to send the latter to a target. In certain situations, a closed-form solution can be found, while in others, a bounding triangle algorithm of iterative nature can be employed. An alternative way of modeling impact is to consider the engaged objects to be elastic rather than rigid. A damped one-dimensional wave equation can model an elastic rod bouncing off the ground at a given initial velocity, under the influence of gravity. We derive an explicit solution based on the Method of Descent and D’Alembert’s formula. We also obtain formulas for the time of contact and analyze the dependence of the energetic coefficient of restitution on the physical constants. I conclude the thesis with two pieces of work involving deformable objects. First, an algorithm for picking up a 3D object is introduced. Homotopy continuation method is applied to solve a non-linear system for slips between objects and fingers. Some simulation and experimental results are compared. Second, I discuss an iterative fixed-point method for recovering the gravity-free shape of an object. An experiment shows that the resulting stiffness matrix gives better predictions on deformations than the conventional stiffness matrix influenced by gravity

Control of constrained robot systems

Ph.DDOCTOR OF PHILOSOPH