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## Impulse-based Dynamic Simulation of Rigid Body Systems (1996)

Citations: | 164 - 6 self |

### Citations

7671 |
Matrix Analysis
- Horn, Ch
- 1986
(Show Context)
Citation Context ...R MdR T � (3.17) where Md is a 2 2 diagonal matrix with positive entries along the diagonal, and R is the orthogonal two dimensional rotation matrix for some angle : R = sin ; sin cos5 : 2 4 cos (See =-=[HJ91]-=- for justi cation of these assertions concerning positive de nite matrices.) Combining results,2 4 u 0 x u 0 y 3 5 = R MdR T 2 4 ; cos ; sin 3 3 5 + s: As the sliding direction varies over [0� 2 ), u ... |

1136 | Curves and surfaces for computer aided geometric design: a practical guide - Farin - 1992 |

860 |
Introduction to robotics: mechanics and control
- Craig
- 2004
(Show Context)
Citation Context ...be built on top of the dynamic simulator. 5.4.1 Types of controllers There are several types of controllers that can be used to control multibodies. More information than appears here can be found in =-=[Cra89]-=-. Many systems contain passive elements such as springs and dampers attached at the joints of a multibody. These are not controllers in a strict sense, however they in uence the dynamics of the system... |

838 | Obbtree: a hierarchical structure for rapid interference detection
- GOTTSCHALK, LIN, et al.
- 1996
(Show Context)
Citation Context ...ncy. These claims are largely mitigated with a hierarchical hash table based on multiple cell sizes. A very e cient collision detection scheme based on boxes that are not axes aligned is described in =-=[GLM96]-=-. 49sy 1 2 3 Figure 2.18: A bad case for coordinate sorting. The dense clustering of box extrema along the y-axis results in O(n 2 ) exchanges for each new sort of the coordinates. 2.5 Generalizing co... |

785 | The Linear Complementarity Problem - Cottle, Pang, et al. - 1992 |

355 |
The Java Language Environment: A White Paper
- Gosling, McGilton
- 1995
(Show Context)
Citation Context ...problem created when di erent versions of Impulse have di erent compiled control laws. A better approach would be to specify high level control laws in an interpreted language, such as Scheme or Java =-=[GM95]-=-. At a control update event, the necessary dynamic states would be passed to the interpreter, which would execute the control law, and pass back control forces and torques. More general state informat... |

354 | A fast procedure for computing the distance between complex objects in three-dimensional space
- Gilbert, Johnson, et al.
- 1988
(Show Context)
Citation Context ...spheres helps, but is not enough. Gilbert, et. al. proposed a O(n) algorithm for determining the distance between convex polyhedra, which also provides a measure of penetration when polyhedra overlap =-=[GJK88]-=-. The biggest improvement over these early algorithms came from the realization that coherence could be used to greatly reduce the computations. In simulation, the collision detection system solves a ... |

345 | Animating human athletics
- Hodgins, Wooten, et al.
- 1995
(Show Context)
Citation Context ...locities. Proportionalderivative (PD) or proportional-integral-derivative (PID) controllers are two common types. PD controllers are used, for example, in the human athlete models of Hodgins, et. al. =-=[HWBO95]-=-. The basic operation of a low level controller is depicted in Figure 5.13. Suppose a particular joint is to be maintained at some desired position, q des . One approach would be to attach a spring wi... |

330 |
Probability and Statistics for Engineering and the Sciences
- Devore
- 1995
(Show Context)
Citation Context ...cumulative normal distribution function. For example, to pinpoint the probability of a particular nal pose to within 5%, with 90% certainty, = 0:05 and =0:10. From (7.3), 385 trials are su cient. See =-=[Dev82]-=- for more information. 7.5.5 Other part feeding experiments Impulse is currently being used for several other studies in part feeding. Impulsebased simulation is a good match to this domain, because t... |

210 | Approximating polyhedra with spheres for time-critical collision detection
- Hubbard
- 1996
(Show Context)
Citation Context ...ble to miss collisions. One pathological example is a bullet speeding toward a thin wall� No matter what the minimum sampling period of the collision detection system (the minimum temporal resolution =-=[Hub96]-=-), one can choose a bullet speed and wall thickness such thatthe bullet passes completely through the wall between collision checks. One correct solution is to apply detection algorithms to the four-d... |

206 | Collision detection for interactive graphics applications
- Hubbard
- 1995
(Show Context)
Citation Context ...bed and compared, and the algorithm is also compared to other bounding box techniques. 17s2.1 Introduction and related work Hubbard gives a comprehensive reference list of work in collision detection =-=[Hub94]-=-. Early approaches to collision detection for simulation solved problem instances from scratch at every time step. An example is the polyhedral collision detection algorithm of Moore and Wilhelms that... |

201 | Realistic Animation of Rigid Bodies
- Hahn
- 1988
(Show Context)
Citation Context ...sically accurate model for collisions. Hahn pioneered this simulation paradigm. This thesis expands upon his work, and improves the methods for collision detection and collision response described in =-=[Hah88]-=-. The collision detection and response modules are critical components of an impulse-based simulator, due to the central role collisions play in the simulation. These modules must be very fast, due to... |

190 | A modeling system based on dynamic constraints - Barzel, Barr - 1988 |

188 | A fast algorithm for incremental distance calculation - Lin, Canny |

178 | Impulse-based Simulation of Rigid Bodies
- Mirtich, Canny
- 1995
(Show Context)
Citation Context ...on an ellipsoid over a ballistic trajectory. ellipsoid, thus k!(t)k kL(t0)k min(Ix�Iy�Iz) = ω(t) ω y 36 qI2 x !x(t0) 2 + I2 y !y(t0) 2 + I2 z !z(t0) 2 : (2.4) min(Ix�Iy�Iz) This bound was reported in =-=[MC95b]-=-, however a slight improvement is possible. The conservation of energy de nes a di erent ellipsoid on which the angular velocity must lie. Since there is no net torque acting on a body in a ballistic ... |

156 | Advanced dynamics - Greenwood - 2003 |

134 |
Design for Assembly
- Dewhurst, Knight
- 1993
(Show Context)
Citation Context ... high frequency, small amplitude vibratory motion to move and orient parts, which are often subsequently handled by a manipulator. More detailed descriptions of these types of feeders may be found in =-=[BPM82]-=-. Vibrational parts feeders naturally led to the idea of modeling contact with impulses, since the contact modes between the part and feeder are 209shighly transient. Many non-vibrational feeders are ... |

124 | Efficient Collision Detection for Animation and Robotics
- Lin
- 1993
(Show Context)
Citation Context ... andsoa and b can not be closest points. A similar results holds if b =2 V (Fa). 2 The fundamental basis of the Lin-Canny algorithm is the converse of Theorem 2, which is true for convex objects (see =-=[Lin93]-=- for the proof). Theorem 2 Given non-intersecting convex polygons A and B, let a and b be the closest points between feature Fa of A, and feature Fb of B, respectively. If a 2 V (Fb) and b 2 V (Fa), t... |

123 |
Collision Detection for moving polyhedra
- Canny
- 1986
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Citation Context ... such thatthe bullet passes completely through the wall between collision checks. One correct solution is to apply detection algorithms to the four-dimensional hyper-polyhedra swept out in space-time =-=[Can84]-=-. These methods are too slow and have not been used in any dynamic simulators described in the literature. Most simulators systems handle the problem of missing collisions by ignoring it [CS89, MW88, ... |

117 | The calculation of robot dynamics using articulatedbody inertias
- Featherstone
- 1983
(Show Context)
Citation Context ...apter develops the forward dynamics algorithms for several classes of multibodies: collections of rigid bodies connected by joints. The algorithms presented here are the original work of Featherstone =-=[Fea83]-=-. Featherstone's algorithm is a generalized coordinate approach, meaning that there are as many state variables as degrees of freedom in the system. The advantage of this approach is that there are no... |

72 | Impulse-based dynamic simulation. In - Mirtich, Canny - 1995 |

70 | Impact With Friction,’’
- Keller
- 1986
(Show Context)
Citation Context ...nent of impulse delivered during the compression phase. This is equivalent to Newton's law for frictionless collisions. Keller uses Poisson's hypothesis to derive equations of collision with friction =-=[Kel86]-=-. Both Newton's impact law andPoisson's hypothesis can cause the total energy of the colliding bodies to increase during a collision, when friction is present. To correct this defect, Stronge proposes... |

66 |
Coulomb friction in two-dimensional rigidbody systems.
- Lotstedt
- 1981
(Show Context)
Citation Context ...rue forces in the continuous system, causing instability. Alternatives to the penalty methods are the analytic (or exact) methods for computing non-penetration contact forces, rst studied by Lotstedt =-=[Lot81]-=-. The idea is to cast the non-penetration constraints as a linear complementarity problem (LCP): 2 a = Af ; b 0 f 0 (1.2) f T a = 0: Here, a is a vector of the relative normal accelerations at the con... |

63 |
A Layered Intelligent Control System for a Mobile Robot
- Brooks
- 1986
(Show Context)
Citation Context ... as ight or loading), and send commands to low level PD controllers based on the phase. Use of state machines for higher level behavior control is described by Brooks in the context of robot planning =-=[Bro86]-=-, and by Ahmad et. al. for scenario control [ACH + 94]. 5.4.2 Controller scheduling There may bemany di erent controllers for a system, running in parallel at di erent rates. In simulation, controller... |

53 | Sensorless manipulation using massively parallel microfabricated actuator arrays,” in
- Bohringer, Donald, et al.
- 1994
(Show Context)
Citation Context ...ices also have applications in video displays. Bohringer et. al. have fabricated a motion array comprising several thousand torsional resonators distributed over a surface of a few square centimeters =-=[BDMM94]-=-, however di culties in producing and testing these motion arrays have hindered experimental results. Reznik and Brown are using Impulse to analyze motion arrays based on the model of Bohringer et. al... |

53 | Object Associations: A Simple and Practical Approach to Virtual 3D Manipulation
- Bukowski, Sequin
- 1995
(Show Context)
Citation Context ...us perspective, this example illustrates the use of simulation as a design or layout tool. Consider the labor intensive job of arranging furniture in a large, architectural virtual environment (as in =-=[BS95]-=-). The task is made easier if the user only speci es the positions of certain objects, like tables, and other objects, like chairs, adjust themselves accordingly. The chairs are intelligent objects, w... |

50 |
Mechanical Impact Dynamics, Rigid Body Collisions,
- Brach
- 1991
(Show Context)
Citation Context ...rections xed allows one to solve for the collision impulse and post-collision velocities of the bodies by solving a system of algebraic equations. Many variations on this theme are described by Brach =-=[Bra91]-=-. In the context of interactive dynamic simulation, this approach is used almost exclusively [Bar92, CS89, Hah88, LRK94, MW88, NM93]. It is often a fairly strong approximation, particularly for collis... |

49 |
Numerical Simulation of Time-Dependent Contact and Friction Problems in Rigid Body Mechanics,"
- Lotstedt
- 1984
(Show Context)
Citation Context ...he LCP (1.2), based on the principal pivoting method of Cottle and Dantzig (see [CPS92] for a detailed treatment of LCPs). Lotstedt's algorithm in the context of rigid body simulation is described in =-=[Lot84]-=-. Bara has also used LCP approaches for simulation of rigid body systems [Bar89, Bar92, Bar94]. When there is no friction in the system, the LCP (1.2) always has a solution for the contact forces, and... |

47 |
A new approach to rectangle intersections, part i&ii
- Edelsbrunner
- 1983
(Show Context)
Citation Context ...ersion of I-COLLIDE's bounding box check. Two boxes overlap if and only if their projections onto the x- andy-axes overlap. the rectangles in O(n log n+k) time, where k is the number of intersections =-=[Ede83]-=-. Hashing schemes do not su er from the clustering problem. Coherence always results in e cient updating of the hash table, unless the number of box overlaps in three dimensions is large. Coordinate s... |

43 |
Efficient Dynamic Simulation of Robotic Mechanisms
- Lilly
- 1993
(Show Context)
Citation Context ...teral constraints. Over limited intervals of motion, however, the contacts can be modeled through bilateral constraints, and closed-loop methods exist for computing the resulting manipulator dynamics =-=[Lil93]-=-. 124 Slightly to the left on the spectrum lie mechanisms, a class of systems whichscolliding contact constrained contact impulse−based domain constraint−based domain part feeders billiards & bowling ... |

39 | Designing parts feeders using dynamic simulation,”
- Berkowitz, Canny
- 1996
(Show Context)
Citation Context ...a related to a particular feeding operation. The data can determine the feeder's susceptibility to jamming, and its ability to singulate the parts. Such an application, using Impulse, is described in =-=[BC96]-=-. Exploding text Physically based modeling is not only a valuable tool for simulation and virtual prototyping, but also for generating animations. One example is the exploding text simulation. The let... |

39 |
A Symbolic Method for Calculating the Integral Properties of Arbitrary Nonconvex Polyhedra.
- Lien, Kajiya
- 1984
(Show Context)
Citation Context ...n fall into two categories, according to whether the decomposition is exact or approximate. Exact decompositions are di cult to obtain for general objects and usually require considerable human labor =-=[LK84]-=-. Approximate decompositions, such as spatial enumerations or octree methods may be easier to generate but yield only estimates of the desired integral properties [LR82b]. The resolution of these repr... |

39 | Variational principles for constrained systems: theory and experiment
- Lewis, Murray
- 1995
(Show Context)
Citation Context ... di erent answers. Lewis and Murray computed simulations based on each of these models, and then performed experiments to test their accuracy, using a large steel ball on a spinning plexiglas surface =-=[LM95]-=-. They note that the general experimental behavior was in good agreement with certain nonholonomic simulations, such as the one pictured in Figure 7.11. Also in the gure is a snapshot from a similar e... |

37 |
Algorithms for computing the volume and other integral properties of solids
- Lee, Requicha
- 1982
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Citation Context ...ensively. Lee and Requicha note that the algorithms are closely tied to the underlying representation of solid objects, and give an excellent survey of the various families of algorithms in existence =-=[LR82a]-=-. Representations based upon primitive instancing and simple sweeping have small domain of application� only simple \canned" objects may be described. Algorithms based on decomposition fall into two c... |

36 | Algorithms for polynomials in Bernstein form - Farouki, Rajan - 1988 |

31 |
Geometric collisions for time-dependent parametric surfaces
- Herzen, Barr, et al.
- 1990
(Show Context)
Citation Context ...by ignoring it [CS89, MW88, Hah88, Bar90]. Ignoring the problem is not a good solution, especially in an impulse-based paradigm, where collisions are used to model contact forces. Von Herzen, et. al. =-=[HBZ90]-=- present an algorithm that uses Lipschitz bounds to derive limits on how far parts of a parametric sur18sfaces can move over atimeinterval� their system is guaranteed to catch all collisions. The boun... |

29 | Controlling dynamic simulation with kinematic constraints, behavior functions and inverse dynamics - Isaaks, Cohen - 1987 |

24 |
Elementary dierential equations and boundary value problems
- Boy, DiPrima
- 2001
(Show Context)
Citation Context ...ay be computed by solving simple algebraic equations. The solutions of three rst order ODEs will be useful� the claims of the following observation are veri ed by separating variables and integrating =-=[BD86]-=-. Observation 1 (solutions of rst order ODEs) Let y be a di erentiable function of an independent variable that varies over the [a� b], and C be aconstant. Then: dy = C d ) y(b) =y(a)+C(b ; a) (3.10) ... |

24 | The Architecture of Newton, a General-Purpose Dynamic Simulator," - Cremer, Stewart - 1989 |

22 |
Fast contact force computation for nonpenetrating rigid bodies
- Bara®
- 1994
(Show Context)
Citation Context ...air amount of contact coherence, and constraint-based approaches can therefore work well. Bara 's blockfeeder and double-action jack are good examples of constrained-based simulation of 2D mechanisms =-=[Bar94]-=-. On the other end of the spectrum are highly unconstrained, collision intensive systems like part feeders. In these types of systems, the almost complete lack of contact coherence makes constraint-ba... |

22 | Control of balance for a nonlinear nonholonomic nonminimum phase model of a bicycle
- Getz
- 1994
(Show Context)
Citation Context ...iors. Bicycle The bicycle simulation involves an unmanned bicycle guided over an obstacle course (Figure 7.19). A controller designed to balance the bike at a speci ed roll angle was provided by Getz =-=[Get94]-=-. In contrast to the bike controller employed by Hodgins, et. al. [HWBO95], Getz's control law is nonlinear, employs a dynamic model of the bicycle, accounts for the nonholonomic constraint between th... |

21 | Curved surfaces and coherence for non-penetrating rigid body simulation - Bara - 1990 |

17 |
Analytical methods for dynamic simulation of non-penetrating rigid bodies
- Bara
- 1989
(Show Context)
Citation Context ...s below some tolerance. The time tm may bechosen as the midpoint oftheinterval (t0�t1), however Bara reports much faster convergence using an interpolation method instead of simple interval bisection =-=[Bar89]-=-. If the penetration function returns a distance of separation or penetration, rather than a simple boolean value, one can more accurately estimate the moment of collision by examining this distance a... |

17 | Dynamic simulation of interactive robotic environment - Lee, Ruspini, et al. - 1994 |

16 |
Matrices and linear transformations
- Cullen
- 1972
(Show Context)
Citation Context ...in the new frame. Matrices can also represent the coordinates of second-order tensors that map two vectors into a scalar. These coordinate matrices are transformed to a new frame in the same way. See =-=[Cul72]-=- for details. 229sA.2 Representing cross products as matrices In the vector space R 3 , the cross product ( )isanoperatortakingtwo vectors to a third vector. In coordinates, the operation can be descr... |

15 | concurrent state machines for behavior modeling and scenario control - Hierarchical - 1994 |

15 |
Interference Detection Between Curved Objects for Comp. Animation
- Lin, Manocha
- 1993
(Show Context)
Citation Context ...many of the simulations described later in the thesis. 2.2.2 Extensions to the Lin-Canny algorithm The extension of the basic Lin-Canny algorithm to curved objects has been studied by Lin and Manocha =-=[LM93]-=-. Curved bodies are approximated with a polyhedral mesh, and closest points are tracked between these meshes. The closest points on the meshes are projected onto the actual curved surfaces, and a nume... |

11 |
Dynamic simulation of nonpenetrating rigid bodies
- Bara
- 1992
(Show Context)
Citation Context ... [Bar89, Bar92, Bar94]. When there is no friction in the system, the LCP (1.2) always has a solution for the contact forces, and this solution is unique, subject to certain non-degeneracy constraints =-=[Bar92]-=-. When friction is added to the model, the corresponding LCP may not have a solution, and if a solution exists it may not be unique. Lotstedt [Lot81] gives existence and uniqueness conditions, which B... |

11 |
Calculus and Analytic Geometry
- Penney
- 1986
(Show Context)
Citation Context ... Z of F into the - plane. Then f( � � ) dA = 1Z f( � � h( � )) d d � j^n j where F h( � )=; 1 ^n (^n +^n + w): Proof: The points ( � � h( � )) lie in the plane of F, soF is the graph of h over . From =-=[EP86]-=- [Section Z 17.5, Formula (6)], s =Z f( � � ) dA f( � � h( � )) 1+ @h @ 2 + @h @ 2 d d : F The square root in the integrand reduces to j^n j ;1 , and the theorem follows. 2 This theorem provides the r... |

9 | Coping with friction for non-penetrating rigid body simulation - Bara↵ - 1991 |

9 |
A Uni ed Approach for Motion and Force Control of Robot Manipulators: the Operational Space Formulation
- Khatib
- 1987
(Show Context)
Citation Context ...gh the Jacobian:2 4! v 3 5 = J(q) _q = J(q) H ;1 (q) J T (q) ^p: The 6 6 matrix J(q) H ;1 (q) J T (q) on the right-hand side is the inverse of the operational space inertia matrix developed by Khatib =-=[Kha87]-=-. This matrix describes the apparent mass of the end e ector to an observer exerting forces and torques on it. The robot is one of two bodies involved in the collision� on the robot, call the velocity... |

8 |
Coello Coello. Automated design of part feeders using a genetic algorithm
- Christiansen, Edwards, et al.
- 1996
(Show Context)
Citation Context ... pivot grasps for a part with n faces and m stable con gurations [RKG95]. Christiansen, Edwards, and 211sCoello Coello give a genetic algorithm for designing e cient part feeders from component gates =-=[CEC96]-=-. Their algorithm takes pose statistics, such asthe ones computable by Impulse, as input. 7.5.2 Quasi-static algorithms For completeness, Problem 10 was also solved using two quasi-static algorithms. ... |

7 | de Jalon and Eduardo Bayo. Kinematic and Dynamic Simulation of Multibody Systems: the Real Time Challenge - Garcia - 1994 |

6 |
MEXX � Numerical Software for the Integration of Constrained Mechanical Multibody Systems. Konrad�Zuse�Zentrum f�ur Informationstechnik Berlin �ZIB�. Available through anonymous ftp at elib.zib� berlin.de in pub�elib�codelib
- �, Engstler�
- 1992
(Show Context)
Citation Context ...al kinematic structures, such as those with kinematic loops. They su er, however, from drift problems due to the coordinate redundancy. Some di erential-algebraic equation (DAE) solvers, such as MEXX =-=[LNPE92]-=-, employ sophisticated methods for maintaining constraints, at the price of added complexity. A summary of the pros and cons of generalized and maximal coordinate approaches is in [Bar96]. Clear compa... |

4 |
Linear�time dynamics using lagrange multipliers
- Bara��
(Show Context)
Citation Context ...uch as MEXX [LNPE92], employ sophisticated methods for maintaining constraints, at the price of added complexity. A summary of the pros and cons of generalized and maximal coordinate approaches is in =-=[Bar96]-=-. Clear comparisons of the speed and accuracy of the two methods have not been published� the best choice may be application dependent. The results of this chapter are not original, but are included f... |

4 |
A comparison of transforms and quaternions in robotics
- Funda, Paul
- 1988
(Show Context)
Citation Context ...it by normalizing the quaternion. This section derives the ODE that needs to be integrated for the orientation of a rigid body as a function of time. A more detailed presentation of quaternions is in =-=[FP88]-=-. Every element ofSO(3) can be identi ed with a rotation about some unit vector u by an angle . The matrix corresponding to this rotation is R = 2 64 u 2 x vers +cos uyuxvers ; uz sin uzuxvers + ky si... |

3 |
Dinesh Manocha, and Madhav K.Ponamgi. I-collide: An interactive and exact collision detection system for large-scaled environments
- Cohen, Lin
- 1995
(Show Context)
Citation Context ...ion detection. The very code which implements the Lin-Canny algorithm in Impulse was subsequently used for the low-level core of the I-COLLIDE collision detection package for large-scale environments =-=[CLMP95]-=-. Both the broad and narrow phases of Impulse's collision detection system rely heavily on dynamics as well. Dynamics are used to compute bounding boxes that enclose bodies' swept volumes during the b... |

2 | A Very E cient Algorithm for the Simulation of Robots and Similar - Brandl, Johanni - 1986 |

2 | Je Koechling. Classifying dynamic behavior during three dimensional frictional rigid body impact - Bhatt - 1994 |

2 |
Partitioning the parameter space according to dierent behaviors during three-dimensional impacts
- Bhatt, Koechling
- 1995
(Show Context)
Citation Context ...his chapter also presents new results concerning the determinacy of collision dynamics under the Coulomb friction model. Recently, Bhatt and Koechling have explored these issues [BK94, BK96b], and in =-=[BK96a]-=- they report some of the same results. The geometric proofs given in this chapter di er signi cantly from theirs, which are based on the roots of polynomials� in our opinion, the geometric proofs are ... |

2 | A di erential approach to graphical interaction - Gleicher - 1994 |

1 | and Je Koechling. Three dimensional frictional rigid body impact - Bhatt - 1996 |

1 |
Estimating throughput for a exible part feeder: Simulation and experiments
- Goldberg, Craig
- 1995
(Show Context)
Citation Context ...ion and orientation) of each part. The robot arm then picks up each part and moves it into a desired nal pose as illustrated in Figure 7.28. A method of estimating the throughput of this feeder is in =-=[GC95]-=-, but the method requires knowledge about the distribution of poses, particularly orientation, when the parts are scattered on the at worktable. More formally, the problem to be solved is: Problem 10 ... |

1 | Lecture notes on the spatial operator algebra for multibody dynamics - Jain, Rodriguez |

1 | Goal-directed animation of tubular articulated gures or how snakes play golf - Miller |