Rigid-body Dynamics Simulation Research Articles

Unbiased Rotational Moves for Rigid-Body Dynamics

We introduce an unbiased protocol for performing rotational moves in rigid-body dynamics simulations. This approach—based on the analytic solution for the rotational equations of motion for an orthogonal coordinate system at constant angular velocity—removes deficiencies that have been largely ignored in Brownian dynamics simulations, namely errors for finite rotations that result from applying the noncommuting rotational matrices in an arbitrary order. Our algorithm should thus replace standard approaches to rotate local coordinate frames in Langevin and Brownian dynamics simulations.

A representation for comparing simulations and computing the purpose of geometric features

We present a new representation that allows a rigid-body dynamic simulation to be described as a set of “causal-processes.” A causal-process is an interval of time during which both the behavior and the causes of the behavior remain qualitatively uniform. The representation consists of acyclic, directed graphs that are isomorphic to the flow of causality through the kinematic chain. Forces are the carriers of causality in this domain; thus they are central to the representation. We use this representation to compute the purposes of the geometric features on the parts of a device. To compute the purpose of a particular feature, we simulate the behavior of the device with and without the feature present. We then re-represent the two simulations as causal-processes and identify any causal-processes that exist in one simulation but not the other. Such processes are indicative of the feature's purpose. Because they are already causal descriptions of behavior, they can be directly translated into natural language descriptions of the feature's purpose. We have implemented our approach in a computer program called ExplainIT II.

Qualitative rigid-body mechanics

We present a theory of qualitative rigid-body mechanics and describe a program that uses this theory to compute qualitative rigid-body dynamic simulations. The program works directly from a qualitative representation of geometry—qualitative configuration space—without need of any metric information. The program can handle devices that are composed of an arbitrary number of fixed-axis components and springs, with driving inputs coming from both applied motions and forces. The program employs quasi-static assumptions, i.e., inertia-free motion, inelastic collisions, and frictionless contacts. It employs a new qualitative representation for forces that reduces ambiguity in force sums and hence reduces unnecessary branching.

A symplectic method for rigid-body molecular simulation

Rigid-body molecular dynamics simulations typically are performed in a quaternion representation. The nonseparable form of the Hamiltonian in quaternions prevents the use of a standard leapfrog (Verlet) integrator, so nonsymplectic Runge–Kutta, multistep, or extrapolation methods are generally used. This is unfortunate since symplectic methods like Verlet exhibit superior energy conservation in long-time integrations. In this article, we describe an alternative method, which we call RSHAKE (for rotation-SHAKE), in which the entire rotation matrix is evolved (using the scheme of McLachlan and Scovel [J. Nonlin. Sci. 16 233 (1995)]) in tandem with the particle positions. We employ a fast approximate Newton solver to preserve the orthogonality of the rotation matrix. We test our method on a system of soft-sphere dipoles and compare with quaternion evolution using a 4th-order predictor–corrector integrator. Although the short-time error of the quaternion algorithm is smaller for fixed time step than that for RSHAKE, the quaternion scheme exhibits an energy drift which is not observed in simulations with RSHAKE, hence a fixed energy tolerance can be achieved by using a larger time step. The superiority of RSHAKE increases with system size.

Small steps for mankind: Towards a kinematically driven dynamic simulation of curved path walking

AbstractA simple approach for the simulation of bipedal locomotion is presented. It is based on a kinematically driven rigid body dynamics simulation. As inputs, our system uses a 14‐DOF simplified human body model, and the instantaneous walking direction and the gait length. From these parameters, the trajectories of the left and right feet are computed over time, using a purely kinematical recipe. Optionally, trajectories of other body parts (head, shoulders, hips, hands, knees, etc.) may be derived from a simple kinematic body model. Using these additional trajectories provides for increased control over the motion, adding extra kinematic constraints to the dynamical system. The trajectories, together with optional force fields (gravity etc.), serve to drive the motion of the articulated human body model. This means that for those points in the body that have not been specified kinematically, a rigid body dynamics calculation is used to describe their motion over time. An implementation of these ideas turns out to allow a frame update rate of about 20 Hz on a personal IRISTM workstation, which is sufficiently fast for real‐time interaction.