Brian Mirtich

Impulse-based simulation of rigid bodies

We introduce a promising new approach to rigid body dynamic simulation called impulse-based simulation. The method is well suited to modeling physical systems with large numbers of collisions, or with contact modes that change frequently. All types of contact (colliding, rolling, sliding, and resting) are modeled through a series of collision impulses between the objects in contact, hence the method is simpler and faster than constraint-based simulation. We have implemented an impulse-based simulator that can currently achieve interactive simulation times, and real time simulation seems within reach. In addition, the simulator has produced physically accurate results in several qualitative and quantitative experiments. After giving an overview of impulse-based dynamic simulation, we discuss collision detection and collision response in this context, and present results from several experiments.

Fast and accurate computation of polyhedral mass properties

The location of a bodys center of mass, and its moments and products of inertia about various axes are important physical quantities needed for any type of dynamic simulation or physical based modeling. We present an algorithm for automatically computing these quantities for a general class of rigid bodies: those composed of uniform density polyhedra. The mass integrals may be converted into volume integrals under these assumptions, and the bulk of the paper is devoted to the computation of these volume integrals. Our algorithm is based on a three-step reduction of the volume integrals to successively simpler integrals. The algorithm is designed to minimize the numerical errors that can result from poorly conditioned alignment of polyhedral faces. It is also designed for efficiency. All required volume integrals of a polyhedron are computed together during a single walk over the boundary of the polyhedron; exploiting common subexpressions reduces floating point operations. We present numerical results detailing the speed and accuracy of the algorithm, and also give a complete low level pseudocode description.

Easily computable optimum grasps in 2-D and 3-D

We consider the problem of finding optimum force closure grasps of two and three-dimensional objects. Our focus is on grasps which are useful in practice, namely grasps with a small number of fingers, with friction at the contacts. Assuming frictional contact and rounded finger tips-very mild assumptions in practice-we give new upper (and lower) bounds on the number of fingers necessary to achieve force closure grasps of 2-D and 3-D objects. We develop an optimality criterion based on the notion of decoupled wrenches, and use this criterion to derive optimum two and three finger grasps of 2-D objects, and optimum three finger grasps for 2-D objects. We present a simple O(n) algorithm for computing these optimum grasps for convex polygons, a O(n log n) algorithm for nonconvex polygons, and an O(n/sup 3/) algorithm for polyhedra. In studying these optimum grasps, we derive several interesting theoretical results concerning grasp geometry.<<ETX>>

Using skeletons for nonholonomic path planning among obstacles

The authors describe a practical path planner for nonholonomic robots in environments with obstacles. The planner is based on building a one-dimensional, maximal clearance skeleton through the configuration space of the robot. Rather than using the Euclidean metric to determine clearance, a special metric which captures information about the nonholonomy of the robot is used. The robot navigates from start to goal states by loosely following the skeleton. The resulting paths taken by the robot are of low complexity. Much of the computation can be done offline for a given robot, making for an efficient planner. The focus is on path planning for mobile robots, particularly the planar two-axle car, but the underlying ideas may be applied to planners for other nonholonomic robots.<<ETX>>

Estimating pose statistics for robotic part feeders

In automated assembly lines, part feeders often impose a bottleneck that restricts throughput. To facilitate the design of parts and assembly lines, the authors estimate feedrates based on CAD models of parts. A previous paper (Golberg and Craig, 1995) described how to predict throughput for a vision-based robotic part feeder given the distribution of part poses when parts are randomly dropped on a conveyor belt. Estimating this distribution is also useful for the design of traditional feeders such as vibratory bowls. In this paper the authors describe three algorithms for estimating pose distributions. The authors review the quasi-static estimate reported in Wiegley et al. (1992) and introduce a refinement that takes into account some measure of dynamic stability. The perturbed quasi-static estimate can be computed very rapidly and is more accurate than the quasi-static. Still more accurate are estimates based on Monte Carlo simulation using Impulse, although the latter comes at the penalty of increased computation time. The authors compare estimates from all three algorithms with physical experiments.

Shortest paths for a car-like robot to manifolds in configuration space

Reeds and Shepp (1990) studied the problem of finding the shortest feasible path for a car-like robot between two points in configuration space. We extend their results to find the shortest feasible path between a point and a manifold in configuration space. Our approach is based on the Lagrange method for optimizing a function while constrained to a manifold. Solving the problem analytically is much faster than numerical dis cretization techniques. In addition to providing insight into the underlying structure of Reeds and Shepp paths, this research has many applications in path planning. Planning algorithms often rely on the notion of clearance from obstacles, and for car-like mobile robots, clearance is closely related to the length of the shortest feasible path to an obstacle. In addition, one may want to bring the robot to a predefined path (such as a skeleton). Skeletonization and potential field methods are two examples of planning paradigms where our algorithm would prove useful.

Part pose statistics: estimators and experiments

Many of the most fundamental examples in probability involve the pose statistics of coins and dice as they are dropped on a flat surface. For these parts, the probability assigned to each stable face is justified based on part symmetry, although most gamblers are familiar with the possibility of loaded dice. In industrial part feeding, parts also arrive in random orientations. We consider the following problem: given part geometry and parameters such as center of mass, estimate the probability of encountering each stable pose of the part. We describe three estimators for solving this problem for polyhedral parts with known center of mass. The first estimator uses a quasistatic motion model that is computed in time O(n log n) for a part with n vertices. The second estimator has the same time complexity but takes into account a measure of dynamic stability based on perturbation. The third estimator uses repeated Monte Carlo experiments with a mechanics simulation package. To evaluate these estimators, we used a robot and computer vision system to record the pose statistics based on 3595 physical drop experiments with four different parts. We compare this data to the results from each estimator. We believe this is the first paper to systematically compare alternative estimators and to correlate their performance with statistically significant experiments on industrial parts.

Sensor based planning for a planar rod robot: incremental construction of the planar rod-HGVG

This work considers sensor based motion planning for rod-shaped robots in unknown environments. The motion planning scheme is based on the rod hierarchical generalized Voronoi graph (rod-HGVG). The rod-HGVG is a roadmap for rod-like robots, and is an extension of a prior roadmap for point-like robots. We give an incremental method to construct the rod-HGVG thereby enabling exploration of unknown environments. An important practical feature of the algorithm is its sole reliance upon the use of work space distance measurements to objects that are within line of sight. Such measurements can be readily provided by conventional range sensors. Moreover, motion planning in a configuration space is achieved without explicitly constructing each configuration space obstacle. A key result derived in this paper is the distance gradient between two convex sets.

Testing control systems through dynamic simulation

We have developed a system for testang control and behavior systems through general dynamic simulation. The video shows three animations produced by this system. The simulator Impulse computes the dynamics of articulated systems built from rigid bodies, and provides general contact and collision support. Two algorithms from computational geometry provide eficient collision detectton. On top of the simulator is a layer of interface routines which allow a control designer to build a control system from common building blocks. The video dlustrates the range of behavioral control that M posstble.