A.F. van der Stappen

The Gaussian sampling strategy for probabilistic roadmap planners

Probabilistic roadmap planners (PRMs) form a relatively new technique for motion planning that has shown great potential. A critical aspect of PRM is the probabilistic strategy used to sample the free configuration space. In this paper we present a new, simple sampling strategy, which we call the Gaussian sampler, that gives a much better coverage of the difficult parts of the free configuration space. The approach uses only elementary operations which makes it suitable for many different planning problems. Experiments indicate that the technique is very efficient indeed.

A computational technique for interactive needle insertions in 3D nonlinear material

We present a computational method for simulating needle insertions interactively in both 2D and 3D models of soft tissue. The approach is based on the Finite Element Method (FEM) and uses quasi-static stick-slip friction for needle/tissue interactions. The FEM equations are solved using an iterative method, and the mesh is refined adaptively near the needle trajectory. The boundary formed by the needle surface is not represented explicitly in the mesh, but its geometry is accounted for in the friction forces. This has the advantage that we can use a simple and therefore fast refinement scheme that is guaranteed to keep the mesh quality at the initial level. This approach can also be applied to the 3D situation as well as to nonlinear geometry and material models. We present results of computational experiments of the 2D simulation, and show promising samples of the 3D implementation.

Computing form-closure configurations

We present the first output-sensitive algorithm for computing all placements of four (frictionless) points that put a polygonal part in form closure. Our efficient algorithm runs in O(n/sup 2+/spl epsiv//+K) time, where n is the number of vertices of the polygon, K is the description size of the set of form closure placements, and /spl epsiv/ is an arbitrarily small constant. The basis of our algorithm is a translation of the problem into geometric searching problems, which are solved with the use of efficient data structures. Our results can be extended to the problem of computing all placements of a line and two points that put a polygonal part in form closure. The resulting algorithm runs in O(n/sup 2/ log/sup 2/ n+K) time, where K is again the description size of the output.

Exact algorithms for single frame selection on multiaxis Satellites

New multi-axis satellites allow camera imaging parameters to be set during each time slot based on competing demand for images, specified as rectangular requested viewing zones over the cameras reachable field of view. The single frame selection (SFS) problem is to find the camera frame parameters that maximize reward during each time window. We formalize the SFS problem based on a new reward metric that takes into account area coverage and image resolution. For a set of n client requests and a satellite with m discrete resolution levels, we give an algorithm that solves the SFS problem in time O(n/sup 2/m). For satellites with continuously variable resolution (m=/spl infin/), we give an algorithm that runs in time O(n/sup 3/). We have implemented all algorithms and verify performance using random inputs. Note to Practitioners-This paper is motivated by recent innovations in earth imaging by commercial satellites. In contrast to previous methods that required waits of up to 21 days for desired earth- satellite alignment, new satellites have onboard pan-tilt-zoom cameras that can be remotely directed to provide near real-time response to requests for images of specific areas on the earths surface. We consider the problem of resolving competing requests for images: Given client demand as a set of rectangles on the earth surface, compute camera settings that optimize the tradeoff between pan, tilt, and zoom parameters to maximize camera revenue during each time slot. We define a new quality metric and algorithms for solving the problem for the cases of discrete and continuous zoom values. These results are a step toward multiple frame selection which will be addressed in future research. The metric and algorithms presented in this paper may also be applied to collaborative teleoperation of ground-based robot cameras for inspection and videoconferencing and for scheduling astronomic telescopes.

Simple data-driven control for simulated bipeds

We present a framework for controlling physics-based bipeds in a simulated environment, based on a variety of reference motions. Unlike existing methods for control based on reference motions, our framework does not require preprocessing of the reference motion, nor does it rely on inverse dynamics or on-line optimization methods for torque computation. It consists of three components: Proportional-Derivative Control to mimic motion characteristics, a specific form of Jacobian Transpose Control for balance control, and Covariance Matrix Adaption for off-line parameter optimization, based on a novel high-level reward function. The framework can easily be implemented using common off-the-shelf physics engines, and generates simulations at approximately 4x realtime on a single core of a modern PC. Our framework advances the state-of-the-art by demonstrating motions of a diversity and dynamic nature previously unseen in comparable methods, including squatting, bowing, kicking, and dancing motions. We also demonstrate its ability to withstand external perturbations and adapt to changes in character morphology.

Fixturing hinged polygons

We study the problem of fixturing a chain of hinged objects in a given placement with frictionless point contacts. We define the notions of immobility and robust immobility - which are comparable to the second and first order immobility for a single object - to capture the intuitive requirement for the fixture of a chain of hinged objects. Robust immobility differs from immobility in that it additionally requires insensitivity to small perturbations of contacts. We show that (p+2) frictionless point contacts can immobilize any chain of p/spl ne/3 polygons without parallel edges; six contacts can immobilize any chain of three such polygons. Any chain of p arbitrary polygons can be immobilized with at most (p+4) contacts. We also show that /spl lceil/(6/5)(p+2)/spl rceil/ contacts suffice to robustly immobilize p polygons without parallel edges, and that /spl lceil/(5/4)(p+2)/spl rceil/ contacts can robustly immobilize p/spl ne/3 arbitrary polygons, and eight contacts can robustly immobilize three polygons.

Trap design for vibratory bowl feeders

The vibratory bowl feeder is the oldest and still most common approach to the automated feeding (orienting) of industrial parts. We consider a class of vibratory bowl filters that can be described by removing polygonal sections from the track; we refer to this class of filters as traps. For an n-sided convex polygonal part and m-sided convex polygonal trap, we give an O((n+m)log(n+m)) algorithm to decide if the part will be rejected by the trap, and an O((nm(n+m))/sup 1+/spl epsiv//) algorithm which deals with non-convex parts and traps. We then consider the problem of designing traps for a given part, and consider two rectilinear subclasses, balconies and gaps. We give linear and O(n/sup 2/) algorithms for designing feeders and have tested the results with physical experiments using a commercial inline vibratory feeder.

Output-Sensitive Computation of Force-Closure Grasps of a Semi-Algebraic Object

We propose a technique which significantly simplifies the computation of frictionless force-closure grasps of a curved planar part <i>P</i>. We use a colored projection scheme from the three-dimensional wrench space to two-dimensional screens, which allows us to reduce the problem of identifying combinations of arcs and concave vertices of <i>P</i> that admit frictionless force-closure grasps, to colored intersection searching problems in the screens. We show how to combine this technique with existing intersection searching algorithms to obtain efficient, output-sensitive algorithms to compute all force-closure grasps of <i>P</i>, where at most four hard, frictionless point contacts exert exactly four wrenches on <i>P</i>. If the boundary of <i>P</i> consists of <i>n</i> algebraic arcs of constant complexity and <i>m</i> concave vertices, we show how to compute all force-closure grasps with: (1) four contacts along four arcs in <i>O</i>(<i>n</i>^8/3log^1/3<i>n</i>+<i>K</i>) time; (2) four contacts along three arcs in O(n^5/2+ε + K) time; (3) one contact at a concave vertex and two contacts along two arcs in O(n²m^1/2+ε + K) time; (4) one contact at a concave vertex and two contacts along a single arc in O(nm) or O(n^3/2+ε + K) time (depending on the size of m); where ε is an arbitrarily small positive constant and K is the output size-that is, the number of combinations of arcs and vertices of each type, that actually admit frictionless force-closure grasps.

An exact algorithm optimizing coverage-resolution for automated satellite frame selection

Near real time satellite imaging provides timely images of the earth for weather prediction, disaster response, search and rescue, surveillance, and defense applications. As the satellite passes over the earth, camera imaging parameters are changed during each time window based on demand for images, specified as user requested zones in the reachable field of view during that time window. The satellite frame selection (SFS) problem is to find the camera frame parameters that maximize reward during each time window. To automate satellite management, we formalize the SFS problem based on a new reward metric that incorporates both image resolution and coverage. For a set of n client requests we give a series of algorithms, the fastest computes optimal results in O(n/sup 3/) for satellites with continuously variable resolution. We have implemented the algorithms and compare computation speed for all algorithms.

Output-Sensitive Computation of All Form-Closure Grasps of a Semi-Algebraic Set

We propose the first efficient output-sensitive algorithms for computing all form-closure grasps of a planar curved part P with at most four frictionless point contacts. The boundary of P consists of m concave vertices and n algebraic arcs with a constant degree. All our algorithms are output-sensitive, which means that their running times largely depend on the actual output size K rather than the (often much larger) maximum size of the output. More specifically, we show how to determine • all form-closure grasps with four points along four arcs in O(n8/3log1/3n + K) time, • all form-closure grasps with four points along three arcs in O(n5/2+ε+ K) time, • all form-closure grasps with one point at a concave vertex and two points along two arcs in O(n2m1/2+ε+ K) time, • all form-closure grasps with one point at a concave vertex and two points along a single arc in O(nm) or O(n3/2+ε+ K) time (depending on the size of m), • all form-closure grasps with two points at concave vertices and one point along arc in O(nm2) or O (n2+ε+ K) time (depending on the size of m), where ε is an arbitrarily small positive constant. All our algorithms rely on the geometric condition in three-dimensional wrench space, which is transformed into two-dimensional geometric intersection problems.