## Fachbereich Informatik

### Refine

#### Year of publication

- 2001 (20) (remove)

#### Language

- English (20) (remove)

#### Keywords

- AG-RESY (9)
- RODEO (7)
- vibration (3)
- genetic algorithms (2)
- trajectory planning (2)
- Assembly (1)
- Force-Torque (1)
- Manipulation skills (1)
- Robotics (1)
- SIMERO (1)

In this work we propose a set of term-rewriting techniques for modelling object-oriented computation. Based on symbolic variants of explicit substitutions calculi, we show how to deal with imperative statements like assignment and sequence in specifications in a pure declarative style. Under our model, computation with classes and objects becomes simply normal form calculation, exactly as it is the case in term-rewriting based languages (for instance the functional languages). We believe this kind of unification between functions and
objects is important because it provides plausible alternatives for using the term-rewriting theory as an engine for supporting the formal and mechanical reasoning about object-oriented specifications.

As opposed to Monte Carlo integration the quasi-Monte Carlo method does not allow for an (consistent) error estimate from the samples used for the integral approximation. In addition the deterministic error bound of quasi-Monte Carlo integration is not accessible in the setting of computer graphics, since usually the integrands are of unbounded variation. The structure of the high dimensional functionals to be computed for photorealistic image synthesis implies the application of the randomized quasi-Monte Carlo method. Thus we can exploit low discrepancy sampling and at the same time we can estimate the variance. The resulting technique is much more efficient than previous bidirectional path tracing algorithms.

We introduce two novel techniques for speeding up the generation of digital \((t,s)\)-sequences. Based on these results a new algorithm for the construction of Owen's randomly permuted \((t,s)\)-sequences is developed and analyzed. An implementation of the new techniques is available at http://www.cs.caltech.edu/~ilja/libseq/index.html

Interleaved Sampling
(2001)

The sampling of functions is one of the most fundamental tasks in computer graphics, and occurs in a variety of different forms. The known sampling methods can roughly be grouped in two categories. Sampling on regular grids is simple and efficient, and the algorithms are often easy to built into graphics hardware. On the down side, regular sampling is prone to aliasing artifacts that are expensive to overcome. Monte Carlo methods, on the other hand,
mask the aliasing artifacts by noise. However due to the lack of coherence, these methods are more expensive and not weil suited for hardware implementations. In this paper, we introduce a novel sampling scheme where samples from several regular grids are a combined into a single irregular sampling pattern. The relative positions of the regular grids are themselves determined by Monte Carlo methods. This generalization obtained by interleaving yields,significantly improved quality compared to traditional approaches while at the same time preserving much of the advantageous coherency of regular sampling. We demonstrate the quality of the new sampling scheme with a number of applications ranging from supersampling over motion blur simulation to volume rendering. Due to the coherence in the interleaved samples, the method is optimally suited for implementations in graphics hardware.

Manipulating Deformable Linear Objects: Attachable Adjustment-Motions for Vibration Reduction
(2001)

This paper addresses the problem of handling deformable linear objects (DLOs) in a suitable way to avoid acute vibration. Different types of adjustment-motions that eliminate vibration of deformable objects and can be attached to the end of an arbitrary end-effector trajectory are presented. For describing the dynamics of deformable linear objects, the finite element method is used to derive the dynamic differential equations. Genetic algorithm is used to find the optimal adjustment motion for each simulation example. Experiments are conducted to verify the presented manipulating method.

This paper deals with the handling of deformable linear objects (DLOs), such as hoses, wires or leaf springs. It investigates the a priori knowledge about the 6-dimensional force/torque signal for a changing contact situation between a DLO and a rigid polyhedral obstacle. The result is a complete list, containing for each contact change the most significant combination of force/torque signal components together with a description of the expected signal curve. This knowledge enables the reliable detection of changes in the DLO contact situation and with it the implementation of sensor-based manipulation skills for all possible contact changes.

The vibration induced in a deformable object upon automatic handling by robot manipulators can often be bothersome. This paper presents a force/torque sensor-based method for handling deformable linear objects (DLOs) in a manner suitable to eliminate acute vibration. An adjustment-motion that can be attached to the end of an arbitrary end-effector's trajectory is employed to eliminate vibration of deformable objects. Differently from model-based methods, the presented sensor-based method does not employ any information from previous motions. The adjustment-motion is generated automatically by analyzing data from a force/torque sensor mounted on the robot wrist. Template matching technique is used to find out the matching point between the vibrational signal of the DLO and a template. Experiments are conducted to test the new method under various conditions. Results demonstrate the effectiveness of the sensor-based adjustment-motion.

Manipulating Deformable Linear Objects: Model-Based Adjustment-Motion for Vibration Reduction
(2001)

This paper addresses the problem of handling deformable linear objects (DLOs) in a suitable way to avoid acute vibration. An adjustment-motion that eliminates vibration of DLOs and can be attached to the end of any arbitrary end-effector's trajectory is presented, based on the concept of open-loop control. The presented adjustment-motion is a kind of agile end-effector motion with limited scope. To describe the dynamics of deformable linear objects, the finite element method is used to derive the dynamic differential equations. Genetic algorithm is used to find the optimal adjustment-motion for each simulation example. In contrast to previous approaches, the presented method can be treated as one of the manipulation skills and can be applied to different cases without major changes to the method.

The task of handling non-rigid one-dimensional objects by a robot manipulation system is investigated. Especially, approaches to calculate motions with specific behavior in point contacts between the object and environment are regarded. For single point contacts, motions based on generalized rotations solving the direct and inverse manipulation problem are investigated. The latter problem is additionally tackled by simple rotation and translation motions. For double and multiple point contacts, motions based on Splines are suggested. In experimental results with steel springs, the predicted and measured effect for each approach are compared.

We survey old and new results about optimal algorithms for summation of finite sequences and for integration of functions from Hölder or Sobolev spaces. First we discuss optimal deterministic and randornized algorithms. Then we add a new aspect, which has not been covered before on conferences
about (quasi-) Monte Carlo methods: quantum computation. We give a short introduction into this setting and present recent results of the authors on optimal quantum algorithms for summation and integration. We discuss comparisons between the three settings. The most interesting case for Monte
Carlo and quantum integration is that of moderate smoothness \(k\) and large dimension \(d\) which, in fact, occurs in a number of important applied problems. In that case the deterministic exponent is negligible, so the \(n^{-1/2}\) Monte Carlo and the \(n^{-1}\) quantum speedup essentially constitute the entire convergence rate.

This article presents contributions in the field of path planning for industrial robots with 6 degrees of freedom. This work presents the results of our research in the last 4 years at the Institute for Process Control and Robotics at the University of Karlsruhe. The path planning approach we present works in an implicit and discretized C-space. Collisions are detected in the Cartesian workspace by a hierarchical distance computation. The method is based on the A* search algorithm and needs no essential off-line computation. A new optimal discretization method leads to smaller search spaces, thus speeding up the planning. For a further acceleration, the search was parallelized. With a static load distribution good speedups can be achieved. By extending the algorithm to a bidirectional search, the planner is able to automatically select the easier search direction. The new dynamic switching of start and goal leads finally to the multi-goal path planning, which is able to compute a collision-free path between a set of goal poses (e.g., spot welding points) while minimizing the total path length.

Point-to-Point Trajectory Planning of Flexible Redundant Robot Manipulators Using Genetic Algorithms
(2001)

The paper focuses on the problem of point-to-point trajectory planning for flexible redundant robot manipulators (FRM) in joint space. Compared with irredundant flexible manipulators, a FRM possesses additional possibilities during point-to-point trajectory planning due to its kinematics redundancy. A trajectory planning method to minimize vibration and/or executing time of a point-to-point motion is presented for FRM based on Genetic Algorithms (GAs). Kinematics redundancy is integrated into the presented method as planning variables. Quadrinomial and quintic polynomial are used to describe the segments that connect the initial, intermediate, and final points in joint space. The trajectory planning of FRM is formulated as a problem of optimization with constraints. A planar FRM with three flexible links is used in simulation. Case studies show that the method is applicable.

We study summation of sequences and integration in the quantum model of computation. We develop quantum algorithms for computing the mean of sequences which satisfy a \(p\)-summability condition and for integration of functions from Lebesgue spaces \(L_p([0,1]^d)\) and analyze their convergence rates. We also prove lower bounds which show that the proposed algorithms are, in many cases, optimal within the setting of quantum computing. This extends recent results of Brassard, Høyer, Mosca, and Tapp (2000) on computing the mean for bounded sequences and complements results of Novak (2001) on integration of functions from Hölder classes.

The simulation of random fields has many applications in computer graphics such as e.g. ocean wave or turbulent wind field modeling. We present a new and strikingly simple synthesis algorithm for random fields on rank-1 lattices that requires only one Fourier transform independent of the dimension of the support of the random field. The underlying mathematical principle of discrete Fourier transforms on rank-1 lattices breaks the curse of dimension of the standard tensor product Fourier transform, i.e. the number of function values does not exponentially depend on the dimension, but can be chosen linearly.

We present a system concept allowing humans to work safely in the same environment as a robot manipulator. Several cameras survey the common workspace. A look-up-table-based fusion algorithm is used to back-project directly from the image spaces of the cameras to the manipulator?s con-figuration space. In the look-up-tables both, the camera calibration and the robot geometry are implicitly encoded. For experiments, a conven-tional 6 axis industrial manipulator is used. The work space is surveyed by four grayscale cameras. Due to the limits of present robot controllers, the computationally expensive parts of the system are executed on a server PC that communicates with the robot controller via Ethernet.

The Analytic Blossom
(2001)

Blossoming is a powerful tool for studying and computing with Bézier and B-spline curves and surfaces - that is, for the investigation and analysis of polynomials and piecewise polynomials in geometric modeling. In this paper, we define a notion of the blossom for Poisson curves. Poisson curves are to analytic functions what Bézier curves are to polynomials - a representation adapted to geometric design. As in the polynomial setting, the blossom provides a simple, powerful, elegant and computationally meaningful way to analyze Poisson curves. Here, we
define the analytic blossom and interpret all the known algorithms for Poisson curves - subdivision, trimming, evaluation of the function and its derivatives, and conversion between the Taylor and the Poisson basis - in terms of this analytic blossom.

The paper focuses on the problem of trajectory planning of flexible redundant robot manipulators (FRM) in joint space. Compared to irredundant flexible manipulators, FRMs present additional possibilities in trajectory planning due to their kinematics redundancy. A trajectory planning method to minimize vibration of FRMs is presented based on Genetic Algorithms (GAs). Kinematics redundancy is integrated into the presented method as a planning variable. Quadrinomial and quintic polynomials are used to describe the segments which connect the initial, intermediate, and final points in joint space. The trajectory planning of FRMs is formulated as a problem of optimization with constraints. A planar FRM with three flexible links is used in simulation. A case study shows that the method is applicable.