## Fachbereich Informatik

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#### Year of publication

- 2001 (21) (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)

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.

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.

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 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 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.

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.

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.

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.