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Due to continuously increasing demands in the area of advanced robot control, it became necessary to speed up the computation. One way to reduce the computation time is to distribute the computation onto several processing units. In this survey we present different approaches to parallel computation of robot kinematics and Jacobian. Thereby, we discuss both the forward and the reverse problem. We introduce a classification scheme and classify the references by this scheme.

A new and systematic basic approach to force- and vision-based robot manipulation of deformable (non-rigid) linear objects is introduced. This approach reduces the computational needs by using a simple state-oriented model of the objects. These states describe the relation between the deformable and rigid obstacles, and are derived from the object image and its features. We give an enumeration of possible contact states and discuss the main characteristics of each state. We investigate the performance of robust transitions between the contact states and derive criteria and conditions for each of the states and for two sensor systems, i.e. a vision sensor and a force/torque sensor. This results in a new and task-independent approach in regarding the handling of deformable objects and in a sensor-based implementation of manipulation primitives for industrial robots. Thus, the usage of sensor processing is an appropriate solution for our problem. Finally, we apply the concept of contact states and state transitions to the description of a typical assembly task. Experimental results show the feasibility of our approach: A robot performs several contact state transitions which can be combined for solving a more complex task.

In this chapter, the quantitative numerical simulation of the behavior of deformable linear objects, such as hoses, wires and leaf springs is studied. We first give a short review of the physical approach and the basic solution principle. Then, we give a more detailed description of some key aspects: We introduce a novel approach concerning dynamics based on an algorithm very similar to the one used for (quasi-) static computation. Then, we look at the plastic workpiece deformation, involving a modified computation algorithm and a special representation of the workpiece shape. Then, we give alternative solutions for two key aspects of the algorithm, and investigate the problem of performing the workpiece simulation efficiently, i.e., with desired precision in a short time. In the end, we introduce the inverse modeling problem which must be solved when the gripper trajectory for a given task shall be generated.

Besides the work in the field of manipulating rigid objects, currently, there are several research and development activities going on in the field of manipulating non-rigid or deformable objects. Several papers have been published on international conferences in this field from various projects and countries. But there has been no comprehensive work which provides both a representative overview of the state of the art and identifies the important aspects in this field. Thus, we collected these activities and invited the corresponding working groups to present an overview of their research. Altogether, nineteen authors coming from Japan, Germany, Italy, Greece, United Kingdom, and Australia contributed to this book. Their research work covers all the different aspects that occur when manipulating deformable objects. The contributions can be characterized and grouped by the following four aspects: * object modeling and simulation, * planning and control strategies, * collaborative systems, and * applications and industrial experiences. In the following, we give a short motivation and overview of the single chapters of the book. The simulation of deformable objects is one way to approach the problem of manipulating these objects by robots. Based on a physical model of the object and the occurring constraints, the resulting object shape is calculated. In Chapter 2, Hirai presents an energy-based approach, where the internal energy under the geometric constraints is minimized. Frugoli et al. introduce a force-based approach, where the forces between discrete particles are minimized meeting given constraints. Finally, Remde and Henrich extend the energy-based approach to plastic deformation and give a solution of the inverse simulation problem. Even if the object behavior is predicted by simulation, there is still the question of how to control the robot during a single manipulation operation. An additional question is how to retrieve an overall plan for the concatenated manipulation operations. In Chapter 3, Wada investigates the control problems when positioning multiple points of a planar deformable object. McCarrager proposes a control scheme exploiting the flexibility, rather than minimizing it. Abegg et al. use a simple contact state model to describe typical assembly tasks and to derive robust manipulation primitives. Finally, Ono presents an automatic sewing system and suggests a strategy for unfolding fabric. In several manipulation tasks, it is reasonable to apply more than one robot. Especially in cases, where the deformable object has to take a specific shape. Since the robots working at the same object are influencing each other, different control algorithms have to be introduced. In Chapter 4, Yoshida and Kosuge investigates this problem for the task of bending a sheet of metal and exploits the relation ship between the static object deformation and the bending moments. Tanner and Kyriakopoulos regard the deformable object as underactuated mechanical system and make use of the existence of non-holonomic constraints. Both approaches model the deformable object as finite elements. All of the above aspects have their counterpart in different applications and industrial experiences. In Chapter 5, Rizzi et al. present test cases and applications of their approach to simulate the manipulation of fabric, wires, cables, and soft bags. Buckingham and Graham give an overview of two European projects processing white fish including locating, gripping, and deheading the fish. Maruyama outlines the three development phases of a robot system for performing outage-free maintenance of live-line power supply in Japan. Finally, Kämper presents the development of a flexible automatic cabling unit for the wiring of long-tube lighting with plug components.

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.

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.

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.

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.

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.