Tobias Bruckmann

A real-time capable force calculation algorithm for redundant tendon-based parallel manipulators

Tendon-based parallel manipulators with n d.o.f. use at least m = n + 1 tendons to guide the end effector along a given trajectory. Since tendons can only transmit limited and tractive forces, it is essential to apply a valid tendon force distribution. Due to safety and precision requirements, a combined position and force control is needed where the force calculation delivers the desired tendon force distributions. The high dynamic potential of the robot demands for realtime capable algorithms. To avoid steps in the motor torques the calculated tension force distributions also have to be continuous along the trajectory. In this paper, a new algorithm for tendon force distribution calculations capable for usage on a realtime system is proposed and its continuity is proven.

Closed-form Force Distribution for Parallel Wire Robots

This paper presents an algorithm to determine feasible force distributions for parallel wire robots in closed-form. The force distributions are continuous along trajectories and differentiable at most of the points. The computational efforts are strictly bounded and small even for large numbers of wires. The algorithm is compared to other approaches for calculation of force distribution in terms of the numerical effort and their applicability for control purposes.

Wire Robots Part I: Kinematics, Analysis & Design

One drawback of classical parallel robots is their limited workspace, mainly due to the limitation of the stroke of linear actuators. Parallel wire robots (also known as Tendon-based Steward platforms or cable robots) face this problem through substitution of the actuators by wires (or tendons, cables, . . .). Tendon-based Steward platforms have been proposed in (Landsberger & Sheridan, 1985). Although these robots share the basic concepts of classical parallel robots, there are some major differences:

A Versatile Tension Distribution Algorithm for

Redundancy resolution of redundantly actuated cable-driven parallel robots (CDPRs) requires the computation of feasible and continuous cable tension distributions along a trajectory. This paper focuses on n-DOF CDPRs driven by n + 2 cables, since, for n = 6, these redundantly actuated CDPRs are relevant in many applications. The set of feasible cable tensions of n-DOF (n + 2)-cable CDPRs is a 2-D convex polygon. An algorithm that determines the vertices of this polygon in a clockwise or counterclockwise order is first introduced. This algorithm is efficient and can deal with infeasibility. It is then pointed out that straightforward modifications of this algorithm allow the determination of various (optimal) cable tension distributions. A self-contained and versatile tension distribution algorithm is thereby obtained. Moreover, the worst-case maximum number of iterations of this algorithm is established. Based on this result, its computational cost is analyzed in detail, showing that the algorithm is efficient and real-time compatible even in the worst case. Finally, experiments on two six-degree-of-freedom eight-cable CDPR prototypes are reported.

n

Welcome.- Motion Planning.- Force Distribution.- Application and Protoypes.- Design and Components.- Kinematics and Interval Methods.- Calibration und Identification.- Control.- Dynamics Modelling.

-DOF Parallel Robots Driven by

Completely and redundantly restraint tendon-based Stewart platforms demand for an appropriate distribution of tendon forces to control the platform on a given trajectory. Thus, position control has to be extended by a tendon force controller which generates continuous and feasible force values. The computation of such force distributions can be formulated as a constrained optimization problem. Solving the problem is numerically expensive and requires an algorithm which is capable to be integrated into a realtime environment. In this paper, a new algorithm for tendon force distribution calculations capable for usage on a realtime system is proposed.

n+2

Human reaction to external stimuli can be investigated in a comprehensive way by using a versatile virtual-reality setup involving multiple display technologies. It is apparent that versatility remains a main challenge when human reactions are examined through the use of haptic interfaces as the interfaces must be able to cope with the entire range of diverse movements and forces/torques a human subject produces. To address the versatility challenge, we have developed a large-scale reconfigurable tendon-based haptic interface which can be adapted to a large variety of task dynamics and is integrated into a Cave Automatic Virtual Environment (CAVE). To prove the versatility of the haptic interface, two tasks, incorporating once the force and once the velocity extrema of a human subjects extremities, were implemented: a simulator with 3-DOF highly dynamic force feedback and a 3-DOF setup optimized to perform dynamic movements. In addition, a 6-DOF platform capable of lifting a human subject off the ground was realized. For these three applications, a position controller was implemented, adapted to each task, and tested. In the controller tests with highly different, task-specific trajectories, the three robot configurations fulfilled the demands on the application-specific accuracy which illustrates and confirms the versatility of the developed haptic interface.

Cables

In (Bruckmann et al., 2008) the kinematics, analysis and design of wire robots were presented. This chapter focuses on control and applications of wire robots. Wire robots are a very recent area of research. Nevertheless, they are well studied and already in application (see section 5). Due to their possible lightweight structure, wire robots can operate at very high velocities. Hence, as can be seen by experiment, only positioning control using the inverse kinematics is not sufficient. In particular, slackness in the wires can be observed at highly dynamic motions. To overcome this problem, force control can be employed. In section 4 different control schemes are proposed. The required dynamical model is obtained in section 2, while for the calculation of feasible wire force distributions are proposed in section 3. Since wire robots are kinematically redundant the latter is not straightforward, but requires advanced approaches. The same holds for the control schemes, since a CRPM as well as a RRPM is a non-linear, coupled, redundant system (Ming & Higuchi, 1994).

Cable-Driven Parallel Robots

Intralogistics systems are a rapidly growing market. Today, high racks and automated storage retrieval machines are widely used to store and handle industrial goods. Conventional storage retrieval machines show a major drawback: While the containers or goods to be moved are often very lightweight, the storage retrieval machine itself may weight up to two tons which limits the energy efficiency and the motion capabilities. This limitation is a problem since the reduction of cycle times is crucial in logistics applications. Therefore, faster motions are desired. At the same time, a main focus in intralogistics development is on energy-saving solutions as part of the ongoing climate change debate. Together with the rising energy costs, this paves the way for radical new concepts which go beyond the lightweight construction of conventional storage retrieval machines. Recently, a huge research project started to realize an alternative approach for a storage retrieval machine system. This approach uses a parallel wire robot system to move the goods to be stored to the desired position. The system is extremely lightweight and therefore, fast motions are possible while the required energy is comparably low. Therefore, cycle times for the transport of the goods can be drastically reduced which is crucial in this application. The paper presented here describes both design concepts which were already presented, as well as optimized geometries which are superior in terms of workspace coverage and stiffness. First simulation results are shown and discussed with a focus on the potential of the system for precise loading and unloading of containers. Besides that, the overall mechatronic system design is introduced.Copyright

A new force calculation algorithm for tendon-based parallel manipulators

Wind tunnels are an experimental tool to evaluate the air flow properties of vehicles in model scale and to optimize the design of aircrafts and aircraft components. Also the hydrodynamic properties of marine components like ship hulls or propulsion systems can be examined. For advanced optimization, it is necessary to guide the models along defined trajectories during the tests to vary the angle of attack. Due to their good aerodynamical properties, parallel wire robots were successfully used to perform these maneuvers in wind tunnels. Compared to aircraft hulls, marine models may be very heavy-weight (up to 150 kg). Thus, the suspension system must be very stiff to avoid vibrations. Additionally, fast maneuvers require powerful drives. On the other hand, the positioning system should not influence the air flow to ensure unaltered experimental results. In this paper, different designs are presented and discussed.