Lars Mikelsons

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 new force calculation algorithm for tendon-based parallel manipulators

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.

Wire Robots Part II Dynamics, Control & Application

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).

A Novel Tensed Mechanism for Simulation of Maneuvers in Wind Tunnels

Wind tunnels are a standard tool to evaluate the air flow properties of aerodynamical vehicles in model scale. This is widely used to optimize the design of aircrafts and aircraft components. Additionally, the hydrodynamic properties of marine components like ship hulls or propulsion systems can be predicted. It is desirable to guide the models along defined trajectories during the tests to vary the angle of attack. Parallel wire robots were successfully used to perform airplane maneuvers in wind tunnels due to their good aerodynamical and mechanical properties. Compared to aircraft design, marine models are very heavy (up to 500kg). Thus, the positioning system must be very stiff to avoid vibrations. Additionally, fast maneuvers require powerful drives. Nevertheless, the positioning system should not influence the air flow. In this contribution, a novel design is presented. Additionally, a new realtime capable force distribution calculation method for parallel tensed systems is presented.Copyright

Continuous Workspace Analysis, Synthesis and Optimization of Wire Robots

Wire robots (also called Tendon-based parallel manipulators) use a movable end-effector which is connected to a machine frame by motor driven tendons. Since tendons can transmit only pulling forces, at least m = n + 1 cables are needed to tense a system having n degrees-of-freedom. The resulting redundancy gives m − n degrees-of-freedom in the wire force distribution, making workspace analysis a complex and computationally expensive task. Discrete methods are widely used to solve this problem, but their drawback is that intermediate points on the discrete calculation grid are neglected which may lead to false results. This paper provides detailed algorithms for continuous workspace analysis for wire robots which avoid the discretization and have additional advantages. Especially, it is easy to extend the analysis methods to methods usable for the workspace synthesis.Copyright

Design Approaches for Wire Robots

Wire robots consist of a movable end-effector which is connected to the machine frame by motor driven wires. Since wires can transmit only tension, positive wire forces have to be ensured. During workspace analysis, the wires forces need to be calculated. Discrete methods do not produce satisfying results, since intermediate points on the discrete calculation grids are neglected. Using intervals instead of points leads to reliable results. Formulating the analysis problem as a Constraint-Satisfaction-Problem (CSP) allows convenient transition to the synthesis problem, i.e. to find suitable designs for practical applications. In this paper, two synthesis approaches are employed: Design-to-Workspace (i.e. calculation of an optimal robot layout for a given workspace) and an extension called Design-to-Task (i.e. calculation of the optimal robot for a specific task). To solve these optimization problems, the paper presents approaches to combine the reliability and robustness of interval-based computations with the effectiveness of available optimizer implementations.Copyright

Symbolic Model Reduction for Interval-Valued Scenarios

In many cases, the quantitative relevance of physical effects for a given technical problem is not known a priori. This holds especially for the analysis of the dynamics. Adopted from nonanalog circuit design, in the last years symbolic model reduction techniques found their way towards mechatronic system modeling. Given a scenario (system inputs, initial values, parameters) and an error bound, symbolic model reduction reduces the detailed model to a less complex model, which is guaranteed to stay within predefined error bounds. However, presently symbolic reduction techniques deliver reduced models, which are only verified for a single scenario. For example a reduced vehicle model emerging from the reduction of a complex multibody vehicle model for a cornering maneuver with a small constant steering angle, is not verified to stay inside the error bounds for any other maneuver. In this contribution this drawback is addressed by the use of interval-valued scenarios.© 2009 ASME

A Design-To-Task Approach for Wire Robots

Wire robots consist of a moveable end-effector which is connected to the machine frame by motor driven wires. Since wires can transmit only tension forces, at least m = n + 1 wires are needed to tense a system having n degrees-of-freedom. This leads to a kinematical redundancy and am–n dimensional solution space for the wire force distribution. For their calculation, sophisticated mathematical methods are required. Nevertheless workspace analysis is an important task in applications. Discrete methods do not produce satisfying results, since intermediate points on the discrete calculation grids are neglected. To overcome this problem, intervals instead of points can be used. On the one hand, this leads to reliable results, on the other hand, the approach can be extended to solve synthesis tasks, which is even more important in practical applications. In this paper, a Design-to-Workspace approach using interval analysis is presented, i.e. calculation of an optimal robot layout for a given workspace. Furthermore, a first extension of this approach to a Design-to-Task approach is presented. Design-to-Task denotes the problem of calculating the optimal robot for a specific task.