Karl Lukas Knierim

Real-time trajectory generation for three-times continuous trajectories

A method for generating Cn, n = {1, 2, 3} close to time optimal trajectories, is presented. Therby constraints within the first n+1 derivatives are considered. The trajectory generator is able to perform within a real-time environment. The algorithm makes use of the recursive structure of the problem. The method can be used in the interpretation of hand lever input signals, to generate smooth transition trajectories between the current reference values and the desired target velocity, which then can be used to generate feed forward control inputs.

Flatness Based Control of a 3-DOF Overhead Crane with Velocity Controlled Drives

Abstract As an example of a spatial manipulator with large work space a 3-DOF overhead crane is considered. A nonlinear model of the overhead crane, including drive dynamics, is derived. The drives of trolley and winch are controlled by velocity controllers. Therefore the dynamics of the drives can be approximated and thus included into the model description. The states of the system are parameterized by the position of the load and its derivatives, therefore a flatness based trajectory tracking controller is derived. The controller achieves good tracking behavior and oscillation damping. It is shown that the controller is independent of the load mass and includes changes of the rope length. The strategy is implemented on an exemplary 3-DOF overhead crane and measurement results are presented.

Analytical Multi-Point Trajectory Generation for Differentially Flat Systems with Output Constraints

Abstract In this paper, an analytical off-line multi-point trajectory generation scheme is presented for differentially flat systems. For control of dynamical systems along a given set of control points, multi-point trajectory generation is required when input and state constraints exist. It is assumed that differential constraints for flat coordinates can be formulated explicitly. The trajectory scheme is based on analytically solving a set of polynomial equations to parameterize n-times continuously differentiable segmented transition polynomials, that approximate time optimal trajectories. The computational effort for determining valid trajectories is low in comparison to numerical optimization. As an example, a multi-point trajectory generation problem for a 3-DOF gantry crane is presented.

SAMMY - an algorithm for efficient computation of a smooth path for reference trajectory generation

An efficient algorithm to generate smooth paths from polygonal lines is presented. The smooth path is used in combination with a trajectory generator to create reference values for the 2DOF control of a multi-sensor measuring system. The algorithm handles large amounts of target points without an increase in computation time and is able to construct a path based on noisy measurement data.

Force trajectory generation for the redundant actuator in a pneumatically actuated Stewart platform

Force distribution is one of the advantage of a redundant parallel manipulator configuration, making the utilization of less powerful actuators feasible. In this contribution, a force trajectory for a redundant actuator in a seven-cylinder pneumatically-actuated Stewart platform is derived analytically using the inverse dynamic model to maximize the benefit of the additional actuator. A feed-forward scheme is proposed with a requirement of good position tracking control. An input/output linearization is applied for the redundant actuator force control design with good force tracking capability. The designed force trajectory generator is implemented in a full-size pneumatically-actuated Stewart platform, and the results show an improvement in form of force reduction on the six outer cylinders and better utilization of the redundant cylinder force capacity.

Multisensorisches Messsystem zur dreidimensionalen Inspektion technischer Oberflächen

Zusammenfassung Um die Fertigungsqualität mechanischer Bauteile aus Kleinserienproduktionen sicherzustellen werden flexible Inspektionssysteme benötigt. Zur Erfüllung dieser Anforderungen wird in diesem Beitrag eine multiskalige Inspektionsstrategie und deren Implementierung an einem Demonstrator vorgestellt. Dieser besteht aus mehreren optischen Sensoren sowie einem Aktoriksystem, das mithilfe einer angepassten Messablaufsteuerung und Regelung zur Inspektion von Unvollkommenheiten an kleinen Bauteilen wie Zahnrädern eingesetzt werden kann.

The Flying-Ball-in-Tube Experiment

One of the challenges in teaching applied control theory is to provide students with easy to understand experimental setups, which show complex but comprehensible dynamical behavior. We propose a flying-ball-in-tube experiment with stable, critically stable and unstable behavior. The benefit of the flying-ball-in-tube experiment are its in respect to time scale observable dynamics as well as the simplicity of the setup. A model of the flying-ball-in-tube experiment is derived and analyzed with respect to its stability properties. The derived model is identified and the predicted behavior is validated. In addition, the use of the experimental setup within a one week undergraduate practical is described. Within the course the students program the control environment on a micro controller within the FreeRTOS real time environment and design their own control structure.Copyright

Parameter identification and controller design for high-rack feeder systems and fork lifts

Fast and precise storing and retrieving processes are essential in a well-functioning warehouse. Floor space is expensive and limited and leads to high-bay warehouses also requiring special order picking trucks adapted to impressing heights. During the transportation of pallets and due to the lateral and rotating movements of the fork, oscillations occur in the entire truck which not only limits the working precision but also affect the material and may lead to earlier machine fatigue. This becomes an even bigger problem when lightweight structures are used for economic reasons and active damping becomes urgent for both the truck and the drivers safety. In this paper, a control approach is presented for an order picking truck based on a simplified linear parameter-varying model. Experimental measurements will be used for parameter identification and the evaluation of a first implementation. Simulations complete the investigated approaches and give information for future measurements.

Modeling of the Rotational Dynamics of a Flexible Manipulator Using FMBS to Derive a Linear Parameter Varying System

This paper deals with the derivation of the rotational dynamic matrix of a flexible large scale manipulator in the horizontal plane using the flexible multi body systems (FMBS) frame-work. It is shown, that the dynamic matrix only depends on the pose of the manipulator itself. The nonlinear dynamics of the FMBS system can be simplified and rewritten in the form of a linear parameter varying system, which can be used in the controller synthesis. The approach is exemplified at a large scale flexible link manipulator, with a range of approximately 13m, which is currently under development as a tool for ordnance and IED clearing.Copyright