Hubert Gattringer

Shape Control of Flexural Vibrations of Circular Plates by Shaped Piezoelectric Actuation

Vibrations of smart elastic plates with integrated piezoelectric actuators are considered. Piezoelastic layers are used to generate a distributed actuation of the plate. A spatial shape function of the piezoelastic actuators is sought such that flexural vibrations induced by external forces can be completely nullified. An analytic solution of this problem is worked out for the case of clamped circular plates with a spatially constant force loading. The Kirchhoff theory of thin plates is used to derive this analytic solution. Our result is successfully validated by means of coupled 3-dimensional finite-element computations.

On time-optimal trajectory planning for a flexible link robot

This article focuses on time-optimal trajectory planning for robots with flexible links. Minimum time trajectories along specified paths as well as time-optimal point-to-point motions, which avoid vibration excitation due to elastic deflections, are determined. This is achieved by additionally constraining parts of the generalized forces and generalized force derivatives, resulting from the elastic potential. Therefore, the dynamical robot model is obtained using the Projection Equation. In a further step, a reduced model with the most essential degrees of freedom and sufficient accuracy is introduced, resulting in a flat system. Utilizing this, a trajectory control with an exact feedforward linearization in combination with a feedback part, consisting of a motor joint as well as a joint torque control, is realized. This nearly ideal control is used for moving on the time-optimal trajectories. The optimization is conducted with respect to velocity, jerk and motor torques as well as the newly introduced constraints, computable due to the flatness of the system. Experimental results demonstrate the improvement concerning vibration avoidance of the considered robot. Furthermore, a comparison between the occurring bending stress and the maximum permissible bending stress shows that mechanical damage is prevented with the use of the additional constraints.

Collocative PD Control of Circular Plates with Shaped Piezoelectric Actuators/Sensors

Abstract: In this paper, flexural vibrations of smart circular plates are considered. Distributed actuators and sensors are realized by means of spatially shaped piezoelastic layers. We use piezoelectric actuating layers shaped in order to annihilate deflections due to known external transverse forces. Such spatial shape functions correspond to the distribution of the static bending moment in the form of the so-called Marcus moment of the plate due to the external forces. When only the spatial distribution of the external forces is known, but their time evolution may be arbitrary, an automatic control system must be used in order to minimize the plate vibrations. To utilize the concept of collocated sensing, a shaped piezoelectric sensor is required that measures the so-called natural output. It is shown that the above shape function of the actuator can be used as the shape function of the sensor in order to achieve this goal. Hence, the shaped piezoelectric layer can be used as a self-sensing actuator without violating the requirements of collocated control. We develop the corresponding transfer function for the case of a clamped circular plate with a space-wise constant transverse force. This transfer function is used for the design of a self-sensing PD controller. It is proven that the energy of the closed-loop system becomes a positive definite function, its time derivative being negative semi-definite, such that the PD-controlled plate is stable. In a numerical study, output and input signals of the closed loop are discussed. This study successfully demonstrates the ability of the proposed method.

Optimizing Industrial Robots for Accurate High-Speed Applications

Today’s standard robotic systems often do not meet the industry’s demands for accurate high-speed robotic applications. Any machine, be it an existing or a new one, should be pushed to its limits to provide “optimal” efficiency. However, due to the high complexity of modern applications, a one-step overall optimization is not possible. Therefore, this contribution introduces a step-by-step sequence of multiple nonlinear optimizations. Included are optimal configurations for geometric calibration, best-exciting trajectories for parameter identification, model-based control, and time/energy optimal trajectory planning for continuous path and point-to-point trajectories. Each of these optimizations contributes to the improvement of the overall system. Existing optimization techniques are adapted and extended for use with a standard industrial robot scenario and combined with a comprehensive toolkit with discussions on the interplay between the separate components. Most importantly, all procedures are evaluated in practical experiments on a standard robot with industrial control hardware and the recorded measurements are presented, a step often missing in publications in this area.

Modeling and Control of a Pneumatically Driven Stewart Platform

Electrically driven Stewart platforms are used in the field of machine tooling and robotics, where very accurate positions have to be reached associated with heavy loads. In this paper we present a pneumatically driven Stewart platform powered by fluidic air muscles. Due to the elasticity of the muscles and air as driving medium, the robot is predestined for applications where compliance plays a major role. Compliant behavior is necessary for direct contact with humans. Fitness is an area, where this contact is given and a fast movement is needed for the body workout. Another field of application are simulators for computer games or 6D cinemas. To realize the six degrees of freedom (x, y, z, α, β, y ) for the Tool Center Point (TCP) there are six fluidic muscles. Due to the fact that the muscles are only able to pull on the platform, there is a spring in the middle that applies a compressive force to the moving part of the robot. The spring is a non modified spiral spring which is commonly used for the suspension of a passenger car. As a result of the kinematical model (inverse kinematics, forward kinematics) the workspace is optimized. To dimension and test the dynamical behavior, a Matlab/Simulink model is derived. This is done by applying the Projection Equation, a synthetical method for obtaining the equations of motions for multi body systems. Based on the dynamical model we develop a control concept in a cascaded structure (pressure control, linearization, position control). A laboratory setup is used to validate the simulation model. Both, simulations as well as experimental results demonstrate the success of the proposed concept.

A persistent method for parameter identification of a seven-axes manipulator

This paper presents a persistent method for the identification problem of open-chained robotic systems. Based on the Projection Equation, a new, direct method to collect the dynamic and friction parameters in linear form is worked out. However, in this form, linear dependencies in the parameters occur and they are canceled out with the help of the QR algorithm. The obtained linear independent parameters are the base parameters of the system. To ensure a good excitation, the identification is improved by using optimized trajectories defined by Fourier-series, taking also physical constraints into account. The evaluation of the dynamic robot parameters is realized with a least squares error optimization. Furthermore, the result strongly depends on a special choice of weighting matrices for the error. Experimental results for a seven-axes robotic system (standard six-axes industrial manipulator mounted on a linear axis) are presented in detail. Additionally, the influence of temperature effects to base parameter changes is discussed.

Efficient Online Computation of Smooth Trajectories Along Geometric Paths for Robotic Manipulators

This paper presents a fast computation method for time-optimal robot state trajectories along specified geometric paths. A main feature of this new algorithm is that joint positions can be generated in realtime. Hence, not only joint velocities and accelerations limits but also constraints on joint jerks and motor torques can be considered. Jerk limits are essential to avoid vibrations due to (not-modeled) gear or structure flexibilities. For the limitation of motor torques a complete dynamic robot model including Coulomb and viscous friction is used. The underlying optimal control problem is found by projecting the problem onto the geometric path. The resulting state vector contains path position, speed and acce- leration while path jerk is used as input. From optimal control theory it follows that the path jerk has to be chosen at its boundaries, which can be computed for each state in each step. Continuous state progress is assured via so called test trajectories which are additionally computed in each step. As an example the algorithm is applied to a six-axis industrial robot moving along a straight line in Cartesian space.

A bipedal walking pattern generator that considers multi-body dynamics by angular momentum estimation

Typically, gait pattern generation for bipedal robots utilizes a simplified model, neglecting the rate of change of the angular momentum. In this paper a linear parameter optimization problem for this simplified model, extended by an estimation of the angular momentum, is proposed to generate stable walking patterns that can be solved online and still consider the nonlinear effects of the multi-body model. The scheme was used successfully to generate trajectories for a full-size humanoid robot.

Real-Time Computation of Inexact Minimum-Energy Trajectories Using Parametric Sensitivities

The exact solution of practical trajectory optimization problems are usually not feasible in real time. The use of approximate solutions deduced form a nominal optimal solution is a potential alternative. This requires evaluation of parametric sensitivities of the nominal solution in real time. This is addressed in this paper. Improvements to existing methods are introduced that not only increase their efficiency but also ensure the constraint satisfaction of the approximation. The proposed methods are applied to a practical trajectory planning problem for a planar manipulator where the initial state is given but the final state is unknown prior to task execution.

Static inertial parameter identification for humanoid robots using a torque-free support

For the control of robots, like bipedal robots, an accurate system model with the corresponding inertial parameters can enhance the performance of the control algorithms significantly. This paper presents a convenient method for identification of the static inertial parameters with minimal sensor effort. Next to the identification method itself an approach for the calculation of optimal exciting identification poses is presented. The method is used successfully to identify the static inertial parameters of a full-size humanoid robot.