Klemens Springer

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.

Active Vibration Control of a Flexible Link Robot with MPC

Abstract In this contribution a model predictive control (MPC) design for a three axes linear robot system with flexible links and fast dynamics is presented. An appropriate model reduction is done and in combinaton with a suboptimal linearization approach, an efficient implementation is developed. Furthermore, the paper draws a performance comparison concerning vibration suppression between the outlined MPC and a convential control strategy.

A Combined Variable Displacement–Digital Cylinder Hydraulic Drive for Large Presses With High Operating Frequencies

In this technical brief, a novel hydraulic drive for large forces and power ratings at relatively high operating frequencies combining variable displacement control and hydraulic digital control is introduced. Basic analog motion control is achieved via variable displacement pumps driving a first cylinder stage. Digital control is realized by switching additional hydraulic cylinder stages on and off to support the analog stage if high forces are needed. The control strategy corresponds to this hydraulic concept. It consists of a feed forward control, a switching logic for the digital booster stages and a feed back proportional-integral (PI) control for stabilization. The validity of this concept and of the control strategy are shown by experiments on a highly downscaled test rig.

A real-time nearly time-optimal point-to-point trajectory planning method using dynamic movement primitives

This paper focuses on highly efficient real-time capable time-optimal trajectory planning for point-to-point motions. A method based on the concept of dynamic movement primitives is developed. Thereby an offline generated time-optimal point-to-point trajectory considering nonlinear physical constraints serves as reference for a movement primitive. Through variation of the goal position in a small range around the reference target, new nearly time-optimal point-to-point trajectories are obtained. For the required reconsideration of the physical constraints, a strategy is derived from a common minimum-time optimization problem formulation. Finally a comparison between this and existing realtime capable time-optimal trajectory planning methods is drawn using a six degree-of-freedom serial robot.

Comparative Study on Sensorless Vibration Suppression of Fast Moving Flexible Linear Robots

This contribution introduces three sensorless vibration suppression methods for flexible, fast moving linear robots. After some investigations concerning the required mathematical models of the flexible linear robot, several vibration suppression techniques are derived in detail. The main idea of all concepts is the specific modification of an arbitrary trajectory in real time. Therefore, all conventional control concepts of the robot may remain unchanged. The application of each technique leads nearly to a complete annihilation of the TCP vibrations immediately after the end of the trajectory. For this reason, the implementation of these methods allows much higher velocities and therefore lower cycle times in nearly every manipulation process. Over and above, these vibration suppression methods enable light-weight construction and therefore lower energy consumption and represent an important step to increase velocity and energy efficiency in automation processes.

An Efficient Method for the Dynamical Modeling of Serial Elastic Link/Joint Robots

This paper treats the dynamical modeling of elastic robots. A structured way to do this is the usage of the Projection Equation in subsystem representation in combination with the Ritz approximation method for the structural elastic degrees of freedom. Typical subsystems for such robots contain a motor, an elastic gear, an elastic link and a tip mass. Also the effect of dynamical stiffening is treated in the subsystem formulation. A final projection into the minimal space leads to the equations of motion for the whole robot. This model is analyzed in detail regarding the choice of ansatz functions for the elastic degrees of freedom. Therefore, the eigenfrequencies resulting from a linearized model are compared when using different ansatz functions. Finally, the influence of dynamical stiffening w.r.t eigenfrequencies is discussed.