Andreas Kugi

On the Passivity-Based Impedance Control of Flexible Joint Robots

In this paper, a novel type of impedance controllers for flexible joint robots is proposed. As a target impedance, a desired stiffness and damping are considered without inertia shaping. For this problem, two controllers of different complexity are proposed. Both have a cascaded structure with an inner torque feedback loop and an outer impedance controller. For the torque feedback, a physical interpretation as a scaling of the motor inertia is given, which allows to incorporate the torque feedback into a passivity-based analysis. The outer impedance control law is then designed differently for the two controllers. In the first approach, the stiffness and damping terms and the gravity compensation term are designed separately. This outer control loop uses only the motor position and velocity, but no noncollocated feedback of the joint torques or link side positions. In combination with the physical interpretation of torque feedback, this allows us to give a proof of the asymptotic stability of the closed-loop system based on the passivity properties of the system. The second control law is a refinement of this approach, in which the gravity compensation and the stiffness implementation are designed in a combined way. Thereby, a desired static stiffness relationship is obtained exactly. Additionally, some extensions of the controller to viscoelastic joints and to Cartesian impedance control are given. Finally, some experiments with the German Aerospace Center (DLR) lightweight robots verify the developed controllers and show the efficiency of the proposed control approach.

A passivity based Cartesian impedance controller for flexible joint robots - part I: torque feedback and gravity compensation

In this paper a novel approach to the Cartesian impedance control problem for robots with flexible joints is presented. The proposed controller structure is based on simple physical considerations, which are motivating the extension of classical position feedback by an additional feedback of the joint torques. The torque feedback action can be interpreted as a scaling of the apparent motor inertia. Furthermore the problem of gravity compensation is addressed. Finally, it is shown that the closed loop system can be seen as a feedback interconnection of passive systems. Based on this passivity property a proof of asymptotic stability is presented.

Unscented Kalman filter for vehicle state estimation

Vehicle dynamics control (VDC) systems require information about system variables, which cannot be directly measured, e.g. the wheel slip or the vehicle side-slip angle. This paper presents a new concept for the vehicle state estimation under the assumption that the vehicle is equipped with the standard VDC sensors. It is proposed to utilise an unscented Kalman filter for estimation purposes, since it is based on a numerically efficient nonlinear stochastic estimation technique. A planar two-track model is combined with the empiric Magic Formula in order to describe the vehicle and tyre behaviour. Moreover, an advanced vertical tyre load calculation method is developed that additionally considers the vertical tyre stiffness and increases the estimation accuracy. Experimental tests show good accuracy and robustness of the designed vehicle state estimation concept.

Tracking control for boundary controlled parabolic PDEs with varying parameters: Combining backstepping and differential flatness

The combination of backstepping-based state-feedback control and flatness-based trajectory planning and feedforward control is considered for the design of an exponentially stabilizing tracking controller for a linear diffusion-convection-reaction system with spatially and temporally varying parameters and nonlinear boundary input. For this, in a first step the backstepping transformation is utilized to determine a state-feedback controller, which transforms the original distributed-parameter system into an appropriately chosen exponentially stable distributed-parameter target system of a significantly simpler structure. In a second step, the flatness property of the target system is exploited in order to determine the feedforward controller, which allows us to realize the tracking of suitably prescribed trajectories for the system output. This results in a systematic procedure for the design of an exponentially stabilizing tracking controller for the considered general linear diffusion-convection-reaction system with varying parameters, whose applicability and tracking performance is evaluated in simulation studies.

Stability and Incremental Improvement of Suboptimal MPC Without Terminal Constraints

The stability of suboptimal model predictive control (MPC) without terminal constraints is investigated for continuous-time nonlinear systems under input constraints. Exponential stability and decay of the optimization error are guaranteed if the number of optimization steps in each sampling instant satisfies a lower bound that depends on the convergence ratio of the underlying optimization algorithm. The decay of the optimization error shows the incremental improvement of the suboptimal MPC scheme.

Nonlinear H/sub /spl infin// controller design for a DC-to-DC power converter

We present a state feedback controller for the Cuk converter. It is shown that a special type of DC-DC switched mode power supply can be handled by the theory of affine-input systems. The controller design is based on the H/sub /spl infin//-theory of nonlinear systems. Using an appropriate exogenous system, the stationary control error can be made arbitrarily small. Furthermore, this design method leads to a simple controller and the stability of the closed loop can be guaranteed in the sense of Lyapunov. The implementation for a laboratory model shows a good tracking and disturbance behavior, which proves the feasibility of the proposed procedure.

Decoupling based Cartesian impedance control of flexible joint robots

This paper addresses the impedance control problem for flexible joint manipulators. An impedance controller structure is proposed, which is based on an exact decoupling of the torque dynamics from the link dynamics. A formal stability analysis of the proposed controller is presented for the general tracking case. Preliminary experimental results are given for a single flexible joint.

Modeling and simulation of a hydrostatic transmission with variable-displacement pump

The S-matic power split drive of Steyr Antriebstechnik is a drive box for vehicular drive systems which combines the advantages of hydrostatic and mechanical transmission. This paper is concerned with the mathematical modeling of the hydrostatic unit of the drive box with special emphasis on the swash-plate mechanism of the variable-displacement pump. For reasons of reliability no measurement device is planned for the variable swash-plate angle. Therefore, a simple discrete on-line simulator for the swash-plate angle is derived by simplifying gradually the mathematical model on the basis of physical considerations.

Trajectory Tracking of a 3DOF Laboratory Helicopter Under Input and State Constraints

This brief deals with the tracking control design of a helicopter laboratory experimental setup. In order to be able to realize highly dynamic flight maneuvers, both input and state constraints have to be systematically accounted for within the control design procedure. The mathematical model being considered constitutes a nonlinear mathematical mechanical system with two control inputs and three degrees of freedom. The control concept consists of an inversion-based feedforward controller for trajectory tracking and a feedback controller for the trajectory error dynamics. The design of the feedforward controller for a point-to-point flight maneuver is traced back to the solution of a 2-point boundary value problem in the Byrnes-Isidori normal form of the mathematical model. By utilizing special saturation functions, the given constraints in the inputs and states can be systematically incorporated in the overall design process. In order to capture model uncertainties and external disturbance, an optimal state feedback controller is designed on the basis of the model linearization along the desired trajectories. The proposed control scheme is implemented in a real-time environment, and the feasibility and the excellent performance are demonstrated by means of experimental results.

Flatness-based tracking control of a piezoactuated Euler–Bernoulli beam with non-collocated output feedback: theory and experiments†

This paper considers the combination of flatness-based motion planning and feedforward control with output feedback to achieve robust tracking of prescribed trajectories for the tip displacement of a multi-layered piezoelectric cantilever beam. Thereby, the flatness property of the distributed-parameter beam model is exploited to derive the infinite-dimensional tracking error system, which serves as the basis for the design of the output error feedback control. The stability of the resulting closed-loop system involving the infinite-dimensional beam model is proven in an input/output sense by utilizing a Nyquist-type stability criterion. Experimental results illustrate the high tracking performance in view of exogenous disturbances. The presented approach provides a systematic extension of the two-degrees-of-freedom control concept to distributed-parameter systems. †This paper is dedicated to Prof. Michel Fliess on the occasion of his 60th birthday.