Olav Egeland

Exponential stabilization of nonholonomic chained systems

This paper presents a feedback control scheme for the stabilization of two-input, driftless, chained nonholonomic systems, also called chained form. These systems are controllable but not asymptotically stabilizable by a smooth static-state feedback control law. In addition, exponential stability cannot be obtained with a smooth, time-varying feedback control law. Here, global, asymptotical stability with exponential convergence is achieved about any desired configuration by using a nonsmooth, time-varying feedback control law. The control law depends, in addition to the state and time, on a function which is constant except at predefined instants of time where the function is recomputed as a nonsmooth function of the state. The inputs are differentiable with respect to time and tend exponentially toward zero. For use in the analysis, a lemma on the exponential convergence of a stable time-varying nonlinear system perturbed by an exponentially decaying signal is presented. Simulation results are also shown. >

Dissipative Systems Analysis and Control: Theory and Applications

This is an up-dated addendum/erratum to the second edition of the book Dissipative Systems Analysis and Control, Theory and Applications, Springer-Verlag London, 2nd Edition, 2007.

Passivity-based adaptive attitude control of a rigid spacecraft

An adaptive control scheme for the attitude control of a rigid spacecraft is derived using a linear parameterization of the equation of motion. The tracking error is described with the Euler parameter vector. Global convergence of the tracking error to zero is shown using passivity theory. This allows for the use of time-varying positive-definite feedback gain matrices, and the results can easily be extended to other passive parameter update laws. >

Review of the damped least-squares inverse kinematics with experiments on an industrial robot manipulator

The goal of this paper is to present experimental results on the implementation of the damped least-squares method for the six-joint ABB IRb2000 industrial robot manipulator. A number of inverse kinematics schemes are reviewed which allow robot control through kinematic singularities. The basic scheme adopts a damped least-squares inverse of the manipulator Jacobian with a varying damping factor acting in the neighborhood of singularities. The effect of a weighted damped least-squares solution is investigated to provide user-defined accuracy capabilities along prescribed end-effector space directions. An online estimation algorithm is employed to measure closeness to singular configurations. A feedback correction error term is introduced to ensure algorithm tracking convergence and its effect on the joint velocity solution is discussed. Computational aspects are discussed in view of real-time implementation of the proposed schemes. Experimental case studies are developed to investigate manipulator performance in the case of critical end-effector trajectories passing through and near the shoulder and wrist singularities of the structure. >

Exponential stabilization of an underactuated surface vessel

The paper shows that a large class of underactuated vehicles cannot be asymptotically stabilized by either continuous nor discontinuous state feedback. Furthermore, stabilization of an underactuated surface vessel is considered. Controllability properties of the surface vessel is presented, and a continuous periodic time-varying feedback law is proposed. It is shown that this feedback law exponentially stabilizes the surface vessel to the origin, and this is illustrated by simulations.

Task-space tracking with redundant manipulators

A controller for redundant manipulators with a small fast manipulator mounted on a positioning part has been developed. The controller distributes the fast motion to the small fast manipulator and the slow gross motion to the positioning part. A position reference is generated on-line to the positioning part to avoid singularities and the loss of degrees of freedom. The task-space position vector is augmented by the generalized coordinates of the positioning part. Feedback linearization and decoupling are then applied in the augmented task space to obtain a model consisting of decoupled double integrators. These decoupled double integrators are controlled by the use of linear quadratic optimal control. In the optimal control problem the performance index is chosen so that the task-space position reference is tracked with a high bandwidth while the reference to the positioning part is tracked with a low bandwidth. The controller has been applied to a simple planar redundant manipulator and an eight-link spray painting robot in simulation experiments. These simulations showed that a high bandwidth was possible with moderate actuator torques.

Time-varying exponential stabilization of the position and attitude of an underactuated autonomous underwater vehicle

The paper considers feedback stabilization of the position and attitude of an autonomous underwater vehicle (AUV) with a reduced number of actuators. A nonlinear model describing both the dynamics and the kinematics of an AUV is studied. The paper shows that previous results on attitude stabilization of a spacecraft can be applied to exponentially stabilize both the position and attitude of an AUV using only four, possibly three, actuators. Simulation results are presented.

Centrifugal compressor surge and speed control

Previous work on stabilization of compressor surge is extended to include control of the angular velocity of the compressor. A low-order centrifugal compressor model is presented, where the states are mass flow, pressure rise, and rotational speed of the spool. Energy transfer considerations are used to develop a compressor characteristic. In order to stabilize equilibria to the left of the surge line, a close coupled valve is used in series with the compressor. Controllers for the valve pressure drop and spool speed are derived. Semiglobal exponential stability is proved using a Lyapunov argument.

On global properties of passivity-based control of an inverted pendulum

The paper adresses the problem of stabilization of a specific target position of underactuated Lagrangian or Hamiltonian systems. We propose to solve the problem in two steps: first to stabilize a set with the target position being a limit point for all trajectories originating in this set and then to switch to a locally stabilizing controller. We illustrate this approach by the well-known example of inverted pendulum on a cart. Particularly, we design a controller which makes the upright position of the pendulum and zero displacement of the cart a limit point for almost all trajectories. We derive a family of static feedbacks such that any solution of the closed loop system except for those originating on some two-dimensional manifold approaches an arbitrarily small neighbourhood of the target position. The proposed technique is based on the passivity properties of the inverted pendulum. A possible extension to a more general class of underactuated mechanical systems is discussed.

A Lyapunov approach to exponential stabilization of nonholonomic systems in power form

In this paper a continuous feedback control law with time-periodic terms is derived for the control of nonholonomic systems in power form. The control law is derived by Lyapunov design from a homogeneous Lyapunov function. Global asymptotic stability is shown by applying the principle of invariance for time-periodic systems. Exponential convergence follows since the vector fields are homogeneous of degree zero.