Pasquale Lucibello

A general algorithm for dynamic feedback linearization of robots with elastic joints

For a general class of robots with elastic joints, we introduce an inversion algorithm for the synthesis of a dynamic feedback control law that gives input-output decoupling and full state linearization. Control design is performed directly on the second-order robot dynamic equations. The linearizing control law is expressed in terms of the original model components and of their time derivatives, allowing an efficient organization of computations. A tight upper bound for the dimension of the needed dynamic compensator is also obtained.

Brief Robust stabilization via iterative state steering with an application to chained-form systems

An approach is presented for the robust stabilization of non-linear systems. The proposed strategy can be adopted whenever it is possible to compute a control law that steers the state in finite time from any initial condition to a point closer to the desired equilibrium. Under suitable assumptions, such control law can be applied in an iterative fashion, obtaining uniform asymptotic stability of the equilibrium point, with exponential rate of convergence. Small non-persistent perturbations are rejected, while persistent perturbations induce limited errors. In order to show the usefulness of the presented theoretical developments, the approach is applied to chained-form systems and, for illustration, simulations results are given for the robust stabilization of a unicycle.

Control experiments on a two-link robot with a flexible forearm

A lightweight robot has been built with the aim of testing advanced control algorithms and demonstrating the engineering feasibility of flexible arm control. The robot is a planar two-link manipulator, with revolute joints and a very flexible forearm. A description of this laboratory facility is given, including mechanical structure, actuators and sensors, and interface electronics. A nonlinear dynamic model of the robot is given, in which link deflection is expressed in terms of orthonormal mode shapes of the associated eigenvalue problem. Simple control algorithms are presented, which are composed of a model-based feedforward term plus a linear feedback. These controllers have been implemented for joint trajectory tracking, and comparative experimental results are reported and discussed.<<ETX>>

Stabilization via iterative state steering with application to chained-form systems

A general approach is presented for the robust stabilization of controllable systems. The proposed strategy is viable whenever one can compute a finite-time control law that steers the state from any initial condition to a point closer to the desired equilibrium. Under suitable hypotheses, such control law can be applied in an iterative fashion, obtaining exponential convergence of the state to the equilibrium point. Moreover, small nonpersistent perturbations are rejected while small persistent perturbations induce limited errors. The proposed approach is applied to chained-form systems and simulation are presented for a unicycle.

On the Control of Robots with Visco-Elastic Joints

Feedback linearization is a viable nonlinear control technique for solving trajectory tracking problems in robots with (and without) elastic joints. However, the additional presence of dissipative effects due to joint viscosity destroys full state feedback linearizability. For robots with visco-elastic joints, the use of a static state feedback can achieve at most input-output linearization and decoupling, since an internal nonlinear dynamics is left in the closed-loop system. Although the stability properties of this unobservable dynamics still guarantee perfect output tracking in nominal conditions, control design based on static feedback becomes ill-conditioned as joint viscosity decreases. Instead, resorting to a nonlinear dynamic state feedback leads to the same closed-loop properties, but with a regularized control effort for any level of joint viscosity and elasticity. Static and dynamic nonlinear feedback control designs are presented for a reduced and a complete dynamic model of visco-elastic joint robots. A numerical comparison on a simple case study illustrates the benefits of the dynamic input-output linearization approach.

Repositioning control of a two-link flexible arm by learning

A finite dimensional algorithm is presented which by trial searches for a control law is able to move a two-link flexible arm between two given equilibrium configurations in a finite time interval. Using a singular perturbation analysis, the possibility of considering the system as a linear perturbed one is shown, allowing the use of a linear learning algorithm which is able to reject all the nonlinear disturbances. The effectiveness of this algorithm is proven by theoretical arguments and experimental results. Robustness with respect to unmodeled high frequency dynamics is also addressed.

State steering by learning for a class of nonlinear control systems

Abstract The problem of steering the state of nonlinearly perturbed linear systems by learning is investigated. A family of algorithms which compute the steering control by means of successive trials on the real plant is presented. Convergence in the face of a class of nonlinear plant perturbations is proven. State feedback linearizable systems are shown to be addressable by the presented algorithms. Two examples illustrate the applicability of algorithms.

Nonlinear regulation, with internal stability, of a two link flexible robot arm

The problem of endpoint asymptotic tracking, with internal stability, of a two-link flexible robot arm is discussed. First the problem of exact tracking with bounded internal evolution is reviewed, and an approach for finding bounded solutions of the inverse dynamics is given. Then the linear regulator problem with internal stability is solved for the one-link case and extended to the nonlinear two-link case.<<ETX>>

Output zeroing with internal stability by learning

We formulate a novel learning algorithm for output zeroing of linear finite-dimensional, control systems. As in classical control systems theory, we start from the knowledge of a nominal plant to develop a feedback algorithm that achieves the control objective by means of successive trials on the plant. Algorithm convergence in the face of linear plant perturbations is proved, and performance in the face of small nonlinear perturbations is discussed. The proposed algorithm does not require output differentiation, and is based upon the learning of the initial conditions that allow the output to remain identically zero, while the state of the system, dynamically extended, freely evolves complying with an internal stability constraint. Implementation of this algorithm requires state initialization at an arbitrary point of the state space. Therefore, for those systems for which direct state initialization is not feasible, we develop a learning procedure that automatically accomplishes this task. By means of a control input generated by the algorithm, the state of the system is steered, during an initial phase, from a point where it is easily initialized to the point from which the output zeroing task starts. An illustrative example is included.

Point to point polynomial control of linear systems by learning

The author considers the problem of finding, by means of a learning algorithm, a control which brings, in a given time interval, the state of a linear system from one point to another in the state space. The algorithm uses only the positional error at the end of a trial to update the control for the next one. After a generic formulation of this problem, the author considers the specific case of controls which are polynomial in time. Finally, for illustration, the procedure developed is applied to the repositioning control of a flexible arm.<<ETX>>