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.

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.

An investigation on the hybrid force control of robot arms by learning is presented. A well-known force control scheme based on feedback linearization is used to build up an algorithm which improves, trial by trial, force and position tracking over a finite time interval. Differently from other published learning control schemes, the proposed algorithm does not rely on high gain feedback. Robustness and convergence in spite of sufficiently small system parameter uncertainties and disturbances is proven by means of the contraction mapping principle.

In this paper we present a novel finite dimensional learning algorithm for end point trajectory control of a flexible link moving on a horizontal plane. Given a desired end point trajectory generated by a finite dimensional exosystem, by means of successive trials, the algorithm proposed learns the initial state and the control needed to exactly track the desired trajectory. An internal stability constraint is also enforced, which prevents undesirable excessive vibrations and control effort. Initialization of the flexible link state is automatically accomplished as a part of the same learning process. Algorithm ability of fully rejecting linear plant perturbations and disturbances which are linear functions of the exosystem state is formally proven. Experimental results show the effectiveness of the algorithm introduced and its robustness with respect to nonlinear plant perturbations and unmodeled dynamics.

An alternative proof of the convergence of known P-type learning control schemes for unconstrained and constrained robot arms is presented. The analysis carried out is based on a singular perturbation approach and points out the role played by high gain velocity and force feedbacks and by actuator/output co-location. The singular perturbation analysis developed clearly displays that the P-type learning algorithm is geometrically convergent, and that, thanks to the high gain feedback, this convergence does not depend on the knowledge of the robot parameters. Robustness with respect to some classes of disturbances is also addressed. The stability of the high gain closed loop system in case of robots in contact with the environment is shown to rely on a sufficiently good knowledge of the constraining surface.

Conformational analysis is the problem of nding all minimal energy three-dimensional con gurations of molecules.Cyclic structures are of particular interest.An ecient algorithm based on a purely geometric approach that generates feasible con gurations very eciently is presented thus making full conformational analysis possible even for fairly large cyclic structures.

Experimental results on the repositioning of a rigid robot link from one equilibrium point to another are presented. By means of a learning algorithm, which uses only the positioning error at the end of a trial, the control torque needed to move the robot is found. After a high gain feedback linearization of the robot dynamics, a simple, finite dimensional learning algorithm is applied. The results of the experiments, carried out on a two link robot under gravity, show that the algorithm is robust and performs quite satisfactorily.>

A novel repetitive control scheme for minimum phase linear systems, which achieves asymptotic output tracking over the whole frequency range, is proposed. It is composed of two parts. The first is a system described by a continuous time difference equation, which asymptotically generates the required exact tracking control. The second one is a system described by ordinary differential equations and time-lag elements, which, through system inversion, online estimates the delayed input. This estimate is then fed back to obtain an exponentially stable closed - loop control scheme, which is robust with respect to linear plant perturbations.