Abstract-This paper presents shared-control algorithms for the kinematic and the dynamic models of a mobile robot with a feasible configuration set defined by means of linear inequalities. The shared-control laws based on a hysteresis switch are designed in the case in which absolute positions are not available. Instead, we measure the distances to obstacles and angular differences. Formal properties of the closed-loop systems with the sharedcontrol are established by a Lyapunov-like analysis. Simulation results and experimental results are presented to show the effectiveness of the algorithm.

In this paper the problem of simulation of constrained mechanical systems is addressed. In modeling multibody mechanical systems, the Lagrange formulation produces a redundant set of differential-algebraic equations, the integration of which can lead to several difficulties, for example the drift of the "constraint violation". One of the most popular approaches to alleviate this issue is the so-called Baumgarte's method that relies on a linear feedback mechanism. This method can however lead to numerical instabilities when applied to nonlinear (mechanical) systems. The objective of this study is to propose a new method that ensures existence of solutions and makes the constraint manifold asymptotically attractive. The proposed technique is illustrated by means of a simple example.

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The problem of the stability analysis for constrained mechanical systems is addressed using tools from classical geometric control theory, such as the notion of zero dynamics. For the special case of linear constrained mechanical systems we show that stability is equivalent to a detectability property. The proposed techniques are illustrated by means of simple examples.

The problem of constraint stabilization and numerical integration for differential-algebraic systems is addressed using Lyapunov theory. It is observed that the application of stabilization methods which rely on a linear feedback mechanism to nonlinear systems may result in trajectories with finite escape time. To overcome this problem we propose a method based on a nonlinear stabilization mechanism which guarantees the global existence and convergence of the solutions. Discretization schemes, which preserve the properties of the method, are also presented. The results are illustrated by means of the numerical integration of a slider-crank mechanism.