This paper presents a discrete-time multirate technique for the set-point stabilization of nonholonomic systems in a chained form. Global practical exponential stabilization of the trivial equilibrium in the continuous-time system dynamics is achieved, by using multirate piecewise inputs and an inter-sampling analysis. As a case study, we consider the car-like robot stabilization problem. The control system quality is assessed through a quadratic cost function associated to the multi-sampling period. Robustness with respect to measurement errors and switching delays is also investigated.

In this paper, a novel adaptive visual feedback scheme is presented to solve the problem of controlling the relative pose between a robot camera and a rigid object of interest. By exploiting nonlinear controllability properties, uniform asymptotic stability in the large of the image reference set-point is proved using Lyapunov's direct method. Moreover, uniform boundedness of the whole state vector is ensured by using an adaptive nonlinear control scheme, in case of unknown object depth. Experimental results with a six-degree-of-freedom robot manipulator endowed with a camera on its wrist validate the framework.

This paper focuses on the problem of controlling dynamic look-and-move systems, taking into account the robot dynamics in the visual control loop. In the case of interconnection to a linear robot subsystem, the problem of local feedback stabilization is solved by using the backstepping approach. Local stability of the equilibrium of the whole system is ensured under the assumption that the linear subsystem is minimum phase of relative degree one. A case study is also reported to validate the developed control design: a PUMA robot including its local controller is approximated by a diagonal linear subsystem and experimental results are shown with the robotic system in eye-in-hand configuration.

A nonhonolomic vehicle is stabilized to a desired pose through a visual servoing technique. The vision-based regulation of the nonholonomic vehicle proposed is built through a discontinuous change of coordinates and Lyapunov-based design, which ensure asymptotic stability of the closed-loop visual system. A dynamic estimation procedure, based on the optical flow equations, is also presented to deal with uncertainties in the obsereved environment. Simulations results on an autonomous mobile robot are reported, that show the practicality of the proposed approach.

This paper focuses on the problem of controlling the relative position between a moving target and an autonomous nonholonomic vehicle. This problem represents a meaningful case study belonging to the class of multirate nonlinear control systems. A multi-level stabilizing control system is synthesized in continuous-time, based on a detailed analytic model of the vehicle, including the robot kinematics and nonholonomic dynamics, and actuators transfer functions. The discrete-time implementation provides a multirate nonlinear digital controller. Simulations in both continuous and discrete-time domain highlights interesting performance variations effects arising from different choices of the sampling frequencies.

We consider a complete dynamic model for the "Sphericle", a spherical vehicle that has been designed and realized in our laboratory. The Sphericle is able to roll on the floor of the laboratory and reach arbitrary positions and orientations, through the use of only two motors placed within the rolling sphere. In this paper, we report on the derivation of the kinematic model of the Sphericle, which incorporates two types of nonholonomic constraints and its dynamic model.

A typical approach for realizing digital controllers is to synthesize the control law in the continuous-time domain and then to implement it as a set of periodic threads complying with tight temporal constraints. The strict respect of all deadlines can often be obtained only by selecting low activation rates which determine a remarkable performance degradation. On the other hand, many control systems are known to tolerate a certain amount of deadline misses. We realized a software tool which allows to numerically evaluate the quality of the control resulting from the scheduling. The tool has been applied to a robotic case study. Considering a meaningful set of trajectories, we have drawn experimental evidence that the use of soft real-time constraints on the threads leads to significant improvements in the system performance. The performance improvement is more evident if scheduling approaches like resource reservation schemes, able to separate the thread importance from its activation rate, are used.