This paper deals with the stabilization problem for a particular class of hybrid systems, namely discrete-time linear systems subject to a uniform (a priori fixed) quantization of the control set. Results of our previous work on the subject provided a description of minimal (in a specific sense) invariant sets that could be rendered maximally attractive under any quantized feedback strategy. In this paper, we consider the design of stabilizing laws that optimize a given cost index on the state and input evolution on a finite, receding horizon. Application of Model Predictive Control techniques for the solution of similar hybrid control problems through Mixed Logical Dynamical reformulations can provide a stabilizing control law, provided that the feasibility hypotheses are met. In this paper, we discuss precisely what are the shortest horizon length and the minimal invariant terminal set for which it can be guaranteed a stabilizing MPC scheme. The final paper will provide an example and simulations of the application of the control scheme to a practical quantized control problem.
This paper is concerned with the stabilization problem for discrete-time linear systems subject to a uniform quantization of the control set and to a regular state quantization, both fixed a priori. As it is well known, for quantized systems only weak (practical) stability properties can be achieved. Therefore, we focus on the existence and construction of quantized controllers (mapping a quantized state into a quantized input set) capable of steering a system to within invariant neighbourhoods of the equilibrium. Such analysis is helpful because it allows to decide a priori whether adesired control objective can be achieved by using a \textit{given} technology (actuators, sensors, communication and computational means).
In this paper we propose Variable Stiffness actuation as a viable mechanical/control co-design approach for guaranteeing control performance for robot arms that are inherently safe to humans in their environment. A new actuator under development in our Lab is then proposed, which incorporate the possibility to vary transmission stiffness during motion execution, thus allowing substantial motion speed-up while maintaining low injury risk levels.
In this chapter, we consider three of the main problems that arise in the navigation of autonomous vehicles in partially or totally unknown environments, i.e. building a map of the environment, self-localizing, and servoing the robot so as to achieve given goals based on sensorial information. As compared to most part of the existing literature on SLAM, we privilege here a system-theoretic view to the problem, which allows the localization and mapping problems to be cast in a unified framework with the control problem. The chapter is an overview of existing results in this vein, and of some interesting directions for research in the field. All chapters of this volume were revised and published online March 2005. The volume number was corrected from 4010 to 10.
The problem to ensure safety of performant robot arms during task execution was previously investigated by authors. The problem can be approached by studying an optimal control policy, the "Safe Brachistocrone", whose solutions are joint impedance trajectories coordinated with desired joint velocities. Transmission stiffness is chosen so as to achieve minimum-time task execution for the robot, while guaranteeing an intrinsic safety level in case of an unexpected collision between a link of the arm and a human operator. In this paper we extend this approach to more general classes of robot actuation systems, whereby other impedance parameters beside stiffness (such as e.g. joint damping and/or plasticity) can vary. We report on a rather extensive experimental campaign validating the proposed approach.
Recent developments in advanced interface technology allowed to implement new haptic device for biomedical applications. Specifically, several innovative and more effective tools that allow people to interact by touch with virtual objects have been developed. Besides several applications such as gaming, entertainment, virtual reality, an important and promising field of application is the surgical simulation. Novice surgeons can be able to practice their first incisions without actually cutting anyone. Simulation for surgical training is a major focus for several research activity during the last few years. Simulating an organ is not easy, because is more complicated to model than is a common physical object, e.g. a ball. In this chapter we report several examples of haptic interfaces and introduce new technologies for implementation.
In this paper we consider some questions in the design of actuators for physical Human-Robot Interaction (pHRI) under strict safety requirements in all circumstances, including unexpected impacts and HW/SW failures. We present the design and optimization of agonistic-antagonistic actuation systems realizing the concept of variable impedance actuation (VIA). With respect to previous results in the literature, in this paper we consider a realistic physical model of antagonistic systems, and include the analysis of the effects of cross-coupling between actuators. We show that antagonistic systems compare well with other possible approaches in terms of the achievable performance while guaranteeing limited risks of impacts. Antagonistic actuation systems however are more complex in both hardware and software than other schemes. Issues are therefore raised, as to fault tolerance and fail safety of different actuation schemes. In this paper, we analyze these issues and show that the antagonistic implementation of the VIA concept fares very well under these regards also.
The problem of coordinated control of a leader-follower system is solved using a virtual vehicle approach to alleviate information requirements on the leader. The virtual vehicle stabilizes to a shifted reference position/heading defined by the leader, and provides a reference velocity for the synchronization control law of the follower. Only position/heading measurements are available from the leader, and the closed-loop errors are shown to be uniformly globally practically asymptotically stable.
We present a solution to the problem of tracking relative translation in a leader-follower spacecraft formation using feedback from relative position only. Three controller configurations are presented which enables the follower spacecraft to track a desired reference trajectory relative to the leader. The controller design is performed for different levels of knowledge about the leader spacecraft and its orbit. The first controller assumes perfect knowledge of the leader and its orbital parameters, and renders the equilibrium points of the closed-loop system uniformly globally asymptotically stable (UGAS). The second controller uses the framework of the first to render the closed-loop system uniformly globally practically asymptotically stable (UGPAS), with knowledge of bounds on some orbital parameters, only. That is, the state errors in the closed-loop system are proved to converge from any initial conditions to a ball in close vicinity of the origin in a stable way, and this ball can be diminished arbitrarily by increasing the gains in the control law. The third controller, based on the design of the second, utilizes adaptation to estimate the bounds that were previously assumed to be known. The resulting closed-loop system is proved to be uniformly semiglobally practically asymptotically stable (USPAS). The last two controllers assume boundedness only of orbital perturbations and the leader control force. Simulation results of a leader-follower spacecraft formation using the proposed controllers are presented.
