Robust hybrid global asymptotic stabilization of rigid body dynamics using dual quaternions

A hybrid feedback control scheme is proposed for stabilization of rigid body dynamics (pose and velocities) using unit dual quaternions, in which the dual quaternions and veloc- ities are used for feedback. It is well-known that rigid body attitude control is subject to topological constraints which often result in discontinuous control to avoid the unwinding phenomenon. In contrast, the hybrid scheme allows the controlled system to be robust in the presence of uncertainties, which would otherwise cause chattering about the point of discontinuous control while also ensuring acceptable closed-loop response characteristics. The stability of the closed-loop system is guaranteed through a Lyapunov analysis and the use of invariance principles for hybrid systems. Simulation results for a rigid body model are presented to illustrate the performance of the proposed hybrid dual quaternion feedback control scheme

Automatic analysis of distance bounding protocols

Distance bounding protocols are used by nodes in wireless networks to calculate upper bounds on their distances to other nodes. However, dishonest nodes in the network can turn the calculations both illegitimate and inaccurate when they participate in protocol executions. It is important to analyze protocols for the possibility of such violations. Past efforts to analyze distance bounding protocols have only been manual. However, automated approaches are important since they are quite likely to find flaws that manual approaches cannot, as witnessed in literature for analysis pertaining to key establishment protocols. In this paper, we use the constraint solver tool to automatically analyze distance bounding protocols. We first formulate a new trace property called Secure Distance Bounding (SDB) that protocol executions must satisfy. We then classify the scenarios in which these protocols can operate considering the (dis)honesty of nodes and location of the attacker in the network. Finally, we extend the constraint solver so that it can be used to test protocols for violations of SDB in these scenarios and illustrate our technique on some published protocols.Comment: 22 pages, Appeared in Foundations of Computer Security, (Affiliated workshop of LICS 2009, Los Angeles, CA)