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If a smooth, closed, and embedded curve is deformed along its normal vector field at a rate proportional to its curvature, it shrinks to a circular point. This curve evolution is called Euclidean curve shortening and the result is known as the Gage-Hamilton-Grayson theorem. Motivated by the rendezvous problem for mobile autonomous robots, we address the problem of creating a polygon shortening flow. A linear scheme is proposed that exhibits several analogues to Euclidean curve shortening: The polygon shrinks to an elliptical point, convex polygons remain convex, and the perimeter of the polygon is monotonically decreasing.

Aims: To assess the safety and efficacy of multiple daily doses of oral insulin (ORMD‐0801) in subjects with type 2 diabetes (T2DM) over 12 weeks. Materials and Methods: Participants with T2DM on metformin or combination oral therapy with glycated haemoglobin (HbA1c) levels ≥ 7.5% (58 mmol/mol) were randomized to receive ORMD‐0801 8 mg or 16 mg once (QD) or twice (BID) daily, or 32 mg QD, BID or three times daily (TID) over a 12‐week period. Results: A total of 373 subjects were randomized to active treatment or placebo (~60% male, age ~ 56 years, HbA1c 9%‐9.8%; 75‐84 mmol/mol). Placebo‐adjusted HbA1c changes from baseline to Week 12 were observed with ORMD‐0801 8 mg BID (−7.15 ± 3.57 mmol/mol [−0.65% ± 0.33%]; P = 0.046). However, a significant site interaction was observed in two sites. After excluding these, HbA1c reduction was observed with 8 mg QD (−0.81 ± 0.37%; −8.89 ± 4.01 mmol/mol; P = 0.028, n = 15), 8 mg BID (−0.82 ± 0.37%; −8.95 ± 4.08 mmol/mol; P = 0.029, n = 17), 32 mg QD (−0.54 ± 0.26%; −5.89 ± 2.78 mmol/mol;P = 0.036, n = 69) and 32 mg BID (−0.53 ± 0.26%; −5.80 ± 2.83 mmol/mol; P = 0.042, n = 68). No effect was observed with 16 mg QD (0.25 ± 0.37%; 2.76 ± 3.99 mmol/mol; P = 0.48, n = 18), 16 mg BID (−0.36 ± 0.40%; −3.97 ± P = 0.36, n = 15) or 32 mg TID (−0.45 ± 0.27%, −4.89 ± 2.90 mmol/mol; P = 0.093, n = 69). Continuous glucose monitor and serum glucose measurements showed similar trends but were not significant. ORMD‐0801 was safe, well tolerated and not associated with weight gain or hypoglycaemia. Conclusions: Oral insulin (ORMD‐0801) induced greater reductions in HbA1c when compared to placebo, and was safe and well tolerated in individuals with uncontrolled T2DM. The efficacy and safety findings support continued development of the 8‐mg dose at bedtime, which is currently being evaluated in two Phase 3 trials. [ABSTRACT FROM AUTHOR]

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.robot.2005.10.004 Byline: Joshua A. Marshall (a), Terence Fung (b), Mireille E. Broucke (c), Gabriele M.T. D'Eleuterio (b), Bruce A. Francis (c) Abstract: Consequent to previously published theoretical work by Marshall, Broucke, and Francis, this paper summarizes the apparatus and results of multirobot coordination experiments conducted at the University of Toronto Institute for Aerospace Studies. These experiments successfully demonstrate the practicality of cyclic pursuit as a distributed control strategy for multiple wheeled-robot systems. The pursuit-based coordination algorithm was found to be surprisingly robust in the presence of unmodelled dynamics and delays due to sensing and information processing. Moreover, the findings of this research not only bode well for continuing research on pursuit-based coordination strategies, but also for other cooperative multirobot control techniques employing similar local interactions. Author Affiliation: (a) MacDonald, Dettwiler and Associates (MDA) Ltd., Space Missions, 9445 Airport Road, Brampton, ON, Canada L6S 4J3 (b) Institute for Aerospace Studies, University of Toronto, 4925 Dufferin Street, Toronto, ON, Canada M3H 5T6 (c) Department of Electrical and Computer Engineering, University of Toronto, 10 King's College Road, Toronto, ON, Canada M5S 3G4 Article History: Received 23 March 2005; Revised 23 October 2005; Accepted 24 October 2005

The feasibility problem is studied of achieving a specified formation among a group of autonomous unicycles by local distributed control. The directed graph defined by the information flow plays a key role. It is proved that formation stabilization to a point is feasible if and only if the sensor digraph has a globally reachable node. A similar result is given for formation stabilization to a line and to more general geometric arrangements. Index Terms--Distributed control, multiagent system, nonholonomic mobile robots.

Inspired by the so-called "bugs" problem from mathematics, we study the geometric formations of multivehicle systems under cyclic pursuit. First, we introduce the notion of cyclic pursuit by examining a system of identical linear agents in the plane. This idea is then extended to a system of wheeled vehicles, each subject to a single nonholonomic constraint (i.e., unicycles), which is the principal focus of this paper. The pursuit framework is particularly simple in that the n identical vehicles are ordered such that vehicle i pursues vehicle i + 1 modulo n. In this paper, we assume each vehicle has the same constant forward speed. We show that the system's equilibrium formations are generalized regular polygons and it is exposed how the multivehicle system's global behavior can be shaped through appropriate controller gain assignments. We then study the local stability of these equilibrium polygons, revealing which formations are stable and which are not. Index Terms--Circulant matrices, cooperative control, multiagent systems, pursuit problems.

The power spectral density of a stationery random signal x (n) is measured with the help of a set of linear multirate sensors. The technical difficulties associated with the maximum entropy (ME) solution are addressed and a practical algorithm for its approximate computation is devised.