Decentralized MPC based Obstacle Avoidance for Multi-Robot Target Tracking Scenarios

In this work, we consider the problem of decentralized multi-robot target tracking and obstacle avoidance in dynamic environments. Each robot executes a local motion planning algorithm which is based on model predictive control (MPC). The planner is designed as a quadratic program, subject to constraints on robot dynamics and obstacle avoidance. Repulsive potential field functions are employed to avoid obstacles. The novelty of our approach lies in embedding these non-linear potential field functions as constraints within a convex optimization framework. Our method convexifies non-convex constraints and dependencies, by replacing them as pre-computed external input forces in robot dynamics. The proposed algorithm additionally incorporates different methods to avoid field local minima problems associated with using potential field functions in planning. The motion planner does not enforce predefined trajectories or any formation geometry on the robots and is a comprehensive solution for cooperative obstacle avoidance in the context of multi-robot target tracking. We perform simulation studies in different environmental scenarios to showcase the convergence and efficacy of the proposed algorithm. Video of simulation studies: \url{https://youtu.be/umkdm82Tt0M

Moduli Entrapment with Primordial Black Holes

We argue that primordial black holes in the early universe can provide an efficient resolution of the Brustein-Steinhardt moduli overshoot problem in string cosmology. When the universe is created near the Planck scale, all the available states in the theory are excited by strong interactions and cosmological particle production. The heavy states are described in the low energy theory as a gas of electrically and magnetically charged black holes. This gas of black holes quickly captures the moduli which appear in the relation between black hole masses and charges, and slows them down with their vevs typically close to the Planck scale. From there, the modulus may slowly roll into a valley with a positive vacuum energy, where inflation may begin. The black hole gas will redshift away in the course of cosmic expansion, as inflation evicts black holes out of the horizon.Comment: 14 pages latex, 7 .eps figures; v2: added references and a few comment

How can a 22-pole ion trap exhibit 10 local minima in the effective potential?

The column density distribution of trapped OH$^-$ ions in a 22-pole ion trap is measured for different trap parameters. The density is obtained from position-dependent photodetachment rate measurements. Overall, agreement is found with the effective potential of an ideal 22-pole. However, in addition we observe 10 distinct minima in the trapping potential, which indicate a breaking of the 22-fold symmetry. Numerical simulations show that a displacement of a subset of the radiofrequency electrodes can serve as an explanation for this symmetry breaking

Towards Resolution of Hierarchy Problems in a Cosmological Context

A cosmological scenario is proposed, which simultaneously solves the mass hierarchy and the small dark energy problem. In the present scenario an effective gravity mass scale (inverse of the Newton's constant) increases during the inflationary period. The small cosmological constant or the dark energy density in the present universe is dynamically realized by introducing two, approximately O(2) symmetric dilatons, taking the fundamental mass scale at TeV.Comment: 12 pages, no figur

Metastability in Bubbling AdS Space

We study the dynamics of probe M5 branes with dissolved M2 charge in bubbling geometries with SO(4) x SO(4) symmetry. These solutions were constructed by Bena-Warner and Lin-Lunin-Maldacena and correspond to the vacua of the maximally supersymmetric mass-deformed M2 brane theory. We find that supersymmetric probe M2 branes polarize into M5 brane shells whose backreaction creates an additional bubble in the geometry. We explicitly check that the supersymmetric polarization potential agrees with the one found within the Polchinski-Strassler approximation. The main result of this paper is that probe M2 branes whose orientation is opposite to the background flux can polarize into metastable M5 brane shells. These decay to a supersymmetric configuration via brane-flux annihilation. Our findings suggest the existence of metastable states in the mass-deformed M2 brane theory.Comment: 38 pages, 8 figure

Anamorphosis in hybrid inflation: How to avoid fine-tuning of initial conditions?

In order to generate more than 60 e-folds of accelerated expansion in original hybrid inflation, 2-fields trajectories are usually required to be initially fine-tuned in a very narrow band along the inflationary valley or in some isolated points outside it. From a more precise investigation of the dynamics, these points which can cover a non-negligible proportion of the space of sub-planckian initial field values, depending on the potential parameters, are shown to be organised in connected domains with fractal boundaries. They correspond to trajectories first falling towards the bottom of the potential, then climbing and slow-rolling back along the inflationary valley. The full parameter space, including initial velocities and all the potential parameters, is then explored by using Monte-Carlo-Markov-Chains (MCMC) methods. Results indicate that successful initial conditions (IC) outside the valley are not localized in the parameter space and are the dominant way to realise inflation, independently of initial field velocities. Natural bounds on parameters are deduced. The genericity of our results is confirmed in 5 other hybrid models from various framework.Comment: AIP Proceedings of the "Invisible Universe" conference, Palais de l'Unesco, Paris, 29 June - 4 July 200