Solving the potential field local minimum problem using internal agent states

We propose a new, extended artificial potential field method, which uses dynamic internal agent states. The internal states are modelled as a dynamical system of coupled first order differential equations that manipulate the potential field in which the agent is situated. The internal state dynamics are forced by the interaction of the agent with the external environment. Local equilibria in the potential field are then manipulated by the internal states and transformed from stable equilibria to unstable equilibria, allowiong escape from local minima in the potential field. This new methodology successfully solves reactive path planning problems, such as a complex maze with multiple local minima, which cannot be solved using conventional static potential fields

Swarm robot social potential fields with internal agent dynamics

Swarm robotics is a new and promising approach to the design and control of multiagent robotic systems. In this paper we use a model for a second order non-linear system of self-propelled agents interacting via pair-wise attractive and repulsive potentials. We propose a new potential field method using dynamic agent internal states to successfully solve a reactive path-planning problem. The path planning problem cannot be solved using static potential fields due to local minima formation, but can be solved by allowing the agent internal states to manipulate the potential field. Simulation results demonstrate the ability of a single agent to perform reactive problem solving effectively, as well as the ability of a swarm of agents to perform problem solving using the collective behaviour of the entire swarm

Wall following to escape local minima for swarms of agents using internal states and emergent behaviour

Natural examples of emergent behaviour, in groups due to interactions among the group's individuals, are numerous. Our aim, in this paper, is to use complex emergent behaviour among agents that interact via pair-wise attractive and repulsive potentials, to solve the local minima problem in the artificial potential based navigation method. We present a modified potential field based path planning algorithm, which uses agent internal states and swarm emergent behaviour to enhance group performance. The algorithm is used successfully to solve a reactive path-planning problem that cannot be solved using conventional static potential fields due to local minima formation. Simulation results demonstrate the ability of a swarm of agents to perform problem solving using the dynamic internal states of the agents along with emergent behaviour of the entire group

Non-linear stability of vortex formation in swarms of interacting particles

We use a particle-based model of a swarm of interacting particles to explore analytically the conditions for the formation of vortexlike behavior. Our model uses pairwise interaction potentials to model weak long-range attraction and strong short-range repulsion with a dissipation function to align particle velocity vectors. We use the effective energy of the swarm as a Lyapunov function to prove convergence to a vortexlike state. Our analysis extends previous work which has relied purely on simulation to explore the formation and stability of vortexlike behavior through analytical rather than numerical methods

An emergent wall following behaviour to escape local minima for swarms of agents

Natural examples of emergent behaviour, in groups due to interactions among the group's individuals, are numerous. Our aim, in this paper, is to use complex emergent behaviour among agents that interact via pair-wise attractive and repulsive potentials, to solve the local minima problem in the artificial potential based navigation method. We present a modified potential field based path planning algorithm, which uses agent internal states and swarm emergent behaviour to enhance group performance. The algorithm is used successfully to solve a reactive path-planning problem that cannot be solved using conventional static potential fields due to local minima formation. Simulation results demonstrate the ability of a swarm of agents to perform problem solving using the dynamic internal states of the agents along with emergent behaviour of the entire group

Cohomology of osp(1∣2)\mathfrak {osp}(1|2) acting on linear differential operators on the supercircle $S^{1|1}

We compute the first cohomology spaces $H^1(\mathfrak{osp}(1|2);\mathfrak{D}_{\lambda,\mu})$ ($\lambda, \mu\in\mathbb{R}$) of the Lie superalgebra $\mathfrak{osp}(1|2)$ with coefficients in the superspace $\mathfrak{D}_{\lambda,\mu}$ of linear differential operators acting on weighted densities on the supercircle $S^{1|1}$. The structure of these spaces was conjectured in \cite{gmo}. In fact, we prove here that the situation is a little bit more complicated. (To appear in LMP.

Internal agent states : experiments using the swarm leader concept

In recent years, an understanding of the operating principles and stability of natural swarms has proven to be a useful tool for the design and control of artificial robotic agents. Many robotic systems, whose design or control principals are inspired by behavioural aspects of real biological systems such as leader-follower relationship, have been developed. We introduced an algorithm which successfully enhances the navigation performance of a swarm of robots using the swarm leader concept. This paper presents some applications based on that work using the simulations and experimental implementation using a swarming behaviour test-bed at the University of Strathclyde. Experimental and simulation results match closely in a way that confirms the efficiency of the algorithm as well as its applicability

Canopy structure and radiation regime in grapevine. 1. Spatial and angular distribution of leaf area in two canopy systems

Grapevine canopies are discontinuous and spatially heterogeneous. Thus, their geometrical structure is difficult to characterize. A method based on a three-dimensional discretion of the volume occupied by foliage elements was used to assess spatial and angular distribution of leaf area. The method was applied to two canopy systems (Open Lyre and Geneva Double Curtain) exhibiting different vigor levels. Leaf area density (LAD, m2·m-3), leaf inclination and leaf azimuth distributions were presented for the canopy systems, as are the distributions of lateral shoot leaves within the canopy. An attempt was made to determine the consequences of the canopy system on the grapevine canopy structure. The canopy structure parameters determined in this study were used in a companion paper as input parameters for a radiation model to describe the grapevine light microclimate

Canopy structure and radiation regime in grapevine. 2. Modeling radiation interception and distribution inside the canopy

A 3D version of the radiation model of SINOQUET and BONHOMME (1992) was used to simulate the light microclimate of grapevine. It was tested against measurements of radiation interception and distribution within two canopy systems (Open Lyre and Geneva Double Curtain) exhibiting different vigor levels. The agreement between the model and the measurements was generally good. Discrepancies may have arisen from incorrect assumptions concerning leaf azimuth distribution and leaf dispersion as well as a lack of accuracy in the description of the distribution of leaf area density inside the canopy. The model also permitted to assess light partitioning between main and lateral shoot leaves which can influence global canopy photosynthesis and berry ripening. As an example of application, the model was used to evaluate the consequences of lateral leaf removing on the interception efficiency of the canopy and the light environment of the fruit zone. The possible use of a geometrical approach to simulate the radiation interception at the canopy scale was also discussed

On the AA-spectrum for AA-bounded operator on von-Neumann algebra

Let $\mathfrak{M}$ be a von Neumann algebra and let $A$ be a nonzero positive element of $\mathfrak{M}$. By $\sigma_A(T)$ and $r_A(T)$ we denote the $A$-spectrum and the $A$-spectral radius of $T\in\mathfrak{M}^A$, respectively. In this paper, we show that $\sigma(PTP, P\mathfrak{M} P)\subseteq \sigma_A(T)$. Sufficient conditions for the equality $\sigma_A(T)=\sigma(PTP, P\mathfrak{M} P)$ to be true are presented. Also, we show that $\sigma_A(T)$ is finite for any $T\in\mathfrak{M}^A$ if and only if $A$ is in the socle of $\mathfrak{M}$. Next , we consider the relationship between elements $S$ and $T\in\mathfrak{M}^A$ that satisfy one of the following two conditions: (1) $\sigma_A(SX)=\sigma_A(TX)$ for all $X\in\mathfrak{M}^A$, (2) $r_A(SX)= r_A(TX)$ for all $X\in\mathfrak{M}^A$. Finally, a Gleason-Kahane-\.Zelazko's theorem for the $A$-spectrum is derived.% Finally, we introduce and study the notion of the $A$-approximate point spectrum for element of $X\in\mathfrak{M}^A$