Formation with Non-Collision Control Strategies for Second-Order Multi-Agent Systems.

This article tackles formation control with non-collision for a multi-agent system with second-order dynamics. The nested saturation approach is proposed to solve the well-known formation control problem, allowing us to delimit the acceleration and velocity of each agent. On the other hand, repulsive vector fields (RVFs) are developed to avoid collisions among the agents. For this purpose, a parameter depending on the distances and velocities among the agents is designed to scale the RVFs adequately. It is shown that when the agents are at risk of collision, the distances among them are always greater than the safety distance. Numerical simulations and a comparison with a repulsive potential function (RPF) illustrate the agents' performance.

Characterization and modelling of looming-sensitive neurons in the crab Neohelice.

Looming-sensitive neurons (LSNs) are motion-sensitive neurons tuned for detecting imminent collision. Their main characteristic is the selectivity to looming (a 2D representation of an object approach), rather than to receding stimuli. We studied a set of LSNs by performing surface extracellular recordings in the optic nerve of Neohelice granulata crabs, and characterized their response against computer-generated visual stimuli with different combinations of moving edges, highlighting different components of the optical flow. In addition to their selectivity to looming stimuli, we characterized other properties of these neurons, such as low directionality; reduced response to sustained excitement; and an inhibition phenomenon in response to visual stimuli with dense optical flow of expansion, contraction, and translation. To analyze the spatio-temporal processing of these LSNs, we proposed a biologically plausible computational model which was inspired by previous computational models of the locust lobula giant motion detector (LGMD) neuron. The videos seen by the animal during electrophysiological experiments were applied as an input to the model which produced a satisfactory fit to the measured responses, suggesting that the computation performed by LSNs in a decapod crustacean appears to be based on similar physiological processing previously described for the LGMD in insects.

Object approach computation by a giant neuron and its relationship with the speed of escape in the crab Neohelice.

Upon detection of an approaching object, the crab Neohelice granulata continuously regulates the direction and speed of escape according to ongoing visual information. These visuomotor transformations are thought to be largely accounted for by a small number of motion-sensitive giant neurons projecting from the lobula (third optic neuropil) towards the supraesophageal ganglion. One of these elements, the monostratified lobula giant neuron of type 2 (MLG2), proved to be highly sensitive to looming stimuli (a 2D representation of an object approach). By performing in vivo intracellular recordings, we assessed the response of the MLG2 neuron to a variety of looming stimuli representing objects of different sizes and velocities of approach. This allowed us to: (1) identify some of the physiological mechanisms involved in the regulation of the MLG2 activity and test a simplified biophysical model of its response to looming stimuli; (2) identify the stimulus optical parameters encoded by the MLG2 and formulate a phenomenological model able to predict the temporal course of the neural firing responses to all looming stimuli; and (3) incorporate the MLG2-encoded information of the stimulus (in terms of firing rate) into a mathematical model able to fit the speed of the escape run of the animal. The agreement between the model predictions and the actual escape speed measured on a treadmill for all tested stimuli strengthens our interpretation of the computations performed by the MLG2 and of the involvement of this neuron in the regulation of the animal's speed of run while escaping from objects approaching with constant speed.