This paper presents a modified pulse-coupled neural network (MPCNN) model for real-time collision-free path planning of mobile robots in nonstationary environments. The proposed neural network for robots is topologically organized with only local lateral connections among neurons. It works in dynamic environments and requires no prior knowledge of target or barrier movements. The target neuron fires first, and then the firing event spreads out, through the lateral connections among the neurons, like the propagation of a wave. Obstacles have no connections to their neighbors. Each neuron records its parent, that is, the neighbor that caused it to fire. The real-time optimal path is then the sequence of parents from the robot to the target. In a static case where the barriers and targets are stationary, this paper proves that the generated wave in the network spreads outward with travel times proportional to the linking strength among neurons. Thus, the generated path is always the global shortest path from the robot to the target. In addition, each neuron in the proposed model can propagate a firing event to its neighboring neuron without any comparing computations. The proposed model is applied to generate collision-free paths for a mobile robot to solve a maze-type problem, to circumvent concave U-shaped obstacles, and to track a moving target in an environment with varying obstacles. The effectiveness and efficiency of the proposed approach is demonstrated through simulation and comparison studies.

Necessary and sufficient conditions for impulsive controllability of linear dynamical systems are obtained, which provide a novel approach to problems that are basically defined by continuous dynamical systems, but on which only discrete‐time actions are exercised. As an application, impulsive maneuvering of a spacecraft is discussed.

This paper presents a simple yet efficient dynamic-programming (DP) shortest path algorithm for real-time collision-free robot-path planning applicable to situations in which targets and barriers are permitted to move. The algorithm works in real time and requires no prior knowledge of target or barrier movements. In the case that the barriers are stationary, this paper proves that this algorithm always results in the robot catching the target, provided it moves at a greater speed than the target, and the dynamic-system update frequency is sufficiently large. Like most robot-path-planning approaches, the environment is represented by a topologically organized map. Each grid point on the map has only local connections to its neighboring grid points from which it receives information in real time. The information stored at each point is a current estimate of the distance to the nearest target and the neighbor from which this distance was determined. Updating the distance estimate at each grid point is done using only the information gathered from the point's neighbors, that is, each point can be considered an independent processor, and the order in which grid points are updated is not determined based on global knowledge of the current distances at each point or the previous history of each point. The robot path is determined in real time completely from the information at the robot's current grid-point location. The computational effort to update each point is minimal, allowing for rapid propagation of the distance information outward along the grid from the target locations. In the static situation, where both the targets and the barriers do not move, this algorithm is a DP solution to the shortest path problem, but is restricted by lack of global knowledge. In this case, this paper proves that the dynamic system converges in a small number of iterations to a state where the minimal distance to a target is recorded at each grid point and shows that this robot-path-planning algorithm can be made to always choose an optimal path. The effectiveness of this algorithm is demonstrated through a number of simulations

The eigenvalue problem for a certain tridiagonal matrix with complex coefficients is considered. The eigenvalues and eigenvectors are shown to be expressible in terms of solutions of a certain scalar trigonometric equation. Explicit solutions of this equation are obtained for several special cases, and further analysis of this equation in several other cases provides information about the distribution of eigenvalues.